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Association Rule Mining - MaxMiner
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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
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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 …
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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
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Maximal Frequent Itemset Border Infrequent Itemsets Maximal Itemsets An itemset is maximal frequent if none of its immediate supersets is frequent
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Closed Itemset An itemset is closed if none of its immediate supersets has the same support as the itemset
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Maximal vs Closed Itemsets Transaction Ids Not supported by any transactions
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Maximal vs Closed Frequent Itemsets Minimum support = 2 # Closed = 9 # Maximal = 4 Closed and maximal Closed but not maximal
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Maximal vs Closed Itemsets
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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 ()
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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 ()
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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 it(N), h(N){i} is NOT frequent, remove i from t(N) before expanding N. Apply global pruning techniques … (ABCD)
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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 ()
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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)
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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
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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
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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
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