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Association Rule Mining - MaxMiner

Association Rule Mining - MaxMiner. 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. Max-patterns & Close-patterns.

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Association Rule Mining - MaxMiner

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  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 {a1, …, a100}  (1001) + (1002) + … + (110000) = 2100-1 = 1.27*1030 frequent sub-patterns! • Max-pattern: frequent patterns without proper frequent super pattern • BCDE, ACD are max-patterns • BCD is not a max-pattern Min_sup=2

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

  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 Closed but not maximal Minimum support = 2 Closed and maximal # Closed = 9 # Maximal = 4

  9. Maximal vs Closed Itemsets

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

  11. A (BCD) C (D) D () B (CD) AB (CD) AC (D) AD () BC (D) BD () CD () ABC (C) ABD () ACD () BCD () ABCD () 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)

  12. Algorithm MaxMiner  (ABCD) • 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…

  13. A (BCD) C (D) D () B (CD) AB (CD) AC (D) AD () BC (D) BD () CD () ABC (C) ABD () ACD () BCD () ABCD () 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)

  14. B (CDE) C (DE) D (E) E () A (BCDE) Example  (ABCDEF) Min_sup=2 Max patterns:

  15. AC (D) AD () Example  (ABCDEF) B (CDE) C (DE) D (E) E () A (BCDE) Min_sup=2 Node A Max patterns:

  16. AC (D) AD () BCDE Example  (ABCDEF) B (CDE) C (DE) D (E) E () A (BCDE) Min_sup=2 Node B Max patterns:

  17. ACD Example  (ABCDEF) B (CDE) C (DE) D (E) E () A (BCDE) AC (D) AD () Min_sup=2 Node AC Max patterns: BCDE

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