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This chapter from the book 'data mining: concepts and techniques' by jiawei han explores the concepts and techniques of mining frequent patterns and association rules. The basics of frequent patterns and association rules, closed patterns and max-patterns, scalable methods for mining frequent patterns, pruning, generating candidates, partitioning patterns and databases, recursion, mining frequent patterns with fp-trees, visualization of association rules, system optimization, and constraints in data mining.
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Jiawei Han Department of Computer Science University of Illinois at Urbana-Champaign www.cs.uiuc.edu/~hanj ©2006 Jiawei Han and Micheline Kamber, All rights reserved Revised by Zhongfei (Mark) Zhang Department of Computer Science SUNY Binghamton
Chapter 5: Mining Frequent Patterns, Association and Correlations
Why Is Freq. Pattern Mining Important? (^) Discloses an intrinsic and important property of data sets (^) Forms the foundation for many essential data mining tasks (^) Association, correlation, and causality analysis (^) Sequential, structural (e.g., sub-graph) patterns (^) Pattern analysis in spatiotemporal, multimedia, time- series, and stream data (^) Classification: associative classification (^) Cluster analysis: frequent pattern-based clustering (^) Data warehousing: iceberg cube and cube-gradient (^) Semantic data compression: fascicles (^) Broad applications
Basic Concepts: Frequent Patterns and Association Rules (^) Itemset X = {x 1 , …, xk} (^) Find all the rules X Y with minimum support and confidence
transaction contains X ∪ Y
probability that a transaction
Let supmin = 50%, confmin = 50% Freq. Pat.: {A:3, B:3, D:4, E:3, AD:3} Association rules: A D (60%, 100%) D A (60%, 75%) Customer buys diaper Customer buys both Customer buys beer 40 B, E, F 50 B, C, D, E, F 30 A, D, E 20 A, C, D 10 A, B, D Transaction-id Items bought
Closed Patterns and Max-Patterns
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Chapter 5: Mining Frequent Patterns, Association and Correlations
(^) Apriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! (Agrawal & Srikant @VLDB’94, Mannila, et al. @ KDD’ 94) (^) Method: Initially, scan DB once to get frequent 1-itemset (^) Generate length (k+1) candidate itemsets from length k frequent itemsets (^) Test the candidates against DB (^) Terminate when no frequent or candidate set can be generated
The Apriori Algorithm—An Example Database TDB 1 st scan
1
1 L 2
nd scan C 3
3 rd^ scan^3 40 B, E 30 A, B, C, E 20 B, C, E 10 A, C, D Tid Items {D} 1 {E} 3 {C} 3 {B} 3 {A} 2 Itemset sup {E} 3 {C} 3 {B} 3 {A} 2 Itemset sup {C, E} {B, E} {B, C} {A, E} {A, C} {A, B} Itemset {A, B} 1 {A, C} 2 {A, E} 1 {B, C} 2 {B, E} 3 {C, E} 2 Itemset sup {A, C} 2 {B, C} 2 {B, E} 3 {C, E} 2 Itemset sup {B, C, E} Itemset {B, C, E} 2 Itemset sup Sup min
Important Details of Apriori (^) How to generate candidates? (^) Step 1: self-joining L k (^) Step 2: pruning (^) How to count supports of candidates? (^) Example of Candidate-generation L 3 ={abc, abd, acd, ace, bcd} (^) Self-joining: L 3 *L 3 abcd from abc and abd acde from acd and ace (^) Pruning: acde is removed because ade is not in L 3 C 4 ={abcd}
How to Generate Candidates?
k- are listed in an order
k- insert into Ck select p.item 1 , p.item 2 , …, p.itemk-1, q.itemk- from Lk-1 p, Lk-1 q where p.item 1 =q.item 1 , …, p.itemk-2=q.itemk-2, p.itemk-1 < q.itemk- (^) Step 2: pruning forall itemsets c in Ck do forall (k-1)-subsets s of c do if (s is not in L k- ) then delete c from C k
Partition: Scan Database Only Twice (^) Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB (^) Scan 1: partition database and find local frequent patterns (^) Scan 2: consolidate global frequent patterns (^) A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association in large databases. In
DIC: Reduce Number of Scans ABCD ABC ABD ACD BCD AB AC BC AD BD CD A B^ C^ D {} Itemset lattice (^) Once both A and D are determined frequent, the counting of AD begins (^) Once all length-2 subsets of BCD are determined frequent, the counting of BCD begins Transactions 1-itemsets 2-itemsets … Apriori 1-itemsets 2-items DIC 3-items S. Brin R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket data. In SIGMOD’
Mining Frequent Patterns Without Candidate Generation
Construct FP-tree from a Transaction Database {} f:4 c: b: p: c:3 b: a: m:2 b: p:2 m: Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 min_support = 3 TID Items bought (ordered) frequent items 100 { f, a, c, d, g, i, m, p } { f, c, a, m, p } 200 { a, b, c, f, l, m, o } { f, c, a, b, m } 300 { b, f, h, j, o, w } { f, b } 400 { b, c, k, s, p } { c, b, p } 500 { a, f, c, e, l, p, m, n } { f, c, a, m, p }
