research article a coupled user clustering algorithm based...

Research ArticleA Coupled User Clustering Algorithm Based onMixed Data for Web-Based Learning Systems

Ke Niu1 Zhendong Niu1 Yan Su1 Can Wang2 Hao Lu1 and Jian Guan1

1School of Computer Science and Technology Beijing Institute of Technology Beijing 100081 China2Digital Productivity Commonwealth Scientific and Industrial Research Organisation Sandy Bay TAS 7005 Australia

Correspondence should be addressed to Zhendong Niu zniubiteducn

Received 24 April 2015 Accepted 15 June 2015

Academic Editor Francisco Alhama

Copyright copy 2015 Ke Niu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In traditional Web-based learning systems due to insufficient learning behaviors analysis and personalized study guides a fewuser clustering algorithms are introduced While analyzing the behaviors with these algorithms researchers generally focus oncontinuous data but easily neglect discrete data each of which is generated from online learning actions Moreover there areimplicit coupled interactions among the data but are frequently ignored in the introduced algorithms Therefore a mass ofsignificant informationwhich can positively affect clustering accuracy is neglected To solve the above issues we proposed a coupleduser clustering algorithm for Wed-based learning systems by taking into account both discrete and continuous data as well asintracoupled and intercoupled interactions of the data The experiment result in this paper demonstrates the outperformance ofthe proposed algorithm

1 Introduction

Information technology and data mining have brought greatchanges to education fieldWeb-based learning is a significantand advanced type of education which utilizes computernetwork technology multimedia digital technology databasetechnology and other modern information technologies tolearn in digital environment

At present many education institutions and researcherscommence the study of Web-based learning systems Theymainly study the systemsrsquo composition the construction ofa learning mode the design and development of hardwarerelevant supportive policies and services and so forthMean-while an increasing number of Web-based learning systemsdevelop rapidly for instance online study communities andvirtual schools [1] MOOCs (Massive Open Online Courses)are open online study platformswhich provide free courses tostudents It was initiated by Americarsquos top universities in 2012and had a participation of more than 6 million students fromaround 220 countries within a year [2] In these systems alllearners received same learning resources but no customizedor personalized learning services They are short of analysis

on learnersrsquo behaviors and individual features thus scientificguidance and help is necessarily needed In addition there isa mass of learning resources in the systems which leads to abig challenge how to tease out the most wanted and suitableresource

User clustering can dig out hidden information froma large amount of data By clustering users in differentways Web-based learning systems can provide personalizedlearning guides and learning resources recommendation tolearnersThis can greatly improve learning efficiency in thesesystems

Recently there have been some cases of applying userclustering algorithms in Web-based learning systems Inorder to choose suitable learning method clustering wasaddressed [3] Lin et al proposed the kernel intuitionisticfuzzy 119888-means clustering (KIFCM) and applied it in e-learning customer analysis [4] Another clustering approachapplied in detecting learnersrsquo behavioral patterns to supportindividual and group-based collaborative learning was putforward by Kock and Paramythis [5]

All the above methods combine traditional clusteringalgorithms and apply them in Web-based learning systems

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 747628 14 pageshttpdxdoiorg1011552015747628

2 Mathematical Problems in Engineering

where learnersrsquo attributes information is extracted conse-quently through analyzing their learning behaviors andfinally utilized for user clustering Most of these attributes arein the category of continuous data From learnersrsquo behavioralinformation we can easily find quite a lot of continuous datasuch as ldquototal time length of learning resourcesrdquo and ldquocom-prehensive test resultrdquo In contrast there also exist attributesdata with categorical features which is easily neglected likeldquochosen lecturerrdquo ldquochosen learning resource typerdquo and soforth Although this kind of data is a smaller component oflearning behavior information it also plays a significant rolein learner clustering

In addition the mixed data of discrete and continuousdata which is extracted from learning behaviors in Wed-based learning systems are interrelated There are implicitcoupling relationships among them Clustering is oftenignored by the traditional clustering algorithms which leadsto massive significant information loss during the processof similarity computation and user clustering Consequentlythe quality of relevant services provided like learning guidesand learning resources recommendation is not satisfactoryFor example we have the common sense that ldquototal timelength of learning resourcesrdquo has positive impact on ldquocom-prehensive test resultrdquo Generally if the ldquototal time length oflearning resourcesrdquo is longer the ldquocomprehensive test resultrdquois better However there are also some special groups ofstudents who behave differently They can either get betterldquocomprehensive test resultrdquo with shorter ldquototal time lengthof learning resourcesrdquo or worse ldquocomprehensive test resultrdquowith longer ldquototal time length of learning resourcesrdquo Thespecial correlation between attributes which is often ignoredis considered in user clustering of our approach This willlead to certain effect on user clustering accuracy but will notlead to guaranteeing that all users can get highly qualifiedpersonalized services easily An effect mechanism is neededto respond to the loss of the ignored information

To solve the above issues this paper proposed a coupleduser clustering algorithm based on mixed data namelyCUCA-MD This algorithm is based on the truth that bothdiscrete and continuous data exist in learning behaviorinformation it respectively analyzes them according to theirdifferent features In the analysis CUCA-MD fully takesinto account intracoupling and intercoupling relationshipsand builds user similarity matrixes respectively for discreteattribute and continuous attributes Ultimately we get theintegrated similarity matrix using weighted summation andimplement user clustering with the help of spectral clusteringalgorithm In this way we take full advantage of the mixeddata generated from learning actions in Web-based learn-ing systems Meanwhile the algorithm well considers thecorrelation and coupling relationships of attributes whichenables us to find interactions between users especially usersof previously mentioned special groups Consequently it canprovide suitable and efficient learning guidance and help forusers

The contributions of this algorithm can be summarizedfrom three aspects Firstly it takes into account the couplingrelationships of attributes in Web-based learning systemswhich is frequently neglected before and improves clustering

accuracy Secondly it fully considers different features ofdiscrete data and continuous data and builds user similaritymatrix based on mixed dataThirdly it captures and analyzesindividualsrsquo learning behaviors and provides customized andpersonalized learning services to different groups of learners

The rest of the paper is organized as follows The nextsection introduces related works The clustering algorithmmodel is proposed in Section 3 Section 4 introduces detailedutilization of the clustering algorithm Discrete and continu-ous data analysis are also studied in this section In Section 5experiments and results analysis are demonstrated Section 6concludes this paper

2 Related Works

Using mixed data to do user clustering has been achieved insome fields but rarely in Web-based learning area Ahmadand Dey came up with a clustering algorithm based onupdated 119896-mean paradigm which overcomes the numericdata only limitation which works well for data with mixednumeric and categorical features [6] A 119896-prototypes algo-rithm was proposed defined as a combined dissimilaritymeasure and further integrates the 119896-means which dealswith numeric data and 119896-modes algorithm which uses asimple matching dissimilarity measure to deal with cat-egorical objects to allow for clustering objects describedby mixed numeric and categorical attributes [7] Anotherautomated technique called SpectralCAT was addressed forunsupervised clustering of high-dimensional data that con-tains numerical or nominal or mix of attributes suggestingautomatically transforming the high-dimensional input datainto categorical values [8]

Recently an increasing number of researchers pay specialattention to interactions of object attributes and have beenaware that the independence assumption on attributes oftenleads to a mass of information loss In addition to the basicPearsonrsquos correlation [9] Wang et al addressed intracoupledand intercoupled interactions of continuous attributes [10]while Li et al proposed an innovative coupled group-basedmatrix factorization model for discrete attributes of rec-ommender system [11] An algorithm to detect interactionsbetween attributes was addressed but it is only applicablein supervised learning with the experimental results [12]Calders et al proposed the use of rank based measuresto score the similarity of sets of numerical attributes [13]Bollegala et al proposed method comprises two stageslearning a lower-dimensional projection between differentrelations and learning a relational classifier for the targetrelation typewith instance sampling [14] From all our vieweddocuments we hardly find anything of taking into accountcoupling relationships of user attributes for user clustering inWeb-based learning systems

3 Clustering Model

User clustering model plays a significant role in user eval-uation framework [15] In this section the coupled userclustering model based on mixed data is illustrated in

Mathematical Problems in Engineering 3

User learning behavior analysis

Intr

acou

pled

Intracoupled and intercoupledrepresentation

Integrated coupling representation

Personalized services

Customizedlearning strategies

Learningguidance

Learning resourcerecommendation

Discreteattribute 1

Discreteattribute 2

Discrete

Inte

rcou

pled

Extract

Spectral clustering algorithm

Compute

Apply

User learning behavior data

Discretedata

Continuousdata

Discrete behavior data




Continuousattribute 1


Continuous

Extract

IntegrateIntegrate

Continuous behavior data

User similarity matrix

Weightedsummation

attribute n attribute n998400

In

trac

oupl

ed

Inte

rcou

pled

Figure 1 The coupled user clustering model based on mixed data

Figure 1 This model respectively takes into account thediscrete data and continuous data generated in learningbehaviors and incorporates intracoupled and intercoupledrelationships of attributes in user clustering Compared withtraditional algorithms it captures the hidden user interactioninformation by fully analyzing mixed data which improvesclustering accuracy

The model is built on the basis of the discrete data andcontinuous data extracted from learning behaviors Accord-ing to their different features we tease out the correspondingattributes in parallel through analyzing the behaviors Thenintracoupled and intercoupled relationships are introducedinto user similarity computation which helps to get usersimilarity matrixes respectively for discrete attributes andcontinuous attributes Finally we use weighted summationto integrate the two matrixes and apply Ng-Jordan-Weiss(NJW) spectral clustering algorithm [16] in user clusteringWith the clustering result applied inWeb-based learning sys-tems various personalized services are provided accordingly

such as learning strategy customization learning tutoringand learning resources recommendation

4 Clustering Algorithm

This paper proposed a coupled user clustering algorithmbased on mixed data which is suitable to be applied ineducation field It fits for not only user clustering analysis inWeb-based learning systems but also corporate training andperformance review as well as other Web-based activities inwhich user participation and behavior recording is involvedThe implementation of the CUCA-MD in Web-based learn-ing systems is introduced in this section

41 Discrete Data Analysis Among the data generated fromusersrsquo learning behaviors discrete data plays a significantrole in user behavior analysis and user clustering In thefollowing section the procedure of how to compute user


Table 1 A fragment example of user discrete attributes

119880

119860

1198861 1198862 1198863

1199061 Wang Video Online1199062 Liu Video Online1199063 Zhao e-book Interactive1199064 Li Audio Offline1199065 Li PPT Offline

similarity using discrete data in Web-based learning systemsis demonstrated during which intracoupled similarity withinan attribute (ie value frequency distribution) and intercou-pled similarity between attributes (ie feature dependencyaggregation) are also considered

411 User Learning Behavior Analysis In Web-based learn-ing systems (httpswwwkhanacademyorg) (httpswwwcourseraorg) usually various discrete datawill be generatedduring learning process such as chosen lecturer chosenlearning resource type and chosen examination form eval-uation on lecturer and learning content main learning timeperiod and uploading and downloading learning resourcesTo make it more explicit we choose ldquochosen lecturerrdquoldquochosen learning resource typerdquo and ldquochosen examinationformrdquo as the attributes for later analysis respectively denotedby 1198861 1198862 and 1198863 we also choose 5 students as the studyobjects denoted by 1199061 1199062 1199063 1199064 and 1199065 The objectsand their attributes values are shown in Table 1 Thus wediscuss the similarity of categorical values by considering datacharacteristics Two attribute values are similar if they presentanalogous frequency distributions for one attribute [17] thisreflects the intracoupled similaritywithin a feature In Table 1for example ldquoWangrdquo ldquoLiurdquo and ldquoZhaordquo are similar becauseeach of them appears once However the reality is ldquoWangrdquoand ldquoLiurdquo are more similar than ldquoWangrdquo and ldquoZhaordquo becausethe ldquochosen learning resource typerdquo and ldquochosen examinationformrdquo of lecturer ldquoWangrdquo and ldquoLiurdquo are identical If we needto recommend a lecturer to students who likeWangrsquos lecturesmore we will prefer Liu instead of Zhao because Liursquos lectureis more easily accepted by students It indicates that thesimilarity between ldquochosen lecturerrdquo should also cater forthe dependencies on other features such as ldquochosen learningresourcesrdquo and ldquochosen examination formrdquo over all objectsnamely the intercoupled similarity between attributes

412 Intracoupled and Intercoupled Representation Dataobjects with features can be organized by the informationtable 119878 = ⟨119880119860 119881 119891⟩ where 119880 = 1199061 1199062 119906119898 iscomposed of a nonempty finite number of users 119860 =

1198861 1198862 119886119899 is a finite set of discrete attributes119881 = ⋃119899

119895=1 119881119895is a set of all attribute values 119881

119895= 119886119895sdot V1 119886119895 sdot V119905119895 is

a set of attribute values of the 119895th attribute namely 119886119895(1 le

119895 le 119899) and 119891 = ⋃119899

119894=1 119891119895 119891119895 119880 rarr 119881119895is an information

function which assigns a particular value of each featureto every user We take Table 2 as an example to explicitly

Table 2 An example of information table

119880

119860

1198861 1198862 1198863

1199061 1198601 1198611 1198621

1199062 1198602 1198611 1198621

1199063 1198602 1198612 1198622

1199064 1198603 1198613 1198622

1199065 1198604 1198613 1198623

represent intracoupled and intercoupled similarity of discreteattributes

To analyze intracoupled and intercoupled correlation ofuser attributes we define a few basic concepts as follows

Definition 1 Given an information table 119878 3 set informationfunctions (SIFs) are defined as follows

119891lowast

119895(1199061198961 119906

119896119905) = 119891

119895(1199061198961) 119891

119895(119906119896119905)

119892119895(119909) = 119906

119894| 119891119895(119906119894) = 119909 1le 119895 le 119899 1le 119894 le119898

119892lowast

119895(119882) = 119906

119894| 119891119895(119906119894) isin119882 1le 119895 le 119899 1le 119894 le119898

(1)

where 119891lowast is the mapping function of user set to attribute

values 119892 is mapping function of attribute values to userand 119892

lowast is mapping function of attribute value set to user119906119894 1199061198961 119906

119896119905isin 119880119882 sube 119881

119895 and 119895 denotes the 119895th attribute

These SIFs describe the relationships between objectsand attribute values from different levels For example119891lowast

2 (1199061 1199062 1199063) = 1198611 1198612 and 1198922(1198611) = 1199061 1199062 for value 1198611while 119892lowast2 (1198611 1198612) = 1199061 1199062 1199063 if given that119882 = 1198611 1198612

Definition 2 Given an information table 119878 an Interinforma-tion Function (IIF) is defined as

120593119895rarr119896

(119909) = 119891lowast

119896(119892119895(119909)) (2)

This IIF 120593119895rarr119896

is the composition of 119891lowast119896and 119892

119895 It obtains

the 119896th attribute value subset for the corresponding objectswhich are derived from 119895th attribute value 119909 For example1205932rarr 1(1198611) = 1198601 1198602

Definition 3 Given an information table 119878 the 119896th attributevalue subset119882 sube 119881

119896 and the 119895th attribute value 119909 isin 119881

119895 the

InformationConditional Probability (ICP) of 119882with respectto 119909 is defined as

119875119896|119895

(119882 | 119909) =

10038161003816100381610038161003816119892lowast

119896(119882) cap 119892

119895(119909)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816

(3)

When given all the objects with the 119895th attribute value 119909ICP means the percentage of users whose 119896th attributes fallin subset119882 and 119895th attribute value is 119909 as well For example1198751|2(1198601 | 1198611) = 05

Intracoupled and intercoupled similarity of attributes arerespectively introduced as follows


Intracoupled Interaction Based on [9] intracoupled similarityis decided by attribute value occurrence times in termsof frequency distribution When we calculate an attributersquosintracoupled similarity we consider the relationship betweenattribute value frequencies on one feature demonstrated asfollows

Definition 4 Given an information table 119878 the IntracoupledAttribute Value Similarity (IaAVS) between attribute values 119909and 119910 of features 119886

119895is defined as

120575Ia119895(119909 119910) =

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

(4)

Greater similarity is assigned to the attribute value pairwhich owns approximately equal frequencies The higherthese frequencies are the closer such two values are Forexample 120575Ia2 (1198611 1198612) = 04

Intercoupled InteractionWehave considered the intracoupledsimilarity that is the interaction of attribute values withinone feature 119886

119895 However this does not cover interaction

between different attributes namely 119886119896(119896 = 119895) and 119886

119895

Cost and Salzberg [18] came up with a method whichis for measuring the overall similarities of classificationof all objects on each possible value of each feature Ifattributes values occur with the same relative frequency forall classifications they are identified as being similar Thisinteraction between features in terms of cooccurrence istaken as intercoupled similarity

Definition 5 Given an information table 119878 the intercoupledrelative similarity based on Intersection Set (IRSI) betweendifferent values119909 and119910of feature 119886

119895regarding another feature

119886119896is formalized as

120575119895|119896

(119909 119910) = sum

120596isincap

min 119875119896|119895

(120596 | 119909) 119875119896|119895

(120596 | 119910) (5)

where 120596 isin cap denote 120596 isin 120593119895rarr119896

(119909) cap 120593119895rarr119896

(119910) respectively

The value subset119882 sube 119881119896is replaced with 120596 isin 119881

119896 which

is considered to simplify computationWith (5) for example the calculation of 1205752|1(1198611 1198612) is

much simplified since only 1198602 isin 1205932rarr 1(1198611) cap 1205932rarr 1(1198612)then we can easily get 1205752|1(1198611 1198612) = 05 Thus this methodis quite efficient in reducing intracoupled relative similaritycomplexity

Definition 6 Given an information table 119878 the IntercoupledAttribute Value Similarity (IeAVS) between attribute values 119909and 119910 of feature 119886

119895is defined as

120575Ie119895(119909 119910) =

119899

sum

119896=1119896 =119895120572119896120575119895|119896

(119909 119910) (6)

where 120572119896is the weight parameter for feature 119886

119896 sum119899119896=1 120572119896 = 1

120572119896isin [0 1] and 120575

119895|119896(119909 119910) is one of the intercoupled relative

similarity candidates

In Table 2 for example 120575Ie2 (1198611 1198612) = 05 sdot 1205752|1(1198611 1198612) +05 sdot 1205752|3(1198611 1198612) = (05 + 0)2 = 025 if 1205721 = 1205723 = 05 is takenwith equal weight

413 Integrated Coupling Representation Coupled AttributeValue Similarity (CAVS) is proposed in terms of both intra-coupled and intercoupled value similarities For examplethe coupled interaction between 1198611 and 1198612 covers both theintracoupled relationship specified by the occurrence timesof values 1198611 and 1198612 2 and 2 and the intercoupled interactiontriggered by the other two features 1198861 and 1198863

Definition 7 Given an information table 119878 the CoupledAttribute Value Similarity (CAVS) between attribute values119909 and 119910 of feature 119886

119895is defined as

120575119860

119895(119909 119910) = 120575

Ia119895(119909 119910) sdot 120575

Ie119895(119909 119910) (7)

where 120575Ia119895and 120575Ie119895are IaAVS and IeAVS respectively

In Table 2 for instance CAVS is obtained as 1205751198602 (1198611 1198612) =

120575Ia2 (1198611 1198612) sdot 120575

Ie2 (1198611 1198612) = 04 times 025 = 01

With the specification of IaAVS and IeAVS a coupledsimilarity between objects is built based on CAVS Then wesum all CAVSs analogous to the construction of Manhattandissimilarity [9] Formally we have the following definition

Definition 8 Given an information table 119878 the Coupled UserSimilarity (CUS) between users 119906

1198941and 119906

1198942is defined as

CUS (1199061198941 1199061198942) =

119899

sum

119895=1120573119895120575119860

119895(1199091198941119895 1199091198942119895) (8)

where 120573119895is the weight parameter of attribute 119886

119895 sum119899119895=1 120573119895 = 1

120573119895isin [0 1] 119909

1198941119895and 119909

1198942119895are the attribute values of feature 119886

119895

for 1199061198941and 119906

1198942 respectively and 1 le 1198941 1198942 le 119898 and 1 le 119895 le 119899

In Table 2 for example CUS(1199062 1199063) = sum3119895=1 120573119895120575

119860

119895(1199092119895

1199093119895) = 13 sdot 1205751198601 (1198602 1198602) + 13 sdot 120575119860

2 (1198611 1198612) + 13 sdot 120575119860

3 (1198621 1198622) =(05 + 01 + 0125)3 asymp 024 if 1205731 = 1205732 = 1205733 = 13 is takenwith equal weight

In this way a user similarity matrix of 119898 times 119898 entriesregarding discrete data can be built as

119872DD

= (

11987811 11987812 sdot sdot sdot 1198781119898

11987821 11987822 sdot sdot sdot 1198782119898

sdot sdot sdot sdot sdot sdot d sdot sdot sdot

1198781198981 1198781198982 sdot sdot sdot 119878

119898119898

) (9)

where 119878119894119894= 1 1 le 119894 le 119898


For instance we get a user similaritymatrix of 5times5 entriesregarding discrete data based on Table 2 as

(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)

42 Continuous Data Analysis Continuous data is withdifferent features when compared with discrete date In thefollowing section user similarity computation is demon-strated using Taylor-like expansion with the involvementof intracoupled interaction within an attribute (ie thecorrelations between attributes and their own powers) andintercoupled interaction among different attributes (ie thecorrelations between attributes and the powers of others)

421 User Learning Behavior Analysis After students logonto a Web-based learning system the system will recordtheir activity information such as times of doing homeworkand number of learning resourcesThis paper refers to aWeb-based personalized user evaluation model [19] and utilizesits evaluation index system to extract studentsrsquo continuousattributes information This index system as shown inTable 3 is based on evaluation standards of America 119870 minus

12 (kindergarten through twelfth grade) [20] and Delphimethod [21] which is a hierarchical structure built accordingto mass of information and data generated during general e-learning activities It is defined with 20 indicators and cancomprehensively represent the studentsrsquo attributes Due to thedifferent units used for measuring extracted attributes liketimes time length amount percentage and so forth we needto normalize them firstly result is shown in Table 4

422 Intracoupled and Intercoupled Representation In thissection intracoupled and intercoupled relationships of aboveextracted continuous attributes are respectively representedHere we use an example to make it more explicate We singleout 6 attributes data with continuous feature of the same5 students mentioned in Section 411 including ldquoaveragecorrect rate of homeworkrdquo ldquotimes of doing homeworkrdquoldquonumber of learning resourcesrdquo ldquototal time length of learningresourcesrdquo ldquodaily average quiz resultrdquo and ldquocomprehensivetest resultrdquo denoted by 11988610158401 119886

1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840

6 in the followingrepresentations shown in Table 4

Here we use an information table 1198781015840 = ⟨1198801198601015840

1198811015840

1198911015840

⟩ torepresent user attributes information 119880 = 1199061 1199062 119906119898means a finite set of users 1198601015840 = 119886

1015840

1 1198861015840

2 1198861015840

119899 refers to a

finite set of continuous attributes 1198811015840 = ⋃119899

119895=1 1198811015840

119895represents

all attributes value sets 1198811015840119895= 1198861015840

119895sdot V10158401 119886

1015840

119895sdot V1015840119905119895 is the value

set of the 119895th attribute 1198911015840 = ⋃119899

119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the

function for calculating a certain attribute value For examplethe information in Table 4 contains 5 users 1199061 1199062 1199063 1199064 1199065and 6 attributes 11988610158401 119886

1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6 the first attribute valueof 1199061 is 061

Table 3 Comprehensive evaluation index system

First-levelindex Second-level index

Autonomiclearning

Times of doing homeworkAverage correct rate of homeworkNumber of learning resourcesTotal time length of learning resourcesTimes of daily quizDaily average quiz resultComprehensive test resultNumber of collected resourcesTimes of downloaded resourcesTimes of making notes

Interactivelearning

Times of asking questionsTimes of marking and remarkingTimes of answering classmatesrsquo questionsTimes of posting comments on the BBSTimes of interaction by BBS messageTimes of sharing resourcesAverage marks made by the teacherAverage marks made by other studentsTimes of marking and remarking made by thestudent for the teacherTimes of marking and remarking made by thestudent for other students

Table 4 A fragment example of user continuous attributes

119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093

The usual way to calculate the interactions between 2attributes is Pearsonrsquos correlation coefficient [9] For instancethe Pearsonrsquos correlation coefficient between 119886

1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)

radicsum119906isin119880

(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583

119896are respectively mean values of 1198861015840

119895and 1198861015840119896

However the Pearsonrsquos correlation coefficient only fits forlinear relationship It is far from sufficient to fully capturepairwise attributes interactions Therefore we expect to usemore dimensions to expand the numerical space spannedby 1198991015840 and then expose attributes coupling relationship by

exploring updated attributes interactions [22]


Table 5 Extended user continuous attributes

⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086

Firstly we use a few additional attributes to expandinteraction space in the original information table Hencethere are 119871 attributes for each original attribute 1198861015840

119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840

119895⟩119871 Each attribute value is

the power of the attribute for instance ⟨1198861015840119895⟩3 is the third

power of attribute 1198861015840119895and ⟨1198861015840

119895⟩119901

(1 le 119901 le 119871) is the 119901th powerof 1198861015840119895 In Table 4 the denotation 119886

1015840

119895and ⟨119886

1015840

119895⟩1 are equivalent

the value of ⟨1198861015840119895⟩2 is the square of 1198861015840

119895value For simplicity we

set 119871 = 2 in Table 5Secondly the correlation between pairwise attributes

is calculated It captures both local and global couplingrelations We take the 119901 values for testing the hypothesesof no correlation between attributes into account 119901 valuehere means the probability of getting a correlation as largeas possible observed by random chance while the truecorrelation is zero If 119901 value is smaller than 005 thecorrelation Cor(1198861015840

119895 1198861015840

119896) is significant The updated correlation

coefficient is as follows

119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)

Here we do not consider all relationships but only takethe significant coupling relationships into account becauseall relationships involvement may cause the overfitting issueon modeling coupling relationship This issue will go againstthe attribute inherent interactionmechanism So based on theupdated correlation the intracoupled and intercoupled inter-action of attributes are proposed Intracoupled interaction isthe relationship between 119886

1015840

119895and all its powers intercoupled

interaction is the relationship between 1198861015840

119895and powers of the

rest of the attributes 1198861015840119896(119896 = 119895)

Intracoupled Interaction The intracoupled interaction withinan attribute is represented as a matrix For attribute 1198861015840

119895 it is

119871 times 119871 matrix 119877Ia(1198861015840

119895) In the matrix (119901 119902) is the correlation

between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902

) is the Pearsonrsquos correla-tion coefficient between ⟨1198861015840

119895⟩119901 and ⟨1198861015840

119895⟩119902

For attribute 11988610158401 in Table 5 we can get the intracoupledinteraction within it as 119877Ia

(1198861015840

1) = (1 0986

0986 1 ) which meansthat the correlation coefficient between attribute ldquoaveragecorrect rate of homeworkrdquo and its second power is as highas 0986 There is close relationship between them

Intercoupled Interaction The intercoupled interactionbetween attribute 119886

1015840

119895and other attributes 119886

1015840

119896(119896 = 119895) is

quantified as 119871 times 119871 lowast (1198991015840

minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840

1198962) sdot sdot sdot 119877

Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895

refers to all the attributes except for 1198861015840

119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902

) is the correlationcoefficient between ⟨1198861015840

119895⟩119901 and ⟨1198861015840

119896119894⟩119902

(1 le 119901 119902 le 119871)For attribute 11988610158401 in Table 5 the intercoupled interaction

between 11988610158401 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)

The 119901 values between 1198861015840

1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)

Based on the result we can find that there is hiddencorrelation between user attributes For instance all the 119901

values between attributes 11988610158401 and 1198861015840

2 are larger than 005 sothe correlation coefficient is 0 based on (12) indicating thereis no significant correlation between ldquoaverage correct rate ofhomeworkrdquo and ldquotimes of doing homeworkrdquo Meanwhile thecorrelation coefficient between 119886

1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840

6 isquite close to 1 it indicates that ldquodaily average quiz resultrdquoand ldquocomprehensive test resultrdquo have close relationshiprespectively with ldquoaverage correct rate of homeworkrdquo whichis consistent with our practical experiences In conclusioncomprehensively taking into account intracoupled and inter-coupled correlation of attributes can efficiently help capturingcoupling relationships between user attributes

423 Integrated Coupling Representation Intracoupled andintercoupled interactions are integrated in this section as acoupled representation scheme

In Table 5 each user is signified by 119871 lowast 1198991015840 updated

variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871

Withthe updated function

1198911015840

119901

119895(119906) the corresponding value of

attribute ⟨11988610158401198991015840⟩119901 is assigned to user 119906 Attribute 1198861015840

119895and all its

powers are signified as (1198861015840119895) = [

1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the

rest of the attributes and all powers are presented in anothervector (1198861015840

119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1

(119906)] For instance in Table 5 1199061(1198861015840

1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]

Definition 9 The coupled representation of attribute 1198861015840

119895is

formalized as 1 times 119871 vector 119906119888

(1198861015840

119895|

1198601015840 119871) where (1 119901)

component corresponds to the updated attribute ⟨1198861015840119895⟩119901 One

has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)

where119908 = [1(1) 1(2) 1(119871)] is a constant 1times119871 vector[119908 119908 119908] is a 1times119871lowast (1198991015840 minus1) vector concatenated by 1198991015840 minus1constant vectors 119908 ⊙ denotes the Hadamard product and otimesrepresents the matrix multiplication

Taking an example in Table 6 the coupled representationfor attribute 11988610158401 is presented as 1199061198881(119886

1015840

1 |1198601015840 2) = [385 380]

The reason why we choose such a representation method isexplained below If (17) is expanded for example we get the(1 119901) elementwhich corresponds to ⟨1198861015840

119895⟩119901 of the vector119906119888(1198861015840

119895|

1198601015840 119871) as below which resembles Taylor-like expansion of

functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)

Finally we obtained the global coupled representation ofall the 1198991015840 original attributes as a concatenated vector

119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)

Incorporated with the couplings of attributes each user isrepresented as 1times119871lowast1198991015840 vector When all the users follow thesteps above we then obtain 119898 times 119871 lowast 119899

1015840 coupled informationtable For example based onTable 4 the coupled informationtable shown in Table 6 is the new representation

With the new user attributes information of the coupledinformation table we utilize the formula below [16] tocompute user similarity and build a matrix 119872CD of 119898 times 119898

entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)

where 119894 = 119895 1198781015840119894119894= 1 and 120590 denotes scaling parameter Here

we take 120590 = 03 Detailed parameter estimation procedure isintroduced in experiment 52

119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)


Table 6 Integrated coupling representation of user continuous attributes

⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590

For instance we get a user similaritymatrix of 5times5 entriesregarding continuous data based on Table 4 as

(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)

43 User Clustering In Sections 41 and 42 we get separateuser similarity matrix 119872

DD regarding discrete attributesand 119872

CD regarding continuous attributes With weightedsummation an integratedmatrix119872MD of119898times119898 entries basedon mixed data can be obtained as

119872MD

= 1205741119872DD

+ 1205742119872CD (25)

where 1205741 and 1205742 are the respective weights of discreteattributes and continuous attributes 1205741 + 1205742 = 1 12057411205742 =

1198991198991015840 and 119899 denotes the number of former attributes while 1198991015840

denotes that of the latter onesFor example in the former examples we listed 3 discrete

attributes and 6 continuous attributes then 1205741 = 13 and1205742 = 23 For users of 1199061 1199062 1199063 1199064 and 1199065 the user similaritymatrix based on the mixed data is obtained as follows

(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)

With consideration of intracoupled and intercoupledcorrelation of user attributes we get the user similaritymatrix 119872

MD based on mixed learning behavior data Nextwith NJW spectral clustering user clustering procedureis described Detailed clustering result is demonstrated inexperiments part

5 Experiments and Evaluation

We conducted experiments and user studies using the cou-pled user clustering algorithm proposed in this paper Thedata for the experiments are collected from a Web-basedlearning system of China Educational Television (CETV)named ldquoNewMedia Learning Resource Platform forNational

Educationrdquo (httpwwwguoshicom) As a basic platformfor national lifelong education which started the earliest inChina has the largest group of users and provides mostextensive learning resources it meets the needs of person-alization and diversity of different users through integratinga variety of fusion network terminals and resources So farthe number of registered users has reached more than twomillion Experiments are carried out to verify the algorithmrsquosvalidity and accuracy The experiment is composed of fourparts user study parameter estimation user clustering andresult analysis

51 User Study In the experiment we asked 180 users(indicated by 1199041 1199042 119904220) to learn Data Structures onlineThe whole learning process including the recording andanalysis of learning activities information was accomplishedin CETV mentioned above

Recently public data sets regarding learnersrsquo learningbehaviors in online learning systems are insufficient andmost of them do not contain labeled user clustering infor-mation Meanwhile because learnersrsquo behaviors are alwayswith certain subjectivity the accuracy of labeling learnerswith different classifiers only based on behaviors but withoutknowing the information behind is not full Therefore weadopt a few user studies directly and respectively collectingrelevant user similarity data from students and teachers asthe basis for verifying the accuracy of learners clustering inWeb-based learning systems

Through analyzing the continuous attributes extractedfrom Table 3 according to user evaluation index system wecan easily find that they can be mainly classified to twokinds one kind of attributes reflecting learnersrsquo learning atti-tude like ldquotimes of doing homeworkrdquo ldquonumber of learningresourcesrdquo and ldquototal time length of learning resourcesrdquo theother kind of attributes reflecting learnersrsquo learning effectlike ldquoaverage correct rate of homeworkrdquo ldquodaily average quizresultrdquo and ldquocomprehensive test resultrdquo Meanwhile we alsoanalyze attributeswith categorical features for example ldquocho-sen lecturerrdquo ldquochosen learning resource typerdquo and ldquochosenexamination formrdquo which all reflect learnersrsquo learning pref-erences Therefore we ask the students and teachers togetherto comprehensively estimate studentsrsquo similarity respectivelyfrom three perspectives which are learning attitude learningeffect and learning preference We request each of the 180students to choose the top 5 of other students who are mostlylike himself and 5 who are hardly like himself taking intoaccount the three perspectives each of the lecturers who aregiving the lesson of data structure also makes options for


Table 7 The clustering results of 1199041

Top 5 ldquomost similarrdquo Top 5 ldquoleast similarrdquo

Before clustering 1199041 1199047 11990416 11990435 11990484 119904103 11990419 11990455 11990482 119904122 119904131

Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041

1199047 11990416 11990435 119904103 stay in the samecluster with 1199041

None of them stays in the samecluster with 1199041

Similarity accuracy 80 Dissimilarity accuracy 100

Mr Liu1199047 11990435 119904103 119904162 stay in the samecluster with 1199041

1199044 stays in the same cluster with 1199041


Comprehensive accuracy Comprehensive similarity accuracy80

Comprehensive dissimilarityaccuracy 91

the same request for every student in his class For instancestudent 1199041 chooses the lesson of lecturer Liu and the optionsrespectively made by them are shown in Table 7

52 Parameter Estimation As indicated in (20) the proposedcoupled representation for numerical objects is stronglydependent on themaximal power 119871 Here we conduct severalexperiments to study the performance of 119871 with regard tothe clustering accuracy of CUCA-MD The maximal power119871 is set to range from 119871 = 1 to 119871 = 10 since 119871 becomesextremely large when 119871 grows which means 119871 = 10 isprobably large enough to obtain most of the information in(20)The experiment verifies that with the increasing value of119871 the clustering accuracy goes higherWhen 119871 = 3 it reachesa stable point for accuracy change when 119871 = 10 comparedwith the former there is only very tiny improvement ofaccuracy Therefore with the precondition for experimentaccuracy we take 119871 = 3 reducing the algorithm complexityas much as possible

We keep adjusting the number of clusters 119896 with a largenumber of experiments Finally we take the number as 6considering the user features in online learning systemsBesides (22) is needed when computing user similarity usingcontinuous data The scaling parameter 120590 of the equationshould be set manually so we test different 120590 values to getdifferent clustering accuracy and then pick up the optimalone In Figure 2 the relation of 120590 values and clusteringaccuracy is illustrated When 120590 = 03 the clustering accuracyis the best when 120590 ge 07 the clustering results stay ina comparatively stable range with no much difference inbetween Thus we take 120590 = 03

53 User Clustering In the following experiments we takeuse of the 20 continuous user attributes in Table 3 and the 8discrete attributes (chosen lecturer chosen learning resourcetype chosen examination form learning time evaluationof lecturer evaluation of learning resources upload anddownload) to do user clustering Because the procedure ofrecording and analyzing usersrsquo learning behaviors is persis-tent we divide the learning process to six phases namely 5 h10 h 15 h 20 h 25 h and 30 h Then with the data of differentphase we do user clustering with different algorithm

10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter

Figure 2 Parameter estimation of 120590

To verify the efficiency of CUCA-MD in user clusteringin Web-based learning systems we compare it with threeother algorithms which are also based on mixed datanamely 119896-prototype [7] mADD [6] and spectralCAT [8]Besides to demonstrate the significance of learning behaviorwith both categorical feature and continuous feature aswell as the different effect of clustering with and withoutcoupling we take six different methods to respectively doclustering The first one is Simple Matching Similarity (SMSwhich only uses 0s and 1s to distinguish similarities betweendistinct and identical categorical values) [9] used to analyzeusersrsquo discrete attributes and compute user similarity andthen applied in user clustering with the help of NJW Thismethod is named NJW-DD The second one is described inSection 41 which analyzes usersrsquo discrete attributes consid-ering intracoupled and intercoupled relationships and thencomputes user similarity and does user clustering combinedwith NJW algorithm This method is called CUCA-DDThe third one is to get clustering result through analyzingcontinuous attributes and utilizing NJW namely NJW-CDHowever the fourth one takes advantage of usersrsquo continuousattributes and their intracoupled and intercoupled correlationto get the user similarity and then with the help of NJWget the user clustering result It is introduced in Section 42already named CUCA-CD The fifth method is utilizing


10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()

Similarity accuracy Dissimilarity accuracy

k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD

CUCA-CDNJW-MDCUCA-MD

(b)

Figure 3 Clustering result analysis (30 h)

NJW to do user clustering based on both discrete andcontinuous attributes but without considering intracoupledand intercoupled correlation of attributes It is named NJW-MDThe sixth is the one proposed in this paper CUCA-MD

With the clustering result we use statistics to make ananalysis In Table 7 taking student 1199041 for example 4 of theldquotop most similarrdquo students chosen by 1199041 stay in the sameclusterwith 1199041 himself which indicates the clustering accuracyis 80 thus we take it as ldquosimilarity accuracyrdquo In contrastnone of the ldquotop least similarrdquo students chosen by 1199041 stays inthe same cluster with him indicating the clustering accuracyis 100 thus we take it as ldquodissimilarity accuracyrdquo In thesame way we also get two accuracy values based on theoptions made by 1199041rsquos lecturer Mr Liu 80 and 80 Takingthe weight of 1199041rsquos option as 55 while taking Mr Liursquos as45 we get the comprehensive accuracy values of 80 and91 using weighted summation In this way we get a pairof accuracy values for each of the 180 students verifying theefficiency of the different clustering methods

54 Result Analysis We do comparison analysis on theclustering results using user similarity accuracy and userdissimilarity accuracy Figure 3 illustrates the clustering accu-racy comparison of CUCA-MD and other algorithms whenthe average learning length of the 180 students is 30 h FromFigure 3(a) we can easily find that the accuracy of CUCA-MD is higher than that of others regarding mixed datano matter on similarity or dissimilarity In Figure 3(b) theclustering results of NJW-DD CUCA-DD NJW-CD CUCA-CD NJW-MD and CUCA-MD 6 are demonstrated andcompared We observe that both of the similarity accuracyand dissimilarity accuracy of NJW-DD are the lowest respec-tively 262 and 323 when compared with others whilethose of CUCA-MD are the highest Meanwhile algorithmsconsidering coupling relationship have higher accuracy than

NJW which does not consider it regardless of discretedata continuous data or mixed data The comprehensiveresults above verify the outperformance of algorithms whichconsiders coupling relations of attributes they can efficientlycapture the hidden information of behavior data and greatlyimprove clustering accuracy

The collection and analysis of learning behaviors are apersistent action so we illustrate the relationship betweenaverage learning length and user clustering accuracy FromFigures 4(a) and 4(b) we can see that with the extensionof learning time the clustering accuracies of the algorithmsbased on mixed data become higher among which CUCA-MD grows the fastest especially after 20 h Figures 4(c)and 4(d) show that all accuracies of the algorithms growexcept for NJW-DD At the same time algorithm CUCAwhich considers coupling relationships grows faster thanNJW which does not With the result above we make theconclusion that is based on only a few attributes and littleextracted information the clustering accuracy of NJW-DDregarding discrete data is not improved much even withmore time and behavior data while the clustering accuracy ofCUCA-MD regarding mixed data which considers couplingrelationship of attributes is distinctly improved with theincrease of behavior data

Besides we can verify clustering accuracy through ana-lyzing the structure of user clustering results The bestperformance of a clustering algorithm is reaching the smallestdistance within a cluster but the biggest distance betweenclusters thus we utilize the evaluation criteria of RelativeDistance (the ratio of average intercluster distance uponaverage intracluster distance) and Sum Distance (the sumof object distances within all the clusters) to present thedistance The larger Relative Distance is and the smaller SumDistance is the better clustering results are From Figure 5we can see that the Relative Distance of CUCA-MD is larger


900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30

Length of learning (h)

k-prototypeSpectralCAT

mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30


NJW-DDCUCA-CDCUCA-DD

NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)

Figure 4 Clustering result of different phases

than that of the other algorithms while the Sum Distance ofCUCA-MD is smaller It indicates that CUCA-MD regardingmixed data which also considers coupling relationshipsoutperforms the rest in terms of clustering structure

6 Conclusion

We proposed a coupled user clustering algorithm based onMixed Data for Web-based Learning Systems (CUCA-MD)in this paper which incorporates intracoupled and intercou-pled correlation of user attributes with different featuresThisalgorithm is based on the truth that both discrete and contin-uous data exist in learning behavior information it respec-tively analyzes them according to different features In theanalysis CUCA-MD fully takes into account intracouplingand intercoupling relationships and builds user similaritymatrixes respectively for discrete attribute and continuousattributes Ultimately we get the integrated similarity matrixusing weighted summation and implement user clusteringwith the help of spectral clustering algorithm In experimentpart we verify the outperformance of proposed CUCA-MD

in terms of user clustering in Web-based learning systemsthrough user study parameter estimation user clusteringand result analysis

In this paper we analyze discrete data and continu-ous data generated in online learning systems with differ-ent methods and build user similarity matrixes regardingattributes with discrete and continuous features respectivelywhich makes the algorithmmore complicated In the follow-ing studies we hope to realize the simultaneous processingcontinuous data and discrete data while taking into accountcoupling correlation of user attributes which will definitelyfurther improve algorithm efficiency

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Project no 61370137) the National


CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)

Figure 5 Clustering structure analysis (30 h)

973 Project of China (no 2012CB720702) and Major Sci-ence and Technology Project of Press and Publication (noGAPP ZDKJ BQ01)

References

[1] S Cai and W Zhu ldquoThe impact of an online learning commu-nity project on universityChinese as a foreign language studentsmotivationrdquo Foreign Language Annals vol 45 no 3 pp 307ndash329 2012

[2] M Ghosh ldquoMOOCM4D an overview and learnerrsquos viewpointon autumn 2013 courserdquo International Journal of InteractiveMobile Technologies vol 8 no 1 pp 46ndash50 2014

[3] F Trif C Lemnaru and R Potolea ldquoIdentifying the usertypology for adaptive e-learning systemsrdquo in Proceedings of the17th IEEE International Conference on Automation Quality andTesting Robotics (AQTR rsquo10) vol 3 pp 1ndash6 IEEE May 2010

[4] K-P Lin C-L Lin K-C Hung Y-M Lu and P-F PaildquoDeveloping kernel intuitionistic fuzzy c-means clustering fore-learning customer analysisrdquo in Proceedings of the IEEE Inter-national Conference on Industrial Engineering and EngineeringManagement (IEEM rsquo12) pp 1603ndash1607 IEEE December 2012

[5] M Kock and A Paramythis ldquoTowards adaptive learning sup-port on the basis of behavioural patterns in learning activitysequencesrdquo in Proceedings of the 2nd International Conferenceon IntelligentNetworking andCollaborative Systems (INCOS rsquo10)pp 100ndash107 IEEE November 2010

[6] A Ahmad and L Dey ldquoA k-mean clustering algorithm formixed numeric and categorical datardquo Data amp Knowledge Engi-neering vol 63 no 2 pp 503ndash527 2007

[7] Z Huang ldquoExtensions to the k-means algorithm for clusteringlarge data sets with categorical valuesrdquo Data Mining andKnowledge Discovery vol 2 no 3 pp 283ndash304 1998

[8] G David and A Averbuch ldquoSpectralCAT categorical spectralclustering of numerical and nominal datardquo Pattern Recognitionvol 45 no 1 pp 416ndash433 2012

[9] G Gan C Ma and J Wu Data Clustering Theory Algorithmsand Applications SIAM 2007

[10] C Wang Z She and L Cao ldquoCoupled attribute analysis onnumerical datardquo in Proceedings of the 23rd International JointConference on Artificial Intelligence pp 1736ndash1742 AAAI PressAugust 2013

[11] F Li G Xu L Cao X Fan and Z Niu ldquoCGMF coupledgroup-based matrix factorization for recommender systemrdquo inWeb Information Systems EngineeringmdashWISE 2013 vol 8180 ofLecture Notes in Computer Science pp 189ndash198 Springer BerlinGermany 2013

[12] A Jakulin and I Bratko Analyzing Attribute DependenciesSpringer Berlin Germany 2003

[13] T Calders B Goethals and S Jaroszewicz ldquoMining rank-correlated sets of numerical attributesrdquo in Proceedings of the12th ACM SIGKDD International Conference on KnowledgeDiscovery and Data Mining (KDD rsquo06) pp 96ndash105 ACMPhiladelphia Pa USA August 2006

[14] D Bollegala Y Matsuo and M Ishizuka ldquoRelation adaptationlearning to extract novel relations with minimum supervisionrdquoin Proceedings of the 22nd International Joint Conference onArtificial Intelligence (IJCAI rsquo11) pp 2205ndash2210 July 2011

[15] K Niu W Chen Z Niu et al ldquoA user evaluation frameworkfor web-based learning systemsrdquo in Proceedings of the 3rd ACM


InternationalWorkshop onMultimedia Technologies for DistanceLearning pp 25ndash30 ACM 2011

[16] A Y Ng M I Jordan and Y Weiss ldquoOn spectral clusteringanalysis and an algorithmrdquo in Advances in Neural InformationProcessing Systems vol 2 pp 849ndash856 2002

[17] S Boriah V Chandola and V Kumar ldquoSimilarity measures forcategorical data a comparative evaluationrdquo Red vol 30 no 2p 3 2008

[18] S Cost and S Salzberg ldquoAweighted nearest neighbor algorithmfor learning with symbolic featuresrdquoMachine Learning vol 10no 1 pp 57ndash78 1993

[19] K Niu Z Niu D Liu X Zhao and P Gu ldquoA personalizeduser evaluation model for web-based learning systemsrdquo inProceedings of the IEEE 26th International Conference on Toolswith Artificial Intelligence (ICTAI rsquo14) pp 210ndash216 LimassolCyprus November 2014

[20] National Academy of Engineering and National ResearchCouncil Engineering in K-12 Education Understanding theStatus and Improving the Prospects National Academies Press2009

[21] C Okoli and S D Pawlowski ldquoTheDelphimethod as a researchtool an example design considerations and applicationsrdquoInformation ampManagement vol 42 no 1 pp 15ndash29 2004

[22] D-C Li and C-W Liu ldquoExtending attribute information forsmall data set classificationrdquo IEEE Transactions on Knowledgeand Data Engineering vol 24 no 3 pp 452ndash464 2012

[23] Y Jia and C Zhang ldquoInstance-level semisupervised multipleinstance learningrdquo in Proceedings of the 23rd National Confer-ence on Artificial intelligence (AAAI rsquo08) pp 640ndash645 2008

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


where learnersrsquo attributes information is extracted conse-quently through analyzing their learning behaviors andfinally utilized for user clustering Most of these attributes arein the category of continuous data From learnersrsquo behavioralinformation we can easily find quite a lot of continuous datasuch as ldquototal time length of learning resourcesrdquo and ldquocom-prehensive test resultrdquo In contrast there also exist attributesdata with categorical features which is easily neglected likeldquochosen lecturerrdquo ldquochosen learning resource typerdquo and soforth Although this kind of data is a smaller component oflearning behavior information it also plays a significant rolein learner clustering

In addition the mixed data of discrete and continuousdata which is extracted from learning behaviors in Wed-based learning systems are interrelated There are implicitcoupling relationships among them Clustering is oftenignored by the traditional clustering algorithms which leadsto massive significant information loss during the processof similarity computation and user clustering Consequentlythe quality of relevant services provided like learning guidesand learning resources recommendation is not satisfactoryFor example we have the common sense that ldquototal timelength of learning resourcesrdquo has positive impact on ldquocom-prehensive test resultrdquo Generally if the ldquototal time length oflearning resourcesrdquo is longer the ldquocomprehensive test resultrdquois better However there are also some special groups ofstudents who behave differently They can either get betterldquocomprehensive test resultrdquo with shorter ldquototal time lengthof learning resourcesrdquo or worse ldquocomprehensive test resultrdquowith longer ldquototal time length of learning resourcesrdquo Thespecial correlation between attributes which is often ignoredis considered in user clustering of our approach This willlead to certain effect on user clustering accuracy but will notlead to guaranteeing that all users can get highly qualifiedpersonalized services easily An effect mechanism is neededto respond to the loss of the ignored information

To solve the above issues this paper proposed a coupleduser clustering algorithm based on mixed data namelyCUCA-MD This algorithm is based on the truth that bothdiscrete and continuous data exist in learning behaviorinformation it respectively analyzes them according to theirdifferent features In the analysis CUCA-MD fully takesinto account intracoupling and intercoupling relationshipsand builds user similarity matrixes respectively for discreteattribute and continuous attributes Ultimately we get theintegrated similarity matrix using weighted summation andimplement user clustering with the help of spectral clusteringalgorithm In this way we take full advantage of the mixeddata generated from learning actions in Web-based learn-ing systems Meanwhile the algorithm well considers thecorrelation and coupling relationships of attributes whichenables us to find interactions between users especially usersof previously mentioned special groups Consequently it canprovide suitable and efficient learning guidance and help forusers

The contributions of this algorithm can be summarizedfrom three aspects Firstly it takes into account the couplingrelationships of attributes in Web-based learning systemswhich is frequently neglected before and improves clustering

accuracy Secondly it fully considers different features ofdiscrete data and continuous data and builds user similaritymatrix based on mixed dataThirdly it captures and analyzesindividualsrsquo learning behaviors and provides customized andpersonalized learning services to different groups of learners

The rest of the paper is organized as follows The nextsection introduces related works The clustering algorithmmodel is proposed in Section 3 Section 4 introduces detailedutilization of the clustering algorithm Discrete and continu-ous data analysis are also studied in this section In Section 5experiments and results analysis are demonstrated Section 6concludes this paper

2 Related Works

Using mixed data to do user clustering has been achieved insome fields but rarely in Web-based learning area Ahmadand Dey came up with a clustering algorithm based onupdated 119896-mean paradigm which overcomes the numericdata only limitation which works well for data with mixednumeric and categorical features [6] A 119896-prototypes algo-rithm was proposed defined as a combined dissimilaritymeasure and further integrates the 119896-means which dealswith numeric data and 119896-modes algorithm which uses asimple matching dissimilarity measure to deal with cat-egorical objects to allow for clustering objects describedby mixed numeric and categorical attributes [7] Anotherautomated technique called SpectralCAT was addressed forunsupervised clustering of high-dimensional data that con-tains numerical or nominal or mix of attributes suggestingautomatically transforming the high-dimensional input datainto categorical values [8]

Recently an increasing number of researchers pay specialattention to interactions of object attributes and have beenaware that the independence assumption on attributes oftenleads to a mass of information loss In addition to the basicPearsonrsquos correlation [9] Wang et al addressed intracoupledand intercoupled interactions of continuous attributes [10]while Li et al proposed an innovative coupled group-basedmatrix factorization model for discrete attributes of rec-ommender system [11] An algorithm to detect interactionsbetween attributes was addressed but it is only applicablein supervised learning with the experimental results [12]Calders et al proposed the use of rank based measuresto score the similarity of sets of numerical attributes [13]Bollegala et al proposed method comprises two stageslearning a lower-dimensional projection between differentrelations and learning a relational classifier for the targetrelation typewith instance sampling [14] From all our vieweddocuments we hardly find anything of taking into accountcoupling relationships of user attributes for user clustering inWeb-based learning systems

3 Clustering Model

User clustering model plays a significant role in user eval-uation framework [15] In this section the coupled userclustering model based on mixed data is illustrated in



Intr

acou

pled





Learningguidance


Discreteattribute 1

Discreteattribute 2

Discrete

Inte

rcou

pled

Extract


Compute

Apply


Discretedata

Continuousdata







Continuous

Extract

IntegrateIntegrate



Weightedsummation


In

trac

oupl

ed

Inte

rcou

pled










119880

119860

1198861 1198862 1198863







119895= 119886119895sdot V1 119886119895 sdot V119905119895 is


119895 le 119899) and 119891 = ⋃119899




119880

119860

1198861 1198862 1198863

1199061 1198601 1198611 1198621

1199062 1198602 1198611 1198621

1199063 1198602 1198612 1198622

1199064 1198603 1198613 1198622

1199065 1198604 1198613 1198623




119891lowast

119895(1199061198961 119906

119896119905) = 119891

119895(1199061198961) 119891

119895(119906119896119905)

119892119895(119909) = 119906

119894| 119891119895(119906119894) = 119909 1le 119895 le 119899 1le 119894 le119898

119892lowast

119895(119882) = 119906

119894| 119891119895(119906119894) isin119882 1le 119895 le 119899 1le 119894 le119898

(1)




119896119905isin 119880119882 sube 119881





120593119895rarr119896

(119909) = 119891lowast

119896(119892119895(119909)) (2)

This IIF 120593119895rarr119896


119895 It obtains




119895 the


119875119896|119895

(119882 | 119909) =

10038161003816100381610038161003816119892lowast

119896(119882) cap 119892

119895(119909)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816

(3)






119895is defined as

120575Ia119895(119909 119910) =

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

(4)





119895





120575119895|119896

(119909 119910) = sum

120596isincap

min 119875119896|119895

(120596 | 119909) 119875119896|119895

(120596 | 119910) (5)


(119909) cap 120593119895rarr119896



119896 which




119895is defined as

120575Ie119895(119909 119910) =

119899

sum

119896=1119896 =119895120572119896120575119895|119896

(119909 119910) (6)


119896 sum119899119896=1 120572119896 = 1

120572119896isin [0 1] and 120575






119895is defined as

120575119860

119895(119909 119910) = 120575

Ia119895(119909 119910) sdot 120575

Ie119895(119909 119910) (7)



120575Ia2 (1198611 1198612) sdot 120575

Ie2 (1198611 1198612) = 04 times 025 = 01



1198941and 119906


CUS (1199061198941 1199061198942) =

119899

sum

119895=1120573119895120575119860

119895(1199091198941119895 1199091198942119895) (8)


119895 sum119899119895=1 120573119895 = 1

120573119895isin [0 1] 119909

1198941119895and 119909


119895

for 1199061198941and 119906



119860

119895(1199092119895

1199093119895) = 13 sdot 1205751198601 (1198602 1198602) + 13 sdot 120575119860

2 (1198611 1198612) + 13 sdot 120575119860



119872DD

= (

11987811 11987812 sdot sdot sdot 1198781119898

11987821 11987822 sdot sdot sdot 1198782119898


1198781198981 1198781198982 sdot sdot sdot 119878

119898119898

) (9)

where 119878119894119894= 1 1 le 119894 le 119898



(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)





1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840



1198811015840

1198911015840


1015840

1 1198861015840

2 1198861015840

119899 refers to a


119895=1 1198811015840

119895represents


119895sdot V10158401 119886

1015840



119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the


1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840




Autonomiclearning


Interactivelearning



119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093


1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)


(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583


119895and 1198861015840119896





⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Intr

acou

pled





Learningguidance


Discreteattribute 1

Discreteattribute 2

Discrete

Inte

rcou

pled

Extract


Compute

Apply


Discretedata

Continuousdata







Continuous

Extract

IntegrateIntegrate



Weightedsummation


In

trac

oupl

ed

Inte

rcou

pled










119880

119860

1198861 1198862 1198863







119895= 119886119895sdot V1 119886119895 sdot V119905119895 is


119895 le 119899) and 119891 = ⋃119899




119880

119860

1198861 1198862 1198863

1199061 1198601 1198611 1198621

1199062 1198602 1198611 1198621

1199063 1198602 1198612 1198622

1199064 1198603 1198613 1198622

1199065 1198604 1198613 1198623




119891lowast

119895(1199061198961 119906

119896119905) = 119891

119895(1199061198961) 119891

119895(119906119896119905)

119892119895(119909) = 119906

119894| 119891119895(119906119894) = 119909 1le 119895 le 119899 1le 119894 le119898

119892lowast

119895(119882) = 119906

119894| 119891119895(119906119894) isin119882 1le 119895 le 119899 1le 119894 le119898

(1)




119896119905isin 119880119882 sube 119881





120593119895rarr119896

(119909) = 119891lowast

119896(119892119895(119909)) (2)

This IIF 120593119895rarr119896


119895 It obtains




119895 the


119875119896|119895

(119882 | 119909) =

10038161003816100381610038161003816119892lowast

119896(119882) cap 119892

119895(119909)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816

(3)






119895is defined as

120575Ia119895(119909 119910) =

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

(4)





119895





120575119895|119896

(119909 119910) = sum

120596isincap

min 119875119896|119895

(120596 | 119909) 119875119896|119895

(120596 | 119910) (5)


(119909) cap 120593119895rarr119896



119896 which




119895is defined as

120575Ie119895(119909 119910) =

119899

sum

119896=1119896 =119895120572119896120575119895|119896

(119909 119910) (6)


119896 sum119899119896=1 120572119896 = 1

120572119896isin [0 1] and 120575






119895is defined as

120575119860

119895(119909 119910) = 120575

Ia119895(119909 119910) sdot 120575

Ie119895(119909 119910) (7)



120575Ia2 (1198611 1198612) sdot 120575

Ie2 (1198611 1198612) = 04 times 025 = 01



1198941and 119906


CUS (1199061198941 1199061198942) =

119899

sum

119895=1120573119895120575119860

119895(1199091198941119895 1199091198942119895) (8)


119895 sum119899119895=1 120573119895 = 1

120573119895isin [0 1] 119909

1198941119895and 119909


119895

for 1199061198941and 119906



119860

119895(1199092119895

1199093119895) = 13 sdot 1205751198601 (1198602 1198602) + 13 sdot 120575119860

2 (1198611 1198612) + 13 sdot 120575119860



119872DD

= (

11987811 11987812 sdot sdot sdot 1198781119898

11987821 11987822 sdot sdot sdot 1198782119898


1198781198981 1198781198982 sdot sdot sdot 119878

119898119898

) (9)

where 119878119894119894= 1 1 le 119894 le 119898



(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)





1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840



1198811015840

1198911015840


1015840

1 1198861015840

2 1198861015840

119899 refers to a


119895=1 1198811015840

119895represents


119895sdot V10158401 119886

1015840



119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the


1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840




Autonomiclearning


Interactivelearning



119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093


1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)


(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583


119895and 1198861015840119896





⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119880

119860

1198861 1198862 1198863







119895= 119886119895sdot V1 119886119895 sdot V119905119895 is


119895 le 119899) and 119891 = ⋃119899




119880

119860

1198861 1198862 1198863

1199061 1198601 1198611 1198621

1199062 1198602 1198611 1198621

1199063 1198602 1198612 1198622

1199064 1198603 1198613 1198622

1199065 1198604 1198613 1198623




119891lowast

119895(1199061198961 119906

119896119905) = 119891

119895(1199061198961) 119891

119895(119906119896119905)

119892119895(119909) = 119906

119894| 119891119895(119906119894) = 119909 1le 119895 le 119899 1le 119894 le119898

119892lowast

119895(119882) = 119906

119894| 119891119895(119906119894) isin119882 1le 119895 le 119899 1le 119894 le119898

(1)




119896119905isin 119880119882 sube 119881





120593119895rarr119896

(119909) = 119891lowast

119896(119892119895(119909)) (2)

This IIF 120593119895rarr119896


119895 It obtains




119895 the


119875119896|119895

(119882 | 119909) =

10038161003816100381610038161003816119892lowast

119896(119882) cap 119892

119895(119909)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816

(3)






119895is defined as

120575Ia119895(119909 119910) =

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

(4)





119895





120575119895|119896

(119909 119910) = sum

120596isincap

min 119875119896|119895

(120596 | 119909) 119875119896|119895

(120596 | 119910) (5)


(119909) cap 120593119895rarr119896



119896 which




119895is defined as

120575Ie119895(119909 119910) =

119899

sum

119896=1119896 =119895120572119896120575119895|119896

(119909 119910) (6)


119896 sum119899119896=1 120572119896 = 1

120572119896isin [0 1] and 120575






119895is defined as

120575119860

119895(119909 119910) = 120575

Ia119895(119909 119910) sdot 120575

Ie119895(119909 119910) (7)



120575Ia2 (1198611 1198612) sdot 120575

Ie2 (1198611 1198612) = 04 times 025 = 01



1198941and 119906


CUS (1199061198941 1199061198942) =

119899

sum

119895=1120573119895120575119860

119895(1199091198941119895 1199091198942119895) (8)


119895 sum119899119895=1 120573119895 = 1

120573119895isin [0 1] 119909

1198941119895and 119909


119895

for 1199061198941and 119906



119860

119895(1199092119895

1199093119895) = 13 sdot 1205751198601 (1198602 1198602) + 13 sdot 120575119860

2 (1198611 1198612) + 13 sdot 120575119860



119872DD

= (

11987811 11987812 sdot sdot sdot 1198781119898

11987821 11987822 sdot sdot sdot 1198782119898


1198781198981 1198781198982 sdot sdot sdot 119878

119898119898

) (9)

where 119878119894119894= 1 1 le 119894 le 119898



(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)





1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840



1198811015840

1198911015840


1015840

1 1198861015840

2 1198861015840

119899 refers to a


119895=1 1198811015840

119895represents


119895sdot V10158401 119886

1015840



119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the


1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840




Autonomiclearning


Interactivelearning



119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093


1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)


(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583


119895and 1198861015840119896





⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119895is defined as

120575Ia119895(119909 119910) =

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816+

10038161003816100381610038161003816119892119895(119909)

10038161003816100381610038161003816sdot

10038161003816100381610038161003816119892119895(119910)

10038161003816100381610038161003816

(4)





119895





120575119895|119896

(119909 119910) = sum

120596isincap

min 119875119896|119895

(120596 | 119909) 119875119896|119895

(120596 | 119910) (5)


(119909) cap 120593119895rarr119896



119896 which




119895is defined as

120575Ie119895(119909 119910) =

119899

sum

119896=1119896 =119895120572119896120575119895|119896

(119909 119910) (6)


119896 sum119899119896=1 120572119896 = 1

120572119896isin [0 1] and 120575






119895is defined as

120575119860

119895(119909 119910) = 120575

Ia119895(119909 119910) sdot 120575

Ie119895(119909 119910) (7)



120575Ia2 (1198611 1198612) sdot 120575

Ie2 (1198611 1198612) = 04 times 025 = 01



1198941and 119906


CUS (1199061198941 1199061198942) =

119899

sum

119895=1120573119895120575119860

119895(1199091198941119895 1199091198942119895) (8)


119895 sum119899119895=1 120573119895 = 1

120573119895isin [0 1] 119909

1198941119895and 119909


119895

for 1199061198941and 119906



119860

119895(1199092119895

1199093119895) = 13 sdot 1205751198601 (1198602 1198602) + 13 sdot 120575119860

2 (1198611 1198612) + 13 sdot 120575119860



119872DD

= (

11987811 11987812 sdot sdot sdot 1198781119898

11987821 11987822 sdot sdot sdot 1198782119898


1198781198981 1198781198982 sdot sdot sdot 119878

119898119898

) (9)

where 119878119894119894= 1 1 le 119894 le 119898



(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)





1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840



1198811015840

1198911015840


1015840

1 1198861015840

2 1198861015840

119899 refers to a


119895=1 1198811015840

119895represents


119895sdot V10158401 119886

1015840



119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the


1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840




Autonomiclearning


Interactivelearning



119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093


1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)


(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583


119895and 1198861015840119896





⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











(

(

(

1 040 014 004 0040 1 024 008 0014 024 1 023 007004 008 023 1 0260 0 007 026 1

)

)

)

(10)





1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 and 1198861015840



1198811015840

1198911015840


1015840

1 1198861015840

2 1198861015840

119899 refers to a


119895=1 1198811015840

119895represents


119895sdot V10158401 119886

1015840



119894=1 1198911015840

119895 1198911015840119895 119880 rarr 119881

1015840

119895is the


1015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840




Autonomiclearning


Interactivelearning



119880

1198601015840

1198861015840

1 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

61199061 061 055 047 072 063 0621199062 075 092 062 063 074 0741199063 088 066 071 074 085 0871199064 024 083 044 029 021 0221199065 093 070 066 081 095 093


1015840

119896and 119886

1015840

119895is

formalized as

Cor (1198861015840119895 1198861015840

119896)

=

sum119906isin119880

(1198911015840

119895(119906) minus 120583

119895) (1198911015840

119896(119906) minus 120583

119896)


(1198911015840

119895(119906) minus 120583

119895)

2sum119906isin119880

(1198911015840

119896(119906) minus 120583

119896)2

(11)

where 120583119895and 120583


119895and 1198861015840119896





⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 061 037 055 030 047 022 072 052 063 040 062 0381199062 075 056 092 085 062 038 063 040 074 055 074 0551199063 088 077 066 044 071 050 074 056 085 072 087 0761199064 024 006 083 069 044 019 029 008 021 004 022 0051199065 093 086 070 049 066 044 081 066 095 090 093 086


119895 including

itself namely ⟨1198861015840119895⟩1 ⟨1198861015840

119895⟩2 ⟨119886

1015840




119895⟩119901


1015840

119895and ⟨119886

1015840






119895 1198861015840



119877 Cor (1198861015840119895 1198861015840

119896) =

Cor (1198861015840119895 1198861015840

119896) if 119901-value lt 005

0 otherwise(12)


1015840






119895 it is

119871 times 119871 matrix 119877Ia(1198861015840


between ⟨1198861015840119895⟩119901 and ⟨1198861015840

119895⟩119902

(1 le 119901 119902 le 119871) Consider

119877Ia(1198861015840

119895) = (

12057211 (119895) 12057212 (119895) sdot sdot sdot 1205721119871 (119895)

12057221 (119895) 12057222 (119895) sdot sdot sdot 1205722119871 (119895)


1205721198711 (119895) 120572

1198712 (119895) sdot sdot sdot 120572119871119871(119895)

) (13)

where 120572119901119902(119895) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119895⟩119902


119895⟩119901 and ⟨1198861015840

119895⟩119902


(1198861015840

1) = (1 0986



1015840


1015840

119896(119896 = 119895) is


minus 1)matrix as

119877Ie(1198861015840

119895| 1198861015840

119896119896 =119895

)

= (119877Ie(1198861015840

119895| 1198861015840

1198961) 119877

Ie(1198861015840

119895| 1198861015840


Ie(1198861015840

119895| 1198861015840

1198961198991015840minus1

))

119877Ie(1198861015840

119895| 1198861015840

119896119894)

= (

12057311 (119895 | 119896119894) 12057312 (119895 | 119896119894) sdot sdot sdot 1205731119871 (119895 | 119896119894)

12057321 (119895 | 119896119894) 12057322 (119895 | 119896119894) sdot sdot sdot 1205732119871 (119895 | 119896119894)


1205731198711 (119895 | 119896119894) 120573

1198712 (119895 | 119896119894) sdot sdot sdot 120573119871119871(119895 | 119896119894)

)

(14)

Here 1198861015840

119896119896 =119895


119895

and 120573119901119902(119895 | 119896

119894) = 119877 Cor(⟨1198861015840

119895⟩119901

⟨1198861015840

119896119894⟩119902


119895⟩119901 and ⟨1198861015840

119896119894⟩119902



3 1198861015840

4 1198861015840

5 1198861015840

6) is calculated as

119877Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6)

= (

0 0 0898 0885 0928 0921 0997 0982 0999 09880 0 0929 0920 0879 0888 0978 0994 0982 0999

)

(15)


1 and others (11988610158402 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) arecalculated as


119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119901Ie(1198861015840

1 | 1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = (

0689 0677 0039 0046 0023 0027 0 0003 0 00020733 0707 0023 0027 0050 0044 0004 0001 0003 0

) (16)




1015840

1 and 1198861015840

5 and 1198861015840

1 and 1198861015840




variables 1198601015840 = ⟨1198861015840

1⟩1 ⟨119886

1015840

1⟩119871

⟨1198861015840

1198991015840⟩

1 ⟨119886

1015840

1198991015840⟩119871


1198911015840

119901



119895and all its


1198911015840

1119895(119906)

1198911015840

119871

119895(119906)] while the


119896119896 =119895

) = [1198911015840

11198961(119906)

1198911015840

119871

1198961(119906)

1198911015840

11198961198991015840minus1

(119906) 1198911015840

119871

1198961198991015840minus1


1) = [061 037]1199061(1198861015840

2 1198861015840

3 1198861015840

4 1198861015840

5 1198861015840

6) = [055 030 047 022 072 052 063040 062 038]


119895is


(1198861015840

119895|

1198601015840 119871) where (1 119901)


has

119906119888

(1198861015840

119895|1198601015840 119871) = 119906

Ia(1198861015840

119895|1198601015840 119871) + 119906

Ie(1198861015840

119895|1198601015840 119871) (17)

119906Ia(1198861015840

119895|1198601015840 119871) = (119886

1015840

119895) ⊙119908otimes [119877

Ia(1198861015840

119895)]

119879

(18)

119906Ie(1198861015840

119895|1198601015840 119871) = (119886

1015840

119896119896 =119895

) ⊙ [119908119908 119908]

otimes [119877Ie| (1198861015840

1198951198861015840

119896119896 =119895

)]

119879

(19)



1015840

1 |1198601015840 2) = [385 380]


119895⟩119901 of the vector119906119888(1198861015840

119895|


functions [23]

119906119888

(1198861015840

119895|1198601015840 119871) sdot ⟨119886

1015840

119895⟩

119901

= 1205721199011 (119895) sdot

1198911015840

1119895(119906) +

1198991015840minus1sum

119894=1

1205731199011 (119895 | 119896119894)

11198911015840

1119896119894(119906)

+

1205721199012 (119895)

21198911015840

2119895(119906) +

1198991015840minus1sum

119894=1

1205731199012 (119895 | 119896119894)

21198911015840

2119896119894(119906) + sdot sdot sdot

+

120572119901119871(119895)

119871

1198911015840

119871

119895(119906) +

1198991015840minus1sum

119894=1

120573119901119871(119895 | 119896119894)

119871

1198911015840

119871

119896119894(119906)

(20)


119906119888

(1198601015840 119871) = [119906

119888

(1198861015840

1 |1198601015840 119871) 119906

119888

(1198861015840

2 |1198601015840 119871)

119906119888

(1198861015840

1198991015840 |

1198601015840 119871)]

(21)




entries

1198781015840

119894119895= exp(minus

10038171003817100381710038171003817119906119894minus 119906119895

10038171003817100381710038171003817

2

21205902) (22)



119872CD

= (

1198781015840

11 1198781015840

12 sdot sdot sdot 1198781015840

1119898

1198781015840

21 1198781015840

22 sdot sdot sdot 1198781015840

2119898


1198781015840

1198981 1198781015840

1198982 sdot sdot sdot 1198781015840

119898119898

) (23)



⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











⟨1198861015840

1⟩1

⟨1198861015840

1⟩2

⟨1198861015840

2⟩1

⟨1198861015840

2⟩2

⟨1198861015840

3⟩1

⟨1198861015840

3⟩2

⟨1198861015840

4⟩1

⟨1198861015840

4⟩2

⟨1198861015840

5⟩1

⟨1198861015840

5⟩2

⟨1198861015840

6⟩1

⟨1198861015840

6⟩2

1199061 385 380 070 070 220 146 324 323 335 370 376 3811199062 454 450 134 134 289 198 366 365 382 431 437 4511199063 551 546 088 088 354 244 446 445 466 522 528 5471199064 153 152 117 117 101 080 103 102 106 142 144 1521199065 594 589 094 094 373 249 495 494 517 568 575 590


(

(

(

1 011 020 008 014011 1 020 006 021020 020 1 003 070008 006 003 1 002014 021 070 002 1

)

)

)

(24)




119872MD

= 1205741119872DD

+ 1205742119872CD (25)





(

(

(

1 021 018 006 009021 1 021 006 014018 021 1 009 049006 006 009 1 010009 014 049 010 1

)

)

)

(26)













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Mr Liu 1199047 11990435 11990460 119904103 119904162 1199044 11990419 11990455 11990482 119904131

After clustering

1199041













10000

8000

6000

4000

2000

000

Accu

racy

()

01 02 03 04 05 07 1 3 5 7 10

120590-value

Scaling parameter

Scaling parameter




10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


k-prototypemADD

SpectralCATCUCA-MD

(a)

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

000

Accu

racy

()


NJW-DDCUCA-DDNJW-CD


(b)









900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



mADDCUCA-MD

(a)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



mADDCUCA-MD

(b)

900

800

700

600

500

400

300

200

100

00

Sim

ilarit

y ac

cura

cy (

)

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(c)

900

800

700

600

500

400

300

200

100

00

Diss

imila

rity

accu

racy

()

5 10 15 20 25 30



NJW-MDNJW-CDCUCA-MD

(d)



6 Conclusion






Acknowledgments



CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










CUCA-MD

SpectralCAT

mADD

k-prototype

Relative distance

0 05 1 15 2

(a)

CUCA-MD

SpectralCAT

mADD

k-prototype

100

101

102

103

104

Sum distance

(b)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Relative distance

0 05 1 15 2

(c)

CUCA-MD

NJW-MD

CUCA-CD

NJW-CD

CUCA-DD

NJW-DD

Sum distance

100

101

102

103

104

(d)



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article a coupled user clustering algorithm based...

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