global distance functioning

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A New Approach to Com positional Adaptation Based on

Optimizing the Global Distance Function and itsapplication in an intelligent tutoring systemNima Reyhani , Kambiz Badie, and Mahm ood Kharra t

Info Socie ty Dept.I ran Telecom R esearch Center, End ofNorth Karega r

Tehran, Iran{nre yhan i, k-badie, khar rat) @itrc.ac.ir

Abstract. In this paper, we propose a new approach tocompositional adaptation basedon the idea of constitutingthe$nal solution in a w ay that its global difference with aset of solutions belonging to the retrieved cases can get

minimized. Within this respect, the normalized distancebetween the current problem and each retrieved caseistaken into account, usingU global distance function, whichmakes use of the normalized local distances between thecandidate final solution and the retrieved cases' solutionsas the variables, and some coef3cients as its parameters.Here, an approach based on secondary CBR can be usedto determine the optimal valuesof these coefficients basedon their pa st experiences in characterization of th e globaldistance function. A n example is illustrated in the paper,which shows the utilityof this approach fo r rearrangingthe necessary course-w ares fo r studentsin the realm ofintelligent tutoring systems.

Keywords: Case Based Reasoning, Global DistanceFunction, Compositional Adaptation, two layered CBR,Intelligent Tutoring Systems

1 INTRODUCTION

Out of the existing approaches to case adaptationin case-based reasoning is compositional adaptation, which can beparticularly significantin the situations where a variety ofsimilar cases can at the same time be retrievable, due to avariety of facts, suchas homogeneousnessof the casesdomain, or infeasibility of having a reliable similarityassessment formalism that can lead to a unique similarcase.

With respectto compositional adaptation, a number ofapproaches have been developed[ I , 2, 31, mainly focusingeither on the idea that the components of the final solutioncan he pr ovided from different cases basedon the statusofthe featuresin the curren t problem , or the idea that the totalsolution can be regardedin terms of some attributes whosevalues can he separately determined through a sort ofaveraging, aggregation,or centeroidization[4, 5 , 61 on thevaluesof these attributesin the retrieved cases.

With respect to the second view, there exist situationswhere the attributes can not hold quantitative values andthe idea of averaging, aggregation,or centeroidization isnot therefore workable in a straightforward manner.

To circumvent the above problem, in this paper wepropose a new approac h to compositiona l adaptation basedon the idea of constituting the final solution in a mannerthat its global difference with the set of the solutionsbelonging to the retrieved cases can get m inimized. Withinthis view, the normalized distance between the currentproblem and each retrieved case isto be taken intoaccount. In this regard, we needto define a global distancefunction which makes use of the normalized local distancesbetween the final solution and the solutions belonging tothe retrieved cases as the variables, and the coefficientsbeing applied to these variables as its parameters. We thenapply the above approach to the problem of rearranging thenecessary course-wares for students as a major issue inintelligent tutoring systems. Since the possibility ofknowing the appropriate parameters values of the globaldistance in an omine wayis far enough,in this paper wepropose a method for determ ination of these coefficientsinan adaptive manner. In this view, we start from somearbitrarily defined coefficients as the initial bias values,and then try to adjust these bias values through learningfrom past experiences of minimizing the global distancefunction.

2 RELATED WORKS

In com positional adaptation , solutions from multiple casesare combinedto produce a new composite solution[ I , 21.Com positional adaptation can be applied in two distinctsituations:

1. When the solution consists of differentindependent components, then each of thesecomponents can be adapted more or lessprecisely. This method is ef fective if there are fewconflicts between these components [l]. Forexample, Prodigy/Analogy constructs a newsolution froma set of guiding casesas opposed to

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a single past case. Here, complex problems mayhe solved by resolving minor interactions amongsimpler past cases[8].

2. The solution could not he divided intoindependent parts,so the solutionsin the similarcases should he combined in some way. InAirquap, which is aCB R system for predictingthe pollution levels, the solution to the targetproblem is the mean value of the solutionsbelonging to the most similar cases in the library[9]. Also, in the Tutoring Library System forgenerating a new set of chapters (to provide a newhook), the solution to the target problemis the setof the chapters that exists in the most of theretrieved cases[3]. In the meantime, in adaptivehyperm edia for Internet portals, the solutio n to thetarget problem is a personalized hypermediadocument which is obtained through user-profiledriven selection of generic information snipersfrom an ensemble of past compiled hypermediadocuments [IO]. In Personalized HealthInformation Generation Delivery System, relevanthealth information elementsfrom the solutioncomponent of multiple similar past cases arecarefully selected and systematically combined toyield a new personalized health informationpackage [I I] .

3 TH E PROPOSED GLOBAL DISTANCEli"CTI0N

Our proposed approach to compositional adaptationisbased on the fact that the final solu tion, whichis a product

of composing the solutions belonging to the retrieved cases(cases whose similarity withthe current problem is higherthan a certain threshold), should he constructed in a such amanner that its normalized distance with respect to thesesolutions can be as close as possible (though notcompletely equal to "0") to the normalized distancesbetween their corresponding case situations and the currentproblem.

Suppose thatthe normalized distance values betweenthe current problem and the retrieved cases, and thenormalized distance values which should exist hetween thefinal solution and the solutions in the retrieved casesarerespectively indicated bywoniand h""i. Also, suppose thatthe status of the k-th and I-th attribute belonging

respectively to the situation and solution of the i-thretrieved case is show n by Sitik, andSolil/. Taking theabove fact into account, the final solutionis constructed atthe stage where the function

is minimized.Since in reality the different attributesin a solution

bold different contributions to the solution, somecoefficients are required to reflect these contributions.Taking this fact into accoun t, the function (1) willturn intothe following form:

Here , Sol"" is the com posite solution or the final result, andLk(.,,) s defined as follow:

\ / = I J

where , is the contribution coefficient for the 1-th attributein the solution, and wan, in (2) can be obtained usingexpression(4), within whichpk indicatesthe weights of k-th attribute in measuring the distance value,M is thenumber of retrieved cases,C is the number of attributesinthe situation, andN s the number of attributes in thesolution, t and t' values depends on the dimensionality ofthe problem and so lution space [12, 13, 141.

j= 1 \ k =lWhere sitonk s the k-th feature of the ongoing/currentproblem , and sit'kis k-th featu re of the i-th retrieved case.It is to be noticed that, there would be situation whereSol'land Sol0", take qualitative valu e, (the va lueof eachattribute in the solution belongs to a discrete set ofpredefined values), Ix-y/s can in general be determinedusing a table lookup method within which the table canhold a predefined format.

In case that the number of retrieved cases andior thenumb er of attributes in the solutions areiis high, optimizingthe global distance function may become time-consuming.To overcome this problem, optimization techniques such as"dynamic programming"[151, "genetic algorithm"[16,

171, or "greedy algorithm" [15] can be utilized to makelimitation on the essential search space.

4 ANEXAMPLE

To show how the proposed approach to compositionaladaptation works, let consider an example in the domain ofintelligent tutoring systems (ITS), within which the

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objective is to rearrange the necessary course-wares forstudents (or learners), preferably basedon leamer modelsavailable [IS, 19, 20, 211. In the example, pattemrecognition has been selected as the focal subject fortutoring. One of the strategies in this respect is case-basedreasoning in which different situationsin tutoring, togetherwith their corresponding formats of courseware and therelated performance are stored in terms of some cases, andthe objective isto adapt the solutions of the retrieved casesin such a way that the final solution can fit the currentproblem in a plausible manner.

In our approach, the situation in a case is c onsidered toconsist of the predicates regarding the learner model(belief, desire, intention, and learning style), which itselfconsists of items such as background knowledge,capabilities, essential mode for leaming (whether thelearner wants to learn as a researcher, practitioner,operator, or in general as a person who wantsto gaingeneral knowledge), and the essential format for teaching

the coursew are to himiher (audio, visual, graphical, textual,. . ) as well. Also, the solution is considered to consist ofthe basic attributes of the texts to be given to the user, andthe text accessories like applet and images, as well.

Figure 4 illustrates an example within which a currentproblem is demonstrated together with a number of similarcases retrieved. To decide which retrieved cases shouldremain, we go through the following procedure: Cases arefirst ranked according to their normalized distance (in anascending trend). Here, Euclidian distance function[12,131, as mentioned in section 3 with t=2,is used as anoption for distance measurement. Next, starting from thecase with the highest rank (lowest normalized distance),the gradients of the similarities calculated. We considerthe set of cases whose gradients is less than standarddeviation of the whole cases distance, seeFigure 2. Thisset is considered to stand for the set of similar cases, whichshould later be subject to com positional adaptation.As it isseen, thepartsof the solution are qualitative in their nature,to the extent that one can not rely on a compositionaladaptation based on averagin gor centeroidization [6] toobtain the final solution.

Now, applying the proposed compositional adaptationapproach, the final solution can be obtained throughminimizing the global distance function of expression( l ) ,as illustrated in Figure3, where the initial values61 s areconsideredto be any positive value less than1. It shouldbe noticed that these initial values can be set somewhatarbitrarily, or according to the past expe riences of using thecorresponding coefficients (as bias values) in similar typesof global distance functions. With respect to the later, asecondary CBR [7 ] has been proposed in which theobjective of solution adaptation isto determine new biasvalues based on past experiences of using them. Thegeneral architecture of the secondary case-based reasoningfor bias adjustment is illustrated in Figure3 [7]. As it isseen from the figure, once a new problem is faced, the

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secondary CBR isfirst activated to estimate the optimalformats for the modules, here, case adaptationsparameters. This means that the very parameters beingused for this modules should first be optimized (using pastexperiences), in order to make the primary CBR asimmune as possible. Obviously,6,s, which activelyparticipate in the module of case adaptation, can be fairlyadjusted through the above process.For the moment, weassume that all theSI s have the same contribution and allare equalto 1.

Age: 24Sex: MaleIntention: ResearcherDesire: Hierarchical ClassifierSystemsBelief: (Fuzzy Set Theory)Perception Level:0.1Inpu tLevel:0. 1Orga nization Level:0.2Understand ing Level:0.3Processing Level:0.2Decision Making Level:0.7Attitude to O utside W orld Level:0.4Organizationto Life Level:0.8

Sex: Male

Intention: ResearcherDesire: ClassifierSystemsBelief: (Structural Pst femRecognition)

Perception Level: 0.1Input Level: 0.7Organization Level: 0.2Understanding Level: 0. 7Processing Level: 0. 2Decision Making Level: 0.7Attit. l o Outside World Level: 0 .4Organization to Lire Le\el: U XSolutio

Difficulty Level: 4Depth Level: 6Example Bared: Y e sExercise Based: YesProblem Based: NoImsgeLDimcul tyLLe~el :4AppletLDiffieulty_Level:4Image-Deplh_Level: 3AppletLDepth_Level: 3

C0CUb

MoreSensitiveMoreVerbalMoreInductiveMoreGlobalMoreActiveMore FeelingMoreJudgmentMore Introvert



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Belief: [Stochastic Process)Perception Level: 0.1Input Level: 0. 7 Mom DeductiveOrganization Level: 0.8Understanding Level: 0 .9Processing Level: 0 .2Decision Making Level: 0.1

Organization to Life Level: 0.8

Difficulty Level: 2Depth Level: 4

Example Based: ye sExercise Based noProblem Based: noImage_Difficulty~Levei:2Appiet_Diffiiculty_Level:2Imagel)epth_Levei:3Applet_Depth_Level:3

Figure 4. Illustrates an example for solution adaptations i n g the proposed compositional approach.

Considering this, the final solution for the above examplewill be obtained as follows:

Difficulty Level: 4Depth Level5Example Based: yesExercise Based:noProblem Based yesImage_Diffcul~_Level:3Applet_Difticulty_Level:3Image_Deptl-Level:4Applet_DeptI_Level:4

Figure 5 . The solution of problem in Fig.4, which isconstructed by the proposed approach to compositionaladaptation

Some human experts in tutoring of the subject patternrecognition (as the domain knowledge in tutoring) werethen requested to assess the solution in Figure2, takinginto account their intuition. After a while, when thenumber of casesin 2ndary case library becomes large, itwas found that the solutionis on average agreeable forthem from the viewpointof their expertise in tutoring

pattern recognition as a subject. The final solutionobtained in the above manner should then be exposed tothe learner, and evaluatedin some way based on theperformance that the learner may exhibit in subsequentactions of problem-solvingor question-answering. Theperformance determined in such a manner together withthe problem situation and the set o fth e values6,s constitutea new case in the secondary case-base, to denote howmuch these bias values have been successful with respectto the corresponding problem.

Now, confronting a new problem in coursewarerearrange ment, the secondary case-ba se is first consulted todecide the optimal bias values, and these bias values willthen activate the global distance function to yield the finalarrangement of the courseware (the final solution) requiredfor tutoring.

5 CONCLUDING REMARKS

In this paper, we proposed an approach to compositionaladaptation based on minimizing a global distance function,which takes into account the local distances between thecurrent problem and the situations in retrieved cases.As itis seen, both the parameters being used in measuring thedistances between the current problem and stored cases,and the contribution coefficients6, can play an efficientrole in conducting compositional adaptation mostsuccessfully. Hopefully, the secondary CBR, discussed inthe paper as a method for bias adjustment, can enhancesuch an opportunity. We therefore expect that acombination of the approach based on global distancefunction and the secondary CBR, can provide a conducivemedium for handling complex adaptation issues.

The proposed approach, can be particularly effectivefor the problems where the solutions are described in termsof some qualities or nominal. Examples can be mentionedfor intelligent tutoring system, mining qualitative data,system design, and action planning as well.

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SecondaryCBR to estimate the

representation, ease re&wd, andcase adaptation

formats for

I.

Primary CBR to mlve thc Ongoingproblem bssed an Ihe formats

estimated for its modulesI

A new c u econtainiog theongoing problem8s ts sifyafion, andthe estimatedoptimal formats forthe modules as thelolution (theusefulness measureobtained throughapplying thesolution shouldalso be included inthe new ease1

6 nticipated So lutionFigure 3. Interaction of the twoCBR stages to actualizetheapproach for optimizing the formatsfor the correspondingmodules

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http://citeseer.nj.nec.com/shiri98student.htmlhttp://citeseer.nj.nec.com/52555http://citeseer.nj/http://citeseer.nj/http://citeseer.nj.nec.com/52555http://citeseer.nj.nec.com/shiri98student.html


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Figure 1. Illustrates the components involving in computing the value of the Global Distance Function

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similar cases (retrievedcases)

0.8

0.6

0.4

0.2

0

0 5 10 15 20 25

Figure 2. This figure demonstrates how we fmd the most closely casesto the current problem. The sourceof this data arethose evaluated for solving problem mentioned inFigure4.

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