Performance and Scalability: Apriori Implementa6on

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Performance and Scalability: Apriori Implementa6on

Apriori R. Agrawal and R. Srikant. Fast algorithms for mining associa6on rules. VLDB, 487 499, 1994

Reducing Number of Comparisons Candidate coun6ng: Scan the database of transac6ons to determine the support of each candidate itemset To reduce the number of comparisons, store the candidates in a hash structure Instead of matching each transac6on against every candidate, match it against candidates contained in the hashed buckets

Generate Hash Tree Suppose you have 15 candidate itemsets of length 3: {1 4 5}, {1 2 4}, {4 5 7}, {1 2 5}, {4 5 8}, {1 5 9}, {1 3 6}, {2 3 4}, {5 6 7}, {3 4 5}, {3 5 6}, {3 5 7}, {6 8 9}, {3 6 7}, {3 6 8} You need: Hash funcdon Max leaf size: max number of itemsets stored in a leaf node (if number of candidate itemsets exceeds max leaf size, split the node) Hash function 3,6,9 1,4,7 2,5,8 1 4 5 1 2 4 4 5 7 1 2 5 4 5 8 2 3 4 5 6 7 3 4 5 3 5 6 1 3 6 3 5 7 6 8 9 1 5 9 3 6 7 3 6 8

Associa6on Rule Discovery: Hash tree Hash Function Candidate Hash Tree 1,4,7 3,6,9 2,5,8 Hash on 1, 4 or 7 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 2 3 4 5 6 7 3 4 5 3 5 6 3 5 7 6 8 9 3 6 7 3 6 8

Associa6on Rule Discovery: Hash tree Hash Function Candidate Hash Tree 1,4,7 3,6,9 2,5,8 Hash on 2, 5 or 8 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 2 3 4 5 6 7 3 4 5 3 5 6 3 5 7 6 8 9 3 6 7 3 6 8

Associa6on Rule Discovery: Hash tree Hash Function Candidate Hash Tree 1,4,7 3,6,9 2,5,8 Hash on 3, 6 or 9 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 2 3 4 5 6 7 3 4 5 3 5 6 3 5 7 6 8 9 3 6 7 3 6 8

Given a transac6on t, what are the possible subsets of size 3? Subset Opera6on

Subset Opera6on Using Hash Tree 1 2 3 5 6 transaction Hash Function 1 + 2 3 5 6 2 + 3 5 6 1,4,7 3,6,9 3 + 5 6 2,5,8 2 3 4 5 6 7 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 3 4 5 3 5 6 3 6 7 3 5 7 3 6 8 6 8 9

Subset Opera6on Using Hash Tree 1 2 3 5 6 transaction Hash Function 1 2 + 1 3 + 3 5 6 5 6 1 + 2 3 5 6 2 + 3 5 6 3 + 5 6 1,4,7 2,5,8 3,6,9 1 5 + 6 2 3 4 5 6 7 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 3 4 5 3 5 6 3 6 7 3 5 7 3 6 8 6 8 9

Subset Opera6on Using Hash Tree 1 2 3 5 6 transaction Hash Function 1 2 + 1 3 + 3 5 6 5 6 1 + 2 3 5 6 2 + 3 5 6 3 + 5 6 1,4,7 2,5,8 3,6,9 1 5 + 6 2 3 4 5 6 7 1 4 5 1 3 6 1 2 4 1 2 5 1 5 9 4 5 7 4 5 8 3 4 5 3 5 6 3 5 7 6 8 9 3 6 7 3 6 8 Match transaction against 11 out of 15 candidates

Prefix Tree Representa6on Efficient ImplementaDons of Apriori and Eclat Chris6an Borgelt., FIMI 03

Prefix Tree

Prefix Tree Structure for Coun6ng

Other key op6miza6on Reordering the items Why is this relevant? Transac6on Tree Organize transac6on into trees Count through two trees

Important websites: FIMI workshop Not only Apriori and FIM FP tree, ECLAT, Closed, Maximal hap://fimi.cs.helsinki.fi/ Chris6an Borgelt s website hap://www.borgelt.net/socware.html Ferenc Bodon s website hap://www.cs.bme.hu/~bodon/en/apriori/

References: Chris6an Borgelt, Efficient Implementa.ons of Apriori and Eclat, FIMI 03 Ferenc Bodon, A fast APRIORI implementa.on, FIMI 03 Ferenc Bodon, A Survey on Frequent Itemset Mining, Technical Report, Budapest University of Technology and Economic, 2006

Scalability How to handle very large dataset? The dataset can not be stored in the main memory Performance of out of core datasets/ Performance of in core datasets

Par66on: Scan Database Only Twice Any itemset that is poten6ally frequent in DB must be frequent in at least one of the par66ons of DB Scan 1: par66on database and find local frequent paaerns Scan 2: consolidate global frequent paaerns A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining associa6on in large databases. In VLDB 95

DHP: Reduce the Number of Candidates A k itemset whose corresponding hashing bucket count is below the threshold cannot be frequent Candidates: a, b, c, d, e Hash entries: {ab, ad, ae} {bd, be, de} Frequent 1 itemset: a, b, d, e ab is not a candidate 2 itemset if the sum of count of {ab, ad, ae} is below support threshold J. Park, M. Chen, and P. Yu. An effec6ve hash based algorithm for mining associa6on rules. In SIGMOD 95

Sampling for Frequent Paaerns Select a sample of original database, mine frequent paaerns within sample using Apriori Scan database once to verify frequent itemsets found in sample, only borders of closure of frequent paaerns are checked Example: check abcd instead of ab, ac,, etc. Scan database again to find missed frequent paaerns H. Toivonen. Sampling large databases for associa6on rules. In VLDB 96

DIC: Reduce Number of Scans ABCD ABC ABD ACD BCD AB AC BC AD BD CD A B C D {} Itemset lattice S. Brin R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket data. In SIGMOD 97 Apriori DIC Once both A and D are determined frequent, the coun6ng of AD begins Once all length 2 subsets of BCD are determined frequent, the coun6ng of BCD begins Transactions 1-itemsets 2-itemsets 1-itemsets 2-items 3-items

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