olap mining: mining multidimensional data

Introduction Mining for Blocks Multiple-Level Multidimensional Sequential Patterns Conclusion and perspectives

OLAP Mining: Mining Multidimensional Data

EXPEDO

LIRMM, UNIVERSITÉ MONTPELLIER II, FRANCEETIS, UNIVERSITÉ CERGY-PONTOISE, FRANCE

HELP UC, KUALA LUMPUR, MALAYSIA

Feb. 20-21 2007

EXPEDO LIRMM-ETIS-HELP UC

OLAP Mining


Outline1 Introduction

OLAP and Data MiningResearch Topics on OLAP Mining (EXPEDO)

2 Mining for BlocksFuzzy and Crisp BlocksGenerating BlocksManaging HierarchiesVisualizing Blocks

3 Multiple-Level Multidimensional Sequential PatternsMultidimensional Sequential PatternsMultiple Level MSPImplementation

4 Conclusion and perspectivesEXPEDO LIRMM-ETIS-HELP UC

OLAP Mining


OLAP and KDD

OLTP vs. OLAP

OLAP UsersDecision makersComplex Queries

Current UsesOLAP framework : mainly provides navigation andreporting tools (pull)Need for Data Mining (push)


OLAP Mining


OLAP and KDD

OLAP MiningFirst introduced in 1997 by Jiawei Han asa mechanism which integrates OLAP with data mining so thatmining can be performed in different portions of databases ordata warehouses and at different levels of abstraction at user’sfinger tips


OLAP Mining


OLAP and KDD

Specificities of the OLAP Framework

On-line analysismeasures described by means of dimensionsaggregated measure valueshierarchiesdisplaying data : the order matters (switch, pivot)


OLAP Mining


OLAP and KDD

Motivating Example

Beer Water Soda Wine MilkEurope 4 4 7 6 5America 4 5 7 7 6Asia 3 3 6 5 5Africa 2 2 6 5 4

Beer Water Milk Wine SodaAmerica 4 5 6 7 7Europe 4 4 5 6 7Asia 3 3 5 5 6Africa 2 2 4 5 6


OLAP Mining


OLAP and KDD

Representing Cubes

Several Ways to represent the same dataFinding the best representations is known as beingNP-Hard


OLAP Mining


Hierarchies

Using Hierarchies

Representativity of extracted Knowledge

high : nothing can be extracted (and trivial knowledge)low : too many patterns extracted, no use for the decisionmakers

Difficulty to choose the best level of granularity to getrelevant knowledge

Taking Hierarchies into account

Extracting rules at different levels of hierarchiesSubrules are automatically discovered (thanks toanti-monotonicity)


OLAP Mining


Research Topics on OLAP Mining (EXPEDO)

Research Topics from EXPEDO

Topics addressed by the projectMining for Rules (e.g. association rules, gradual rules,sequential patterns)Mining for homogeneous parts and compressing (e.g.blocks)Navigating by means of intelligent queries

To be addressed in this talkMining for BlocksMining for Multidimensional Sequential Patterns


OLAP Mining







OLAP Mining


Why Blocks ?

Impossibe to Mine for the Best RepresentationDifferent kinds of relevant representationsOther criteria may be considered : pointing outhomogeneous parts

What are Blocks ?Blocks are subcubes defined over all dimensionssome dimensions may appear completely : ALL levelBlocks must be large enough (Support)Blocks must be homogeneous enough (Confidence)


OLAP Mining


��

��

��

��

��

��

��

��

P1

P2

P3

P4

C1 C2 C3 C4 C5 C6 CITY

PRODUCT

6 6

6

8

8 8

5

8

8

5

5

8 2

2

5

5 5

6

2

2 2

8

75

2

Block Valuethe number of measure values may be numerous, thuspreventing from discovering blocks


OLAP Mining


Fuzzy and Crisp Blocks

Partitioning the measure : Crisp Blocks

6

6.1

5.9 0 10

0 2 5 8 10

8

58.1

7.9

7.8 4.8

4.75.1

8.1

4.9

8.2

2.4

2.2

5

5.3

1.8

1.9


OLAP Mining


Fuzzy and Crisp Blocks

Partitioning the measure : Fuzzy Blocks

6

6.1

5.9

8

58.1

7.9

7.8 4.8

4.75.1

8.1

4.9

8.2

2.4

2.2

5

5.3

1.8

1.9

0 10

0 2 5 8 10


OLAP Mining


Generating Blocks

Given a k -dimensional cube C, a support threshold σ and aconfidence threshold γ.For each measure values m :

1 For every dimension, compute all maximal intervals ofvalues containing enough matching measure values m

2 Combine the intervals in a level wise manner3 Considering the set of all blocks computed in the previous

step, sort out those that are not minimal with respect to theinclusion ordering and then those having a confidence form less than or equal to γ.


OLAP Mining


Example

# 82

1

0

# 812 03

P1

P2

P3

P4

C1 C2 C3 C4 C5 C6

PRODUCT

6 6 5 5 2

7565586

8

8 8

5 5

8 2

2 2

2 2

8

8


OLAP Mining


Problem

On real data :it may be the case that no (or very few) slice is relevantregarding the support : not enough cell with the measure valuebeing consideredAlternatives :

Decrease the minimum support valueMerge slicesNote that, in this case, considering hierarchies leads tosemantically-founded merged slicesNote that the support must remain anti-monotonic


OLAP Mining


Managing Hierarchies

water

soda

butter

bread

City1

City2City3City4City5City6

FoodBeverage

7.8

8.28.4

7.9

8.3

4.818

12

6.2

4.1

2.9

8

17

14

12.8

water

soda

butter

bread

City1

City2City3City4City5City6

7.8

8.28.4

7.9

8.3

4.818

12

6.2

4.1

2.9

8

17

14

12.8

South

North


OLAP Mining


Visualizing Blocks

Visualizing Blocks

Users can only have 2D (possibly 3D) visions of their dataAnd thus use projections over some values on theremaining invisible dimensions ...... But they are interested to know about the rest

− > Coloring cells depending on the block informations


OLAP Mining


Visualizing Blocks

Example


OLAP Mining


Visualizing Blocks

INTERLUDE

INTERLUDEon SEQUENTIAL PATTERNS


OLAP Mining







OLAP Mining


Sequential Patterns

Relations between eventsPartial Order on the data (e.g. temporal order)Many applications : marketing-CRM, decision making,bioinformatics, . . .

§Sequential Patterns only use a small part of the dataavailable (single dimension)What about the other dimensions ?


OLAP Mining


Goal : Combining several dimensions in the patterns

an item from a sequence is defined over severaldimensions

classical item : cmultidimensional item : (Pakistan, c)

multidimensional sequence :


OLAP Mining



an item from a sequence is defined over severaldimensionsclassical item : c

multidimensional item : (Pakistan, c)



OLAP Mining



an item from a sequence is defined over severaldimensionsclassical item : cmultidimensional item : (Pakistan, c)



OLAP Mining



an item from a sequence is defined over severaldimensionsclassical item : cmultidimensional item : (Pakistan, c)


〈{(Pakistan, carpet1), (Pakistan, pashmina1)}{(France, carpet1)}〉instead of simply 〈(carpet1, pashmina1), carpet1〉Warning : clients are usually groups


OLAP Mining


Multidimensional Sequential Patterns

Data Model : Blocks again !

DB partitioned into blocks regarding some dimensions, e.g.customer group. A block is considered as a client.

BlocID Date Place Product1 January Pakistan c11 January Pakistan c21 January Pakistan p11 March France c11 March Pakistan c12 February UK p22 June Pakistan c12 June Pakistan p22 July France c13 April Pakistan p13 April Pakistan c13 September France c1


OLAP Mining



Dimension Partition

D = DF ⊕DR ⊕DA ⊕Dt

Dt : temporal dimensionsDA : analysis dimensionsDR : reference dimensionsDF : forgotten dimensions


OLAP Mining



Support of a sequence

considering a particular sequence ς

support computed over reference dimensions

Support of ς

support(ς) = number of blocks supporting ςnumber of blocks


OLAP Mining



Example

DR = {Bid}, DA = {Place, Product} and DT = {Date},minsupp = 2Compute support ofς = 〈{(Pakistan, c1), (Pakistan, p1)}{(France, c1)}〉


OLAP Mining



ς = 〈{(Pakistan, c1), (Pakistan, p1)}{(France, c1)}〉

Block 11 January Pakistan c11 January Pakistan c21 January Pakistan p11 March France c11 March Pakistan c1

Block 1 supports ς : support(ς) + +

Block 2Block 2 does not support ς :

2 February UK p22 June Pakistan c12 June Pakistan p22 July France c1


OLAP Mining



ς = 〈{(Pakistan, c1), (Pakistan, p1)}{(France, c1)}〉

block 33 April Pakistan p13 April Pakistan c13 2 France c1

block 3 supports ς : support(ς) + +

support(ς) = 2 ≥ minsupp

ς is frequent


OLAP Mining


Multiple Level MSP

Need for Hierarchies

what if minsup=3 ? ς would not have been frequentUsing all the dimensions at the lowest granularity level maylead to ... nothingthen necessary to consider aggregationthe dimension may then be rolled up, or simply ignored(ALL level)ς ′ =〈{(Pakistan, c1), (Pakistan, pashmina)}{(France, c1)}〉


OLAP Mining


Multiple Level MSP

Managing Hierarchies

describing hierarchies between elementsonly the leaves can appear in the DB

Example of hierarchies on dimensions PRODUCT :

c1 c2 ... p1 p2 ... ...

carpet pashmina

Product (ALL)


OLAP Mining


Multiple Level MSP

Agrawal & Srikant (1996) :taking hierachies into account.the database is rewritten by putting the itemstogether with their ancestors (not possible ifseveral dimensions with several levels)

J. Han (2001) :Extraction of knowledge level by levelbut the mined knowledge concerns only onelevel at one time

Choong et al. (2005) :many dimension appear in the patternsthey can appear at any granularity level


OLAP Mining


Multiple Level MSP

Item, itemset and h-generalized sequences

Multidimensional h-generalized Item :tuple with labels taken at any ganularity levelExamples : (Pakistan, c2)

(EU, p1)

(EU, pashmina)


OLAP Mining


Multiple Level MSP

Item, itemset and h-generalized sequences

Multidimensional h-generalized Item :tuple with labels taken at any ganularity levelExamples : (Pakistan, c2)

(EU, p1)

(EU, pashmina)

Hierarchical InclusionGiven e = (d1, . . . , dm) and e′ = (d ′

1, . . . , d ′m), e can be :

more general than e′ (e >h e′)more specific than e′ (e <h e′)not comparable to e′ (e ≯h e′ and e′ ≯h e)


OLAP Mining


Multiple Level MSP

Example :

(Pakistan, carpet) >h (Pakistan, c1).(France, c4) <h (EU, carpet).(EU, c1) and (France, carpet) are not comparable(France, c1) and (Pakistan, c1) are not comparable


OLAP Mining


Multiple Level MSP

Itemset and h-generalized sequence

h-generalized Itemset :

set of non comparable items

{(France, c1), (USA, p1)} YES{(France, c1), (France, carpet)} NO because(France, c1) <h (France, carpet)

Multidimensional h-generalized Sequence

s = 〈i1, . . . , ij〉 is an ordered non empty list of multidimensionalh-generalized itemsets.

〈{(India, c1), (Pakistan, c1)}{(EU, c1)}〉


OLAP Mining


Multiple Level MSP

Support

Item supported by a transactionA transaction supports an item e if the value is equal to e orunder e in the hierarchy

(Block_1, February , France, c1) supports the item(EU, carpet).

sequence supported by a blockA block supports a sequence if all itemsets are supported(provided that the order is respected)


OLAP Mining


Implementation

Algorithms

Generation of candidate itemsextract all the maximally specific itemslevelwise generation

Generation of candidate sequencesanti-monotonicity of the supportApriori like approach (generate - prune)Use of a prefix tree to store candidate sequences (PSP)


OLAP Mining


Implementation

Experiments

Indicatorstime consumptionmemory consumptionnumber of patterns being discovered

Datasynthetic datareal data (examples from our industrial collaborations)

National French Electricity Agency (marketing)Follow-up of long term care patients to improve facilitiese-couponing (customized coupons sent to mobile phones)


OLAP Mining







OLAP Mining


Conclusion

SummaryOLAP Mining must not only plug data mining on top ofmultidimensional databases without any consideration ofthe specificitiesDiscovery of homogeneous partsHierarchy-aware Multidimensional Sequential PatternsWork has also been done on fuzzy sequential patterns


OLAP Mining


Further Work

Next Challenges

CausalityOutliersSupport counting and measure valuesCondensed representationsGradual Rules (generalization of the ordered/temporaldimension),Enrol the userTest on real data


OLAP Mining

olap mining: mining multidimensional data

Documents