Mining for Patterns Based on Contingency Tables by KL-Miner

First Experience

Jan Rauch Milan Šimůnek (PhD. student)

Václav Lín (student)University of Economics Prague

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… KL-Miner, First Experience

KL-Miner Basic features

Application example

Implementation principles

Scalability

Concluding remarks

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KL-Miner -- Data and Patterns

M A1 A2 … AP

o1 2 12 … 1

o2 1 5 … 4

… … … … …

on 3 9 … 2

Data:

Data Matrix

Patterns i.e. KL-hypothesis: R C /

row attribute R {A1, …, AP}, possible values i.e. categories: r1, …, rK

column attribute C {A1, …, AP}, possible values i.e. categories: c1, …, cL

Boolean attribute derived from other attributes A1, …, AP

KL quantifier …. Condition imposed on contingency table of R and C

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KL – quantifiers

Contingency table

of R and C:

Examples of quantifiers:

Simple aggregate function:

Kendall’s quantifier: e.g. |b | P

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Kendall’s quantifier

b 0;1

b > 0 … positive ordinal dependence

b < 0 … negative ordinal dependence

b = 0 … ordinal independence

| b | = 1 … C is a function of R

Kendall’s quantifier: e. g. | b | p or | b | p

:Kendall’s coeficient:

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KL-Miner application example STULONG Project, 1419 patients, entry examination

See http://euromise.vse.cz

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STULONG attributes examples (1)

Systolic blood pressure

Smoking

Group of patients

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STULONG attributes examples (2)

Skinfold above musculus triceps (mm)

Beer – amount / day

219 attributes total

38 ordinal attributes

We use 17 ordinal attributes

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Example - analytic questionAre there any ordinal dependencies among attributes under some conditions?

at least 50 patients

| b | 0.75

relevant conditions :

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Example – relevant condition specification (1)

Group of patients (normal), Group of patients (risk), …

Beer 10(yes), Beer 12(yes), …, Beer 10(yes) Beer 12(yes)

Sliding windows …

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Example – relevant condition specification (2)

4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, ....., 43, 44, 45, 46, 47, 48, 49, 504, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, ....., 43, 44, 45, 46, 47, 48, 49, 50 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, ....., 43, 44, 45, 46, 47, 48, 49, 50

...........

4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, ....., 43, 44, 45, 46, 47, 48, 49, 50

4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, ....., 43, 44, 45, 46, 47, 48, 49, 50

Sliding window

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Example – output overview2 min 1sec

550 310 verifications

25 hypotheses

3.06 GHz

512 MB DDR SDRAM

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Example – output detail (1)

b = 0.82 (i.e. strong positive ordinal dependence)

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Example – output detail (2)

b = 0.78 (i.e. strong positive ordinal dependence)

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Implementation principles (1)

M A1 A2 … AP A1[1] A1 [2] A1 [3]

o1 2 12 … 1 0 1 0

o2 1 5 … 4 1 0 0

… … … … … … … …

on 3 9 … 2 0 0 1

Attributes Cards of categories of A1

Attributes are represented by cards of categories i.e. strings of bits

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Implementation principles (2)

CARD [] = bit string representation of Booelan attribute

CARD [ Group of patients (normal) Beer 10(yes) Beer 12(yes) ]

= Group of patients [normal] Beer 10[yes] Beer 12[yes]

Count() – number of “1” in the bit string

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Implementation principles (3)

n1,1 = Count( R[r1] C[c1] CARD [])

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Scalability

75 000 verifications

approximately linear

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Concluding remarks

KL-Miner practically interesting results

Suitable for interactive work

Further quantifiers

Combinations with further mining procedures