2006/9/7 1

Mining Negative Association Rules

Xiaohui Yuan, Bill P. Buckles

Zhaoshan Yuan

Jian Zhang

ISCC 2002

2006/9/7 2

Outline

Motivation Problem define Algorithm Conclusion & Thought

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Motivation

conf(age < 30 →coupe ) = 0.3/0.4 =75% conf(age > 30 →not buy coupe) = 0.5/0.6 =

83.3%

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Problem

The difficulty for mining negative rulesCan’t simply pick threshold values for support

and confidence.Thousands of items are included in the

transaction records.

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Positive association rule, supp() and conf()

( )supp X Y

( )( )

( )

P X Yconf X Y

P X

, , , and = 0X Y X I Y I X Y

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Negative association rule, supp() and conf()

( ) 1 ( )conf X Y conf X Y

( ) ( ) ( )supp X Y supp Y supp Y X

( ) ( ) ( )supp X Y supp X supp X Y

( )( ) (1 ( ))

1 ( )

P Yconf X Y conf Y X

P X

( ), , , and 0X Y X Y X I Y I X Y

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Sibling relationships

Called LOS and denote as[i1,i2…..,im][IBM Aptiva , Compaq]Extend [IBM Aptiva , Compaq, Notebook]

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LOS

Locality of Similarity (LOS)Similarity assumption

Sibling rule If the item set X’ = {i1, i2,….ik,…,im} is the same as X ex

cept item ik is substituted for ih.

Rule r ： X→Y and Rule r’： X’→Y

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Discover Negitive Rule

If rule r’： X’→Y is not support ,it may exist negative rule.

Salience measure (distance betewwn conf level)

E()： estimated conf

( ') E( ( '))SM conf r conf r

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Condictions

for qualify a negative rule

1. there must exist a large deviation between the estimated and actual confidence.

2. the support and confidence are greater than the minima required.

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Pruning

Equivalent or similar pair

Exam：

Negative rule and positive rule are couple

Exam：” female →BuyHat “ and “﹁male→BuyHat”

, andX Y Y X

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Algorithm

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Conclusion

It’s not depend on numbers of transactions Complexity O(P x L)

P ： number of positive ruleL ： average size of LOS

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Thought

Estimate from postive to find negative cost , how ?