# Mining Association Rules between Sets of Items in Large Databases - PowerPoint PPT Presentation

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Mining Association Rules between Sets of Items in Large Databases. presented by Zhuang Wang. Outline. Introduction Formal Model Apriori Algorithm Experiments Summary. Introduction. Association rule:

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Mining Association Rules between Sets of Items in Large Databases

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## Mining Association Rules between Sets of Items in Large Databases

presented by Zhuang Wang

### Outline

• Introduction

• Formal Model

• Apriori Algorithm

• Experiments

• Summary

### Introduction

• Association rule:

- Association rules are used to discover elements that co-occur frequently within a dataset consisting of multiple independent selections of elements (such as purchasing transactions), and to discover rules.

• Applications:

- Questions such as "if a customer purchases product A, how likely is he to purchase product B?" and "What products will a customer buy if he buys products C and D?" are answered by association-finding algorithms.(market basket analysis)

### Formal Model

• Let I = I_1, I_2,. . ., I_n be a set of items.

Let T be a database of transactions.

Each transaction t in T is represented as a subset of I .

Let X be a subset of I.

• Support and Confidence:

By an association rule, we mean an implication of the form X  I_k, where X is a set of some items in I, and I_k is a single item in I that is not present in X.

support: probability that a transaction contains X and I_k.

P(X ,I_k)

confidence: conditional probability that a transaction having X also contains I_k.

P(l_k | X)

### Support and Confidence - Example

• Let minimum support 50%, and minimum confidence 50%, we have

• A  C (50%, 66.6%)

• C  A (50%, 100%)

### Apriori Algorithm

• To find subsets which are common to at least a minimum confidence of the itemsets.

• Using a "bottom up" approach, where frequent itemsets (the sets of items that follows minimum support) are extended one item at a time (a step known as candidate generation), and groups of candidates are tested against the data.

• The algorithm terminates when no further successful extensions are found.

• Generating from each large itemset, rules that use items from the large itemset

Database D

L1

C1

Scan D

C2

C2

L2

Scan D

L3

C3

Scan D

### Experiments

• We experimented with the rule mining algorithm using

the sales data obtained from a large retailing company.

• There are a total of 46,873 customer transactions in

this data. Each transaction contains the department

numbers from which a customer bought an item in

a visit.

• There are a total of 63 departments. The

algorithm finds if there is an association between

departments in the customer purchasing behavior.

• The following rules were found for a minimum support of 1% and minimum condence of 50%.

• [Tires]  [Automotive Services] (98.80, 5.79)

• [Auto Accessories], [Tires]  [Automotive Services] (98.29, 1.47)

• [Auto Accessories]  [Automotive Services] (79.51, 11.81)

• [Automotive Services]  [Auto Accessories] (71.60, 11.81)

• [Home Laundry Appliances]  [Maintenance Agreement Sales] (66.55, 1.25)

• [Children's Hardlines]  [Infants and Children's wear] (66.15, 4.24)

• [Men's Furnishing]  [Men's Sportswear] (54.86, 5.21)

### Summary

• Apriori, while historically significant, suffers from a number of inefficiencies or trade-offs, which have spawned other algorithms.

• Hash tables: uses a hash tree to store candidate itemsets. This hash tree has item sets at the leaves and at internal nodes

• Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB

• Sampling: mining on a subset of given data, need a lower support threshold + a method to determine the completeness.

### Reference

• R. Agrawal, T. Imielinski, A. Swami: “Mining Associations between Sets of Items in Massive Databases”, Proc. of the ACM SIGMOD Int'l Conference on Management of Data, Washington D.C., May 1993, 207-216.

• http://knight.cis.temple.edu/~vasilis/Courses/CIS664/

• http://en.wikipedia.org/wiki/Apriori_algorithm