ch06FPBasic

9
Mining Association Rules
TID Items
Example of Rules:
{Milk,Diaper} {Beer} (s=0.4, c=0.67) {Milk,Beer} {Diaper} (s=0.4, c=1.0) {Diaper,Beer} {Milk} (s=0.4, c=0.67) {Beer} {Milk,Diaper} (s=0.4, c=0.67) {Diaper} {Milk,Beer} (s=0.4, c=0.5) {Milk} {Diaper,Beer} (s=0.4, c=0.5)
Example of Association Rules
{Diaper} {Beer}, {Milk, Bread} {Eggs,Coke}, {Beer, Bread} {Milk},
Market-Basket transactions
TID Items
1 2 3 4 5
Bread, Milk Bread, Diaper, Beer, Eggs Milk, Diaper, Beer, Coke Bread, Milk, Diaper, Beer Bread, Milk, Diaper, Coke
Chapter 6: Mining Frequent Patterns, Association and Correlations: Basic Concepts and Methods
Basic Concepts Frequent Itemset Mining Methods
Which Patterns Are Interesting?—Pattern
1 2 3 4 5
Bread, Milk Bread, Diaper, Beer, Eggs Milk, Diaper, Beer, Coke Bread, Milk, Diaper, Beer Bread, Milk, Diaper, Coke
Observations:
• All the above rules are binary partitions of the same itemset: {Milk, Diaper, Beer} • Rules originating from the same itemset have identical support but can have different confidence
Association rules: A D (60%, 100%)(3/5,1)
D A (60%, 75%)(3/5,3/4)
Strong association rule
Customer buys beer
8
Association Rule Mining Task


Given a set of transactions T, the goal of association rule mining is to find all rules having support ≥ minsup threshold confidence ≥ minconf threshold Brute-force approach: List all possible association rules Compute the support and confidence for each rule Prune rules that fail the minsup and minconf thresholds Computationally prohibitive!
Evaluation Methods Summary
1
What Is Frequent Pattern Analysis?

Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule mining Motivation: Finding inherent regularities in data
5
Basic Concepts: Association Rules
Tid
Items bought Beer, Nuts, Diaper Beer, Coffee, Diaper
10 20

30 40 50
Beer, Diaper, Eggs Nuts, Eggs, Milk
Nuts, Coffee, Diaper, Eggs, Milk
Transaction-id Items bought
10
20 30 40 50 Customer buys both
A, B, D
A, C, D A, D, E B, E, F B, C, D, E, F Customer buys diaper
Let supmin = 50%, confmin = 50% Minimum support number is 3 Freq. Pat.: {A:3, B:3, D:4, E:3, AD:3}
{Beer, Diaper}:3
Let minsup = 50%, minconf = 50% Freq. Pat.: Beer:3, Nuts:3, Diaper:4, Eggs:3,

Customer buys beer
Association rules: (many more!) Beer Diaper (60%, 100%) Diaper Beer (60%, 75%)


Customer buys beer
itemset: A set of one or more items k-itemset X = {x1, …, xk} (absolute) support, or, support count of X: Frequency or occurrence of an itemset X (relative) support, s, is the fraction of transactions that contains X (i.e., the probability that a transaction contains X) An itemset X is frequent if X’s support is no less than a minsup threshold
4
Basic Concepts: Frequent Patterns
Tid 10 20 Items bought Beer, Nuts, Diaper Beer, Coffee, Diaper

30
40 50
Beer, Diaper, Eggs
Nuts, Eggs, Milk Nuts, Coffee, Diaper, Eggs, Milk Customer buys both Customer buys diaper
Customer buys both
Customer buys diaper
Find all the rules X Y with minimum support and confidence support, s, probability that a transaction contains X Y confidence, c, conditional probability that a transaction having X also contains Y
sup port( A B) P( A B)

confidence, c, conditional probability that a confidence ( A B) P( B | A) transaction having X also contains Y
7
Basic Concepts: Frequent Patterns and Association Rules
• Thus, we may decouple the support and confidence requirements
10
Computational Complexity of Frequent Itemset Mining

How many itemsets are potentially to be generated in the worst case?
6
Basic Concepts: Frequent Patterns and Association Rules

Itemset X = {x1, …, xk} Find all the rules X Y with minimum support and confidence


support, s, probability that a transaction contains X Y
2

Applications

Association Rule Mining

Given a set of transactions, find rules that will predict the occurrence of an item based on the occurrences of other items in the transaction