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Mining Association Rules between Sets of Items in Large DatabasesPowerPoint Presentation

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 Databases

- Introduction
- Formal Model
- Apriori Algorithm
- Experiments
- Summary

Introduction Databases

- 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 Databases

- 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 Databases

- Let minimum support 50%, and minimum confidence 50%, we have
- A C (50%, 66.6%)
- C A (50%, 100%)

Apriori Algorithm Databases

- 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

Experiments Databases

- 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 and minimum condence of 50%.

- 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 and minimum condence of 50%.

- 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

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