1. Association Rule Mining - MaxMiner

2. Mining Association Rules in Large Databases  Association rule mining  Algorithms Apriori and FP-Growth  Max and closed patterns  Mining various kinds of association/correlation rules

3. Max-patterns & Close-patterns  If there are frequent patterns with many items, enumerating all of them is costly.  We may be interested in finding the ‘ boundary ’ frequent patterns.  Two types …

4. Max-patterns  Frequent pattern {a 1, …, a 100 }  ( 100 1 ) + ( 100 2 ) + … + ( 1 1 0 0 0 0 ) = 2 100 -1 = 1.27*10 30 frequent sub-patterns!  Max-pattern: frequent patterns without proper frequent super pattern BCDE, ACD are max-patterns BCD is not a max-pattern TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F Min_sup=2

5. Maximal Frequent Itemset Border Infrequent Itemsets Maximal Itemsets An itemset is maximal frequent if none of its immediate supersets is frequent

6. Closed Itemset  An itemset is closed if none of its immediate supersets has the same support as the itemset

7. Maximal vs Closed Itemsets Transaction Ids Not supported by any transactions

8. Maximal vs Closed Frequent Itemsets Minimum support = 2 # Closed = 9 # Maximal = 4 Closed and maximal Closed but not maximal

9. Maximal vs Closed Itemsets

10. MaxMiner: Mining Max-patterns  Idea: generate the complete set- enumeration tree one level at a time, while prune if applicable.  (ABCD) A (BCD) B (CD) C (D)D () AB (CD)AC (D)AD () BC (D)BD () CD ()ABC (C) ABCD () ABD ()ACD ()BCD ()

11. Local Pruning Techniques (e.g. at node A) Check the frequency of ABCD and AB, AC, AD.  If ABCD is frequent, prune the whole sub-tree.  If AC is NOT frequent, remove C from the parenthesis before expanding.  (ABCD) A (BCD) B (CD) C (D)D () AB (CD)AC (D)AD () BC (D)BD () CD ()ABC (C) ABCD () ABD ()ACD ()BCD ()

12. Algorithm MaxMiner  Initially, generate one node N=, where h(N)= and t(N)={A,B,C,D}.  Consider expanding N, If h(N)t(N) is frequent, do not expand N. If for some it(N), h(N){i} is NOT frequent, remove i from t(N) before expanding N.  Apply global pruning techniques …  (ABCD)

13. Global Pruning Technique (across sub-trees)  When a max pattern is identified (e.g. ABCD), prune all nodes (e.g. B, C and D) where h(N)t(N) is a sub-set of it (e.g. ABCD).  (ABCD) A (BCD) B (CD) C (D)D () AB (CD)AC (D)AD () BC (D)BD () CD ()ABC (C) ABCD () ABD ()ACD ()BCD ()

14. Example TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F  (ABCDEF) ItemsFrequency ABCDEF0 A2 B2 C3 D3 E2 F1 Min_sup=2 Max patterns: A (BCDE) B (CDE)C (DE)E ()D (E)

15. Example TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F  (ABCDEF) ItemsFrequency ABCDE1 AB1 AC2 AD2 AE1 Min_sup=2 A (BCDE) B (CDE)C (DE)E ()D (E) AC (D)AD () Max patterns: Node A

16. Example TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F  (ABCDEF) ItemsFrequency BCDE2 BC BD BE Min_sup=2 A (BCDE) B (CDE)C (DE)E ()D (E) AC (D)AD () Max patterns: BCDE Node B

17. Example TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F  (ABCDEF) ItemsFrequency ACD2 Min_sup=2 A (BCDE) B (CDE)C (DE)E ()D (E) AC (D)AD () Max patterns: BCDE ACD Node AC