Mining Association Rules between Sets of Items in Large Databases

1. Mining Association Rules between Sets of Items in Large Databases presented by Zhuang Wang

2. Outline • Introduction • Formal Model • Apriori Algorithm • Experiments • Summary

3. 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)

4. 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)

5. Support and Confidence - Example • Let minimum support 50%, and minimum confidence 50%, we have • A  C (50%, 66.6%) • C  A (50%, 100%)

6. 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

7. Find Frequent Itemsets - Example Database D L1 C1 Scan D C2 C2 L2 Scan D L3 C3 Scan D

8. 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.

9. 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)

10. 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.

11. 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