1. 1 ACCTG 6910 Building Enterprise & Business Intelligence Systems (e.bis) Association Rule Mining Olivia R. Liu Sheng, Ph.D. Emma Eccles Jones Presidential Chair of Business

2. 2 Main Expectations Knowledge pattern in focus Definitions and examples A basic method How to tune the method Decision support applications When to use association rule mining Reading – T2, pp. 225 - 236

3. 3 Association Under a given condition, a set of objects  (implies) another set of objects Examples Retail items purchased together Services subscribed by the same customer Web pages a user access in a session Courses taken by the same student Medications prescribed by a doctor for a patient visit Genes that are expressed at the same level

4. 4 Decision Support Applications Customer relationship management Retail merchandise placement Online retail catalog design Website link re-organization Fraud detection Gene analysis for cancer prevention

5. 5 Preliminary Set Theory –A set is a collection of objects. E.g., set A = {3,5} and set B= {1,3,5} –Elements of a set are the objects belong to it. E.g., 3 {3,5}, 3 {1,3,5}, 3 A and 3 B –Set X is a subset of set Y if any element in X belongs to Y, denoted as X Y. E.g., A B or {3,5} {1,3,5}

6. 6 Preliminary Two properties of set –An element in a set is counted only once E.g., {1,3,5} = {1,3,3,5} –There is no order of elements in a set E.g., {3,1,5} = {1,3,5}

7. 7 Association Rules Given: A database of transactions Example of transactions: a customer’s visit to a grocery store an online purchase at a virtual store such as ‘Amazon.com’ Format of transactions: datetransaction IDcustomer IDItem 1/1/99001001egg 1/1/99001001milk

8. 8 Association Rules Find: patterns in the form of association rules Association rules : correlate the presence of one set of items (X) with the presence of another set of items (Y), denoted as X  Y Example : {purchase egg,milk}  {bread} How to measure correlations in association rules?

9. 9 Association Rules Itemset: a set of items, ex. {egg, milk} Size of Itemset: number of items in that itemset. The ratio of the number of transactions that purchases all items in an itemset to the total number of transactions is called the support of the itemset.

10. 10 Association Rules Example: TIDCIDItem PriceDate 101201Computer15001/4/99 101201MS Office3001/4/99 101201MCSE Book1001/4/99 102201Hard disk5001/8/99 102201MCSE Book1001/8/99 103202Computer15001/21/99 103202Hard disk5001/2199 103202MCSE Book1001/2199

11. 11 Association Rules In this example: The support of the 2-itemset {Computer,Hard disk} is 1/3=33.3%. What is the support of 1-itemset {Computer}?

12. 12 Association Rules Two important metrics for association rules: If two itemsets X and Y co-exist in a transaction database, the association rule X  Y holds with supports s which is the ratio of the # of transactions purchasing both X and Y to (÷) the total # of transactions confidence c which is the ratio of the # of transactions purchasing both X and Y to (÷) the # of transactions purchasing X only.

13. 13 Association Rules Association rule: {Computer}  {Hard disk} Support: 1/3=33.3% Confidence: 1/2=50% How about {Computer}  {MCSE book} {Computer, MCSE book}  {Hard disk}???

14. 14 Association Rule Mining Association rule mining: find all association rules with support no less than user-specified minimum support and confidence no less than user-specified minimum confidence in a database For small problems, the process of mining association rules is not that complex. How about a transaction database with 1billion transactions and 1million different items? An efficient algorithm is needed!

15. 15 Association Rules Two Steps in Association rule mining: 1. Find all large or frequent itemsets that have support above user-specified minimum support. 2.For each large itemset L, find all association rules in the form of a  (L-a) where a and (L-a) are non-empty subsets of L. Example: find all association rules in the example with minimum support 60% and minimum confidence 80%.

16. 16 Association Rule Mining Step 2 is trivial compared to step 1: Exponential search space Size of transaction database

17. 17 Apriori Algorithm Apriori is an efficient algorithm to discover all large itemsets from a huge database with large number of items. Apriori is developed by two researchers from IBM Almaden Research Lab.

18. 18 Apriori Algorithm Apriori algorithm is based on Apriori property. Apriori property is that any subset of a large itemset must be large.

19. 19 Apriori Algorithm Step 1: Scan DB one time to find all large 1- itemsets. Step 2: Generate candidate K-itemsets from large (k-1)-itemsets. Step 3: Find all large k-itemsets from candidate k-itemsets by scanning DB once Go back to step 2 and stop until no cadidate itemsets can be generated.

20. 20 Apriori Algorithm Step 2 –Candidate k-itemsets are k-itemsets that could be large. –Why generate candidate k-itemsets only from large (k-1) itemsets? –How to generate? Step 2-1: Join: Two large (k-1)-itemsets, L1 amd L2, that are joinable must satisfy the following conditions: –L1(1)=L2(1) and L1(2)=L2(2) and …. L1(K-2)=L2(K-2) –L1(K-1)<L2(K-1) Step 2-2: Prune: prune itemsets generated in step 2-1 that have subset not large.

21. 21 Apriori Algorithm Minimum support =40% Minimum confidence =70% Transaction IDItems 1001,3,4,6 2002,3,5,7 3001,2,3,5,8 4002,5,9,10 5001,4

22. 22 Association Rule Mining Large 1-itemset: {1}support=3/5=60% {2} support=3/5=60% {3}support=3/5=60% {4}support=2/5=40% {5}support=3/5=60% Tid items 1001, 3, 4, 6 2002, 3, 5, 7 3001, 2, 3, 5, 8 400 2, 5, 9, 10 500 1, 4 Minimum Support: 40%

23. 23 Association Rule Mining Large 1-itemset: {1}support=3/5=60% {2} support=3/5=60% {3}support=3/5=60% {4}support=2/5=40% {5}support=3/5=60% Candidate 2-itemset: {1, 2}{1, 3}{1, 4}{1, 5} {2, 3}{2, 4}{2, 5} {3, 4}{3, 5} {4, 5}

24. 24 Association Rule Mining Candidate 2-itemset: {1, 2}{1, 3}{1, 4}{1, 5} {2, 3}{2, 4}{2, 5} {3, 4}{3, 5} {4, 5} Large 2-itemset: {1, 3}support=2/5=40% {1, 4} support=2/5=40% {2, 3}support=2/5=40% {2, 5}support=3/5=60% {3, 5}support=2/5=40%

25. 25 Association Rule Mining Candidate 3-itemset: {1, 3, 4} {2, 3, 5} Large 2-itemset: {1, 3}support=2/5=40% {1, 4} support=2/5=40% {2, 3}support=2/5=40% {2, 5}support=3/5=60% {3, 5}support=2/5=40%

26. 26 Association Rule Mining Candidate 3-itemset: {1, 3, 4} {2, 3, 5} Large 3-itemset: {2, 3, 5}support=2/5=40% Candidate 4-itemset: No candidate 4-itemset. Stop.