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Data Mining: Association Rules 46

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Data Mining: Association Rules 48

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).) /0 /1 / 00 01 , 1/ 10 11 ,

• Contingency table for X → Y

f11: support of X and Y f10: support of X and Y f01: support of X and Y f00: support of X and Y Used to define various measures

support, confidence, lift, Gini,

J-measure, etc.

Data Mining: Association Rules 49

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Data Mining: Association Rules 50

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basketball not basketball sum(row) cereal 400 350 750 not cereal 200 50 250 sum(col.) 600 400 1000

Data Mining: Association Rules 51

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X 1 1 1 1 0 0 0 0 Y 1 1 0 0 0 0 0 0 Z 0 1 1 1 1 1 1 1

Rule Support Confidence X=>Y 25% 50% X=>Z 37.50% 75%

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B P A P B A P corr B

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Itemset Support Interest X,Y 25% 2 X,Z 37.50% 0.9 Y,Z 12.50% 0.57 Data Mining: Association Rules 53

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Data Mining: Association Rules 54

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( 1 )[ ( )] ( 1 )[ ( ) ( ) ( ) , ( ) ( ) ( ) , ( ) ( ) ( ) , ( ) ( ) | ( Y P Y P X P X P Y P X P Y X P t coefficien Y P X P Y X P PS Y P X P Y X P Interest Y P X Y P Lift − − − = − − = = = φ

Data Mining: Association Rules 55

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Data Mining: Association Rules 56

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) 1 . )( 1 . ( 1 . = = Lift 11 . 1 ) 9 . )( 9 . ( 9 . = = Lift

Statistical independence: If P(X,Y)=P(X)P(Y) => Lift = 1

Data Mining: Association Rules 57

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Data Mining: Association Rules 58

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B B A p q A r s A A B p r B q s Does M(A,B) = M(B,A)? Symmetric measures:

support, lift, collective strength, cosine, Jaccard, etc

Asymmetric measures:

confidence, conviction, Laplace, J-measure, etc

Data Mining: Association Rules 59

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10 5 B 4 = 1 K: 4 B 6 L M D 5< 50 < =6 =0 6 K: B= B0 = L M D

Grade-Gender Example (Mosteller, 1968): Mosteller: Underlying association should be independent of the relative number of male and female students in the samples

2x 10x

Data Mining: Association Rules 60

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 A B C D (a) (b) 1 1 1 1 1 1 1 1 1 (c) E F

Transaction 1 Transaction N

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Data Mining: Association Rules 61

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φ φ φ φ Coefficient is the same for both tables

5238 . 3 . 7 . 3 . 7 . 3 . 3 . 2 . = × × × × − = φ

Data Mining: Association Rules 62

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B B A p q A r s B B A p q A r s + k Invariant measures:

support, cosine, Jaccard, etc

Non-invariant measures:

correlation, Gini, mutual information, odds ratio, etc

Data Mining: Association Rules 63

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