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### ASSOCIATION RULES & THE APRIORI ALGORITHM

BY: JOE CASABONA

INTRODUCTION

- Recap
- Data Mining
- Three types
- Association Rules
- Apriori Algorithm

ASSOCIATION RULES

- Most apparent form of Data Mining
- Objective: Find all co-occurrence relationships among data items
- Strength: Support & Confidence

SUPPORT

- Those who buy X buy Y, where X and Y are sets
- X => Y
- .count = number of occurences
- n = number of total transactions
- Number produced is % of all transactions (T)

CONFIDENCE

- % of transactions where X also contains Y
- Determines predictability of the rule
- Min Support and Confidence Determined.

EXAMPLE

- AR 1: Xbox ---> Controller
- Support: 5/8
- Confidence: 3/5
- AR 2: COD4 ---> Xbox
- Support: 5/8
- Confidence: 2/5
- AR 1 passes, AR 2 fails

APRIORI ALGORITHM

- Generate all frequent item sets
- All item sets with min support
- Generate all confident ARs from frequent item sets
- Downward Closure Property

GENERATE FREQUENT ITEM SETS

- Count supports of each individual item
- Create a set F with all individual items with min support
- Creates "Candidate Set" C[k] based on F[k-1].
- Check each element c in C[k] to see if it meets min support
- Return set of all frequent item sets.

GENERATE CANDIDATE SETS

- Create two sets differing only in the last element, based on some seed set
- Join those item sets into c
- Compare each subset s of c to F[k-1]- if s is not in F[k-1], delete it.
- Return final candidate set

RULE GENERATE

- Take Frequent Item Set F
- If {F[1], F[2],...F[k-1]} => {F[k]}meets some min confidence, make it a rule
- Remove last element from antecedent, insert into consequent, check again

OTHER ALGORITHMS

- Eclat algorithm
- FP-Growth algorithm
- One-attribute-rule
- Zero-attribute-rule

SAMPLE DATA

- Xbox, Controller, COD4
- Xbox, COD4
- Xbox, Controller
- Controller, COD4
- Xbox, Rock Band, Controller
- Xbox, PS3
- COD4, COD5, Rock Band
- COD4, Rock Band
- Min Support: 60%
- Min Confidence: 50%

RERERENCES

The Book I am using:

Liu, Bing. Web Data Mining, Chapter 2: Association Rules and Sequential Patterns. Springer, December, 2006

Wikipedia:

"Apriori Algorithm." http://en.wikipedia.org/wiki/Apriori_algorithm March 23, 2009

"Association rule learning." http://en.wikipedia.org/wiki/Association_rulesMarch 25, 2009

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