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The AIM-F Algorithm review

The AIM-F Algorithm review. Presented by Sagi Shporer. Frequent Itemset Problem. Let I={i 1 ,i 2 ,…,i m } be a set of items Let T I be a transaction Let D be a dataset of n transactions.

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The AIM-F Algorithm review

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  1. The AIM-F Algorithm review Presented by Sagi Shporer

  2. Frequent Itemset Problem • Let I={i1,i2,…,im} be a set of items • Let TI be a transaction • Let D be a dataset of n transactions. • Task: Find all X  I s.t. support(X)≥minsupport (e.g. there are at least minsupport transactions for which X T).

  3. Dataset id: item set 1: a b c d e 2: a b c d 3: b c d 4: b e 5: c d e MinSup=2 Example – Frequent Itemsets What itemsets are frequent itemsets (FI)? a, b, c, d, e, ab, ac, ad, bc, bd, be, cd, ce, de, abc, abd, acd, bcd, cde, abcd

  4. Previous research work • Candidate set generate-and-test approach • Apriori, VLDB 94, R. Agrawal. • Sampling technique • H. Toivonen • Adaptive Support • SLPMiner, ICDM 2002, M. Seno & G. Karypis • Data transform • FP-tree, SIGMOD 2000, J. Han.

  5. General • Goal : Mining Frequent Itemsets • Main features: • DFS generate-and-test • Compressed vertical database • Diffsets • PEP • Dynamic reordering • Vector projection • Optimized Initialization

  6. :abcde a:bcde b:cde c:de d:e e: ab:cde ac:de ad:e ae: bc:de bd:e be: cd:e ce: de: abc:de abd:e abe: acd:e ace: ade: bcd:e bce: bde: cde: abcd:e abce: abde: acde: bcde: Cut abcde: Enumeration tree

  7. Pruning - PEP

  8. FI Dataset |D|=5 2 4 4 4 3 id: item set abcd: :a b c d e 1: a b c d e 2: a b c d 3: b c d 4: b e 5: c d e eb: :a e b c d ecd: |Da|=2 1 2 2 2 |De|=3 2 2 2 a: e b c d c: d d: e: b c d ed: ec: d eb: c d b: c d e: b c d MinSup=2 |Deb|=2 1 1 |Dec|=2 2 eb: ecd: An Example (Illustration only) abcd:

  9. Diffsets • Let t(P) be the set of transactions (TIDs) supporting P. • Define diffset d(PX)=t(P)\t(X) • Then support(PX)=support(P)-|d(PX)| Amir Epstein

  10. Diffsets • How to Calculate support(PXY) using d(PX) and d(PY) ? • support(PXY)=support(PX)-|d(PXY)| • d(PXY)=d(PY) - d(PX) Amir Epstein

  11. Example t(X) t(P) t(Y) d(PY) d(PX) d(PXY) t(PXY) Amir Epstein

  12. Contributions • Dynamical use of various itemset mining optimizations (Specifically diffsets). • Use of compressed vertical bit vector with diffsets.

  13. Dynamic Optimization Usage • Every optimization has strengths and weaknesses. • Optimizations should be used only when they give some benefit.

  14. Dynamic Optimization Usage Cont. • Diffsets – Start using diffsets only when d(PX) < t(PX) • Optimized Initialization – Use only for sparse datasets (when the number of ‘1’s reach a threshold)

  15. Compressed Bit Vector • Sparse Vertical Bit Vector – Hold only the needed cells in the vertical bit vector

  16. Compressed Bit Vector Cont. • Use of diffsets directly from the compressed form • Faster than tid-list for dense datasets. • Competitive with tid-list for sparse datasets

  17. Optimization Contributions

  18. Questions & Comments THANK YOU !

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