Mining Generalized Association Rules

1
Mining Generalized Association Rules

• R. Srikant R. Agrawal (IBM)
• Presentation by Colin Cherry

2
Objectives

• What are generalized association rules?
• Why do we care?
• How can we get them efficiently?
• How can we reduce rule redundancy?
• Is the efficient method any good?

3
Motivation

• Association rules find rules of the form
• X?Y, where X and Y are sets of items
• What if there is structure over your items?
• Structure can be used to generalize

4
Hierarchy Example
Beverage
Soft Drink

Cola

Pepsi
Coke


5
Hierarchy Example
On Sale
Not On Sale

• Goal of this paper
• Given hierarchies over items
• Capture interesting rules at all levels of
  multiple hierarchies

6
Simple Fix

• Just add parents to each transaction.
• Coke, 7-up, ranch Doritos, bananas
• would become
• Coke, 7-up, ranch Doritos, bananas, Doritos,
  cola, clear pop, soft drink, chips, junk food,
  fruit, produce

7
Fix Contd

• Run Apriori on expanded database
• Redefine association rules
• Make sure
• X?Y
• X?Y
• Y contains no ancestors of any item in X

8
Problems with the fix

• Counting may slow down
• Total number of items average transaction size
  will grow
• Could get a lot of redundant rules
• Milk ? Cereal (70)
• Skim Milk ? Cereal (70)
• Do we care?

9
An Efficient Algorithm

• Cumulate
• Filtering ancestors added to transactions
• Hierarchy-aware itemset pruning
• For more complicated, speculative algorithms, see
  paper

10
Filtering Ancestors

• Not counting soft drink? Dont add it.
• Only add ancestors that are in at least one of
  the candidate itemsets
• Delete any items we are not counting
• Not counting Doritos? Replace with chips
• Each iteration
• Pre-compute the ancestors for each item

11
Itemset Pruning

• No sense counting both coke,cola,chips and
  coke,chips, theyll always be the same
• Take out coke,cola during count size2 and
  youll never have to deal with it

12
Reducing Redundancy

• Milk ? Cereal (8 sup, 70 conf)
• Skim Milk ? Cereal (2 sup, 70 conf)
• If Skim Milk accounts for 1/4 of Milk sales, then
  the 2nd rule is redundant
• Expected support and confidence (wrt hierarchy)
  will define interesting

13
Close Ancestors

• An itemset Z is an ancestor of Z if
• Z Z with some items replaced by ancestors
• Z has the same number of items as Z
• Z is a close ancestor of Z if
• No ancestor of Z has Z as an ancestor
• Take coke,bananas as Z
• Zcola, bananas is a close ancestor
• Zsoft drink, bananas is not close
• Zcola,fruit is not close

14
Interestingness

• A rule X?Y is interesting if for all interesting,
  close ancestors X?Y
• Sup(X,Y) gt RExpSup(X,YX,Y)
• or
• Conf(X?Y) gt RExpConf(X?YX?Y)
• R is defined by the user

15
Putting it all together

• 1 is interesting - has no ancestor
• 2 is interesting - twice expected support
• 3 is not interesting
• Has exactly expected support according to closest
  ancestor (2)

16
Experiments

• Lots of experiments on artificial data in paper.
• Well look at the results of using Cumulate on
  real data
• Compare to the quick fix - just adding in
  ancestors to transactions

17
Supermarket
18
Department Store
19
Interestingness Results

• Hierarchical Interestingness pruning
• R 25 resulted in pruning roughly 40 of the
  rules
• R 50 resulted in pruning roughly 50 of the
  reuslts
• Pruning had a significant impact!

20
Objectives Revisited

• What are generalized association rules?
• Rules aware of hierarchies over items
• Why do we care?
• Support can be low for individual items
• How can we get them efficiently?
• Cumulate algorithm - hierarchy aware counting
• How can we reduce rule redundancy?
• Check surprise with respect to ancestors
• Is the efficient method any good?
• Yeap!

21
Questions?

• ?

22
Hierarchy Example
Impulse
Fridge

Beverage

Cans
Bottles


23
Pros

• Rules over items low in the tree may not have
  minimum support
• Can raise min support
• Shoot for fewer, more general rules
• BUT You can catch rules at any level of the
  hierarchy

24
Data Sets

• Supermarket
• 500,000 items
• 1.5 million transactions
• Hierarchy has 4 levels, 118 roots
• Department Store
• 200,000 items
• 500,000 transactions
• Hierarchy has 7 levels, 89 roots

25
Summary

• Nothing ground-breaking in this paper
• But, it provides a solid, efficient method for
  working with hierarchies
• Generalization is a powerful tool to have
  available in association rules