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 Scan D C1C1 L1L1 L2L2 C2C2 C2C2 C3C3 L3L3

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