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September 2, 2014Data Mining: Concepts and Techniques1 Association Rule Mining

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September 2, 2014Data Mining: Concepts and Techniques2 Chapter 5: Mining Frequent Patterns, Association and Correlations Basic concepts and a road map Efficient and scalable frequent itemset mining methods Mining various kinds of association rules From association mining to correlation analysis Constraint-based association mining Summary

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September 2, 2014Data Mining: Concepts and Techniques3 What Is Frequent Pattern Analysis? Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule mining Motivation: Finding inherent regularities in data What products were often purchased together?— Beer and diapers?! What are the subsequent purchases after buying a PC? What kinds of DNA are sensitive to this new drug? Can we automatically classify web documents? Applications Basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis.

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September 2, 2014Data Mining: Concepts and Techniques4 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

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September 2, 2014Data Mining: Concepts and Techniques5 Basic Concepts: Frequent Patterns and Association Rules Itemset X = {x 1, …, x k } Find all the rules X Y with minimum support and confidence support, s, probability that a transaction contains X Y confidence, c, conditional probability that a transaction having X also contains Y Let sup min = 50%, conf min = 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 Transaction-idItems bought 10A, B, D 20A, C, D 30A, D, E 40B, E, F 50B, C, D, E, F

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September 2, 2014Data Mining: Concepts and Techniques6 Closed Patterns and Max-Patterns A long pattern contains a combinatorial number of sub- patterns, e.g., {a 1, …, a 100 } contains ( 100 1 ) + ( 100 2 ) + … + ( 1 1 0 0 0 0 ) = 2 100 – 1 = 1.27*10 30 sub-patterns! Solution: Mine closed patterns and max-patterns instead An itemset X is closed if X is frequent and there exists no super-pattern Y כ X, with the same support as X (proposed by Pasquier, et al. @ ICDT’99) An itemset X is a max-pattern if X is frequent and there exists no frequent super-pattern Y כ X (proposed by Bayardo @ SIGMOD’98) Closed pattern is a lossless compression of freq. patterns Reducing the # of patterns and rules

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Given a database D we wish to find all the frequent itemsets (F) and then use this knowledge to produce high confidence association rules. Note: Finding F is the most computationally expensive part, once we have the frequent sets generating ARs is straight forward ARM Problem Definition

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a 6 b6 ab3 c6 ac3 bc3 abc1 d6 ad6 bd3 abd1 cd3 acd1 bcd1 abcd0 e6 ae3 be3 abe1 ce3 ace1 bce1 abce0 de3 ade1 bde1 abde0 cde1 acde0 bcde0 abcde0 List all possible combinations in an array. For each record: 1.Find all combinations. 2.For each combination index into array and increment support by 1. Then generate rules BRUTE FORCE

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a 6 b6 ab3 c6 ac3 bc3 abc1 d6 ad6 bd3 abd1 cd3 acd1 bcd1 abcd0 e6 ae3 be3 abe1 ce3 ace1 bce1 abce0 de3 ade1 bde1 abde0 cde1 acde0 bcde0 abcde0 Support threshold = 5% (count of 1.55) Frequents Sets ( F ): ab(3) ac(3) bc(3) ad(3) bd(3) cd(3) ae(3) be(3) ce(3) de(3) Rules: a b conf=3/6=50% b a conf=3/6=50% Etc.

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Advantages: 1)Very efficient for data sets with small numbers of attributes (<20). Disadvantages: 1)Given 20 attributes, number of combinations is 2 20 -1 = 1048576. Therefore array storage requirements will be 4.2MB. 2)Given a data sets with (say) 100 attributes it is likely that many combinations will not be present in the data set --- therefore store only those combinations present in the dataset! BRUTE FORCE

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September 2, 2014Data Mining: Concepts and Techniques11 Chapter 5: Mining Frequent Patterns, Association and Correlations Basic concepts and a road map Efficient and scalable frequent itemset mining methods Mining various kinds of association rules From association mining to correlation analysis Constraint-based association mining Summary

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September 2, 2014Data Mining: Concepts and Techniques12 Scalable Methods for Mining Frequent Patterns The downward closure property of frequent patterns Any subset of a frequent itemset must be frequent If {beer, diaper, nuts} is frequent, so is {beer, diaper} i.e., every transaction having {beer, diaper, nuts} also contains {beer, diaper} Scalable mining methods: Three major approaches Apriori (Agrawal & Srikant@VLDB’94) Freq. pattern growth (FPgrowth—Han, Pei & Yin @SIGMOD’00) Vertical data format approach (Charm—Zaki & Hsiao @SDM’02)

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September 2, 2014Data Mining: Concepts and Techniques13 Apriori: A Candidate Generation-and-Test Approach 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

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September 2, 2014Data Mining: Concepts and Techniques14 The Apriori Algorithm—An Example Database TDB 1 st scan C1C1 L1L1 L2L2 C2C2 C2C2 2 nd scan C3C3 L3L3 3 rd scan TidItems 10A, C, D 20B, C, E 30A, B, C, E 40B, E Itemsetsup {A}2 {B}3 {C}3 {D}1 {E}3 Itemsetsup {A}2 {B}3 {C}3 {E}3 Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} Itemsetsup {A, B}1 {A, C}2 {A, E}1 {B, C}2 {B, E}3 {C, E}2 Itemsetsup {A, C}2 {B, C}2 {B, E}3 {C, E}2 Itemset {B, C, E} Itemsetsup {B, C, E}2 Sup min = 2

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September 2, 2014Data Mining: Concepts and Techniques15 The Apriori Algorithm Pseudo-code: C k : Candidate itemset of size k L k : frequent itemset of size k L 1 = {frequent items}; for (k = 1; L k != ; k++) do begin C k+1 = candidates generated from L k ; for each transaction t in database do increment the count of all candidates in C k+1 that are contained in t L k+1 = candidates in C k+1 with min_support end return k L k ;

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September 2, 2014Data Mining: Concepts and Techniques16 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}

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September 2, 2014Data Mining: Concepts and Techniques17 Sampling for Frequent Patterns Select a sample of original database, mine frequent patterns within sample using Apriori Scan database once to verify frequent itemsets found in sample, only borders of closure of frequent patterns are checked Example: check abcd instead of ab, ac, …, etc. Scan database again to find missed frequent patterns H. Toivonen. Sampling large databases for association rules. In VLDB’96

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September 2, 2014Data Mining: Concepts and Techniques18 DIC: Reduce Number of Scans ABCD ABC ABDACD BCD ABACBC AD BDCD A BCD {} 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 3-itemsDIC S. Brin R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket data. In SIGMOD’97

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September 2, 2014Data Mining: Concepts and Techniques19 Bottleneck of Frequent-pattern Mining Multiple database scans are costly Mining long patterns needs many passes of scanning and generates lots of candidates To find frequent itemset i 1 i 2 …i 100 # of scans: 100 # of Candidates: ( 100 1 ) + ( 100 2 ) + … + ( 1 1 0 0 0 0 ) = 2 100 - 1 = 1.27*10 30 ! Bottleneck: candidate-generation-and-test Can we avoid candidate generation?

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September 2, 2014Data Mining: Concepts and Techniques20 Mining Frequent Patterns Without Candidate Generation Grow long patterns from short ones using local frequent items “abc” is a frequent pattern Get all transactions having “abc”: DB|abc “d” is a local frequent item in DB|abc abcd is a frequent pattern

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September 2, 2014Data Mining: Concepts and Techniques21 Construct FP-tree from a Transaction Database {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3 min_support = 3 TIDItems 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} 1.Scan DB once, find frequent 1-itemset (single item pattern) 2.Sort frequent items in frequency descending order, f-list 3.Scan DB again, construct FP-tree F-list=f-c-a-b-m-p

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September 2, 2014Data Mining: Concepts and Techniques22 Benefits of the FP-tree Structure Completeness Preserve complete information for frequent pattern mining Never break a long pattern of any transaction Compactness Reduce irrelevant info—infrequent items are gone Items in frequency descending order: the more frequently occurring, the more likely to be shared

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September 2, 2014Data Mining: Concepts and Techniques23 Find Patterns Having P From P-conditional Database Starting at the frequent item header table in the FP-tree Traverse the FP-tree by following the link of each frequent item p Accumulate all of transformed prefix paths of item p to form p’s conditional pattern base Conditional pattern bases itemcond. pattern base cf:3 afc:3 bfca:1, f:1, c:1 mfca:2, fcab:1 pfcam:2, cb:1 {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3

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September 2, 2014Data Mining: Concepts and Techniques24 From Conditional Pattern-bases to Conditional FP-trees For each pattern-base Accumulate the count for each item in the base Construct the FP-tree for the frequent items of the pattern base m-conditional pattern base: fca:2, fcab:1 {} f:3 c:3 a:3 m-conditional FP-tree All frequent patterns relate to m m, fm, cm, am, fcm, fam, cam, fcam {} f:4c:1 b:1 p:1 b:1c:3 a:3 b:1m:2 p:2m:1 Header Table Item frequency head f4 c4 a3 b3 m3 p3

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September 2, 2014Data Mining: Concepts and Techniques25 Recursion: Mining Each Conditional FP-tree {} f:3 c:3 a:3 m-conditional FP-tree Cond. pattern base of “am”: (fc:3) {} f:3 c:3 am-conditional FP-tree Cond. pattern base of “cm”: (f:3) {} f:3 cm-conditional FP-tree Cond. pattern base of “cam”: (f:3) {} f:3 cam-conditional FP-tree

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26 Mining Frequent Patterns by Creating Conditional Pattern-Bases Empty f {(f:3)}|c{(f:3)}c {(f:3, c:3)}|a{(fc:3)}a Empty{(fca:1), (f:1), (c:1)}b {(f:3, c:3, a:3)}|m{(fca:2), (fcab:1)}m {(c:3)}|p{(fcam:2), (cb:1)}p Conditional FP-treeConditional pattern-base Item

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27 Single FP-tree Path Generation Suppose an FP-tree T has a single path P The complete set of frequent pattern of T can be generated by enumeration of all the combinations of the sub-paths of P {} f:3 c:3 a:3 m-conditional FP-tree All frequent patterns concerning m m, fm, cm, am, fcm, fam, cam, fcam

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September 2, 2014Data Mining: Concepts and Techniques28 A Special Case: Single Prefix Path in FP-tree Suppose a (conditional) FP-tree T has a shared single prefix-path P Mining can be decomposed into two parts Reduction of the single prefix path into one node Concatenation of the mining results of the two parts a 2 :n 2 a 3 :n 3 a 1 :n 1 {} b 1 :m 1 C 1 :k 1 C 2 :k 2 C 3 :k 3 b 1 :m 1 C 1 :k 1 C 2 :k 2 C 3 :k 3 r1r1 + a 2 :n 2 a 3 :n 3 a 1 :n 1 {} r1r1 =

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September 2, 2014Data Mining: Concepts and Techniques29 Mining Frequent Patterns With FP-trees Idea: Frequent pattern growth Recursively grow frequent patterns by pattern and database partition Method For each frequent item, construct its conditional pattern-base, and then its conditional FP-tree Repeat the process on each newly created conditional FP-tree Until the resulting FP-tree is empty, or it contains only one path—single path will generate all the combinations of its sub-paths, each of which is a frequent pattern

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September 2, 2014Data Mining: Concepts and Techniques30 FP-Growth vs. Apriori: Scalability With the Support Threshold Data set T25I20D10K

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September 2, 2014Data Mining: Concepts and Techniques31 Why Is FP-Growth the Winner? Divide-and-conquer: decompose both the mining task and DB according to the frequent patterns obtained so far leads to focused search of smaller databases Other factors no candidate generation, no candidate test compressed database: FP-tree structure no repeated scan of entire database basic ops—counting local freq items and building sub FP-tree, no pattern search and matching

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32 null A:7 B:5 B:3 C:3 D:1 C:1 D:1 C:3 D:1 E:1 Pointers are used to assist frequent itemset generation D:1 E:1 Transaction Database Header table Frequent Itemset Using FP-Growth (Example)

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33 null A:7 B:5 B:3 C:3 D:1 C:1 D:1 C:3 D:1 E:1 D:1 E:1 Build conditional pattern base for E: P = {(A:1,C:1,D:1), (A:1,D:1), (B:1,C:1)} Recursively apply FP-growth on P E:1 D:1 FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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34 Frequent Itemset Using FP-Growth (Example)

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35 null A:2 B:1 C:1 D:1 E:1 Conditional Pattern base for E: P = {(A:1,C:1,D:1,E:1), (A:1,D:1,E:1), (B:1,C:1,E:1)} Count for E is 3: {E} is frequent itemset Recursively apply FP-growth on P ( Conditional tree for D within conditional tree for E) E:1 Conditional tree for E: FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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36 Frequent Itemset Using FP-Growth (Example)

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37 Conditional pattern base for D within conditional base for E: P = {(A:1,C:1,D:1), (A:1,D:1)} Count for D is 2: {D,E} is frequent itemset Recursively apply FP-growth on P (Conditional tree for C within conditional tree D within conditional tree for E) Conditional tree for D within conditional tree for E: null A:2 C:1 D:1 FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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38 Conditional pattern base for C within D within E: P = {(A:1,C:1)} Count for C is 1: {C,D,E} is NOT frequent itemset Recursively apply FP- growth on P (Conditional tree for A within conditional tree D within conditional tree for E) Conditional tree for C within D within E: null A:1 C:1 FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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39 Count for A is 2: {A,D,E} is frequent itemset Next step: Construct conditional tree C within conditional tree E Conditional tree for A within D within E: null A:2 FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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40 null A:2 B:1 C:1 D:1 E:1 Recursively apply FP-growth on P ( Conditional tree for C within conditional tree for E) E:1 Conditional tree for E: FP Growth Algorithm: FP Tree Mining Frequent Itemset Using FP-Growth (Example)

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41 null A:1 B:1 C:1 E:1 FP Growth Algorithm: FP Tree Mining Conditional pattern base for C within conditional base for E: P = {(B:1,C:1), (A:1,C:1) } Count for C is 2: {C,E} is frequent itemset Recursively apply FP-growth on P (Conditional tree for B within conditional tree C within conditional tree for E) Conditional tree for C within conditional tree for E: Frequent Itemset Using FP-Growth (Example)

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September 2, 2014Data Mining: Concepts and Techniques42 Chapter 5: Mining Frequent Patterns, Association and Correlations Basic concepts and a road map Efficient and scalable frequent itemset mining methods Mining various kinds of association rules From association mining to correlation analysis Constraint-based association mining Summary

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September 2, 2014Data Mining: Concepts and Techniques43 Interestingness Measure: Correlations (Lift) play basketball eat cereal [40%, 66.7%] is misleading The overall % of students eating cereal is 75% > 66.7%. play basketball not eat cereal [20%, 33.3%] is more accurate, although with lower support and confidence Measure of dependent/correlated events: lift BasketballNot basketballSum (row) Cereal200017503750 Not cereal10002501250 Sum(col.)300020005000

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September 2, 2014Data Mining: Concepts and Techniques44 Are lift and 2 Good Measures of Correlation? “Buy walnuts buy milk [1%, 80%]” is misleading if 85% of customers buy milk Support and confidence are not good to represent correlations So many interestingness measures? (Tan, Kumar, Sritastava @KDD’02) MilkNo MilkSum (row) Coffeem, c~m, cc No Coffeem, ~c~m, ~c~c Sum(col.)m~m DBm, c~m, cm~c~m~cliftall-confcoh 22 A11000100 10,0009.260.910.839055 A21001000 100,0008.440.090.05670 A3100010010000100,0009.180.09 8172 A41000 10.50.330

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Data Set MCmCMcmcx2LiftAllC onf Coh eren ce Cosi ne KulcMax Conf D110,0 00 1,00 0 100, 000 D210,0 00 1,00 0 100 D31001,00 0 100, 000 D41,00 0 100, 000 D51,00 0 10010,0 000 100, 000 D61,00 0 10100, 000 September 2, 2014Data Mining: Concepts and Techniques45

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September 2, 2014Data Mining: Concepts and Techniques46 Data Set MCmCMcmcx2LiftAllC onf Coh eren ce Cosi ne KulcMax Conf D110,0 00 1,00 0 100, 000 9055 7 9.260.910.830.91 D210,0 00 1,00 0 100010.910.830.91 D31001,00 0 100, 000 6708.440.090.050.09 D41,00 0 100, 000 2474 0 25.7 5 0.50.330.5 D51,00 0 10010,0 000 100, 000 81739.180.09 0.290.50.91 D61,00 0 10100, 000 9651.970.01 0.100.50.99

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September 2, 2014Data Mining: Concepts and Techniques47 Which Measures Should Be Used? lift and 2 are not good measures for correlations in large transactional DBs all-conf or coherence could be good measures (Omiecinski@TKDE’03) Both all-conf and coherence have the downward closure property Efficient algorithms can be derived for mining (Lee et al. @ICDM’03sub)

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September 2, 2014Data Mining: Concepts and Techniques48 Chapter 5: Mining Frequent Patterns, Association and Correlations Basic concepts and a road map Efficient and scalable frequent itemset mining methods Mining various kinds of association rules From association mining to correlation analysis Constraint-based association mining Summary

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September 2, 2014Data Mining: Concepts and Techniques49 Chapter 5: Mining Frequent Patterns, Association and Correlations Basic concepts and a road map Efficient and scalable frequent itemset mining methods Mining various kinds of association rules From association mining to correlation analysis Constraint-based association mining Summary

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September 2, 2014Data Mining: Concepts and Techniques50 Frequent-Pattern Mining: Summary Frequent pattern mining—an important task in data mining Scalable frequent pattern mining methods Apriori (Candidate generation & test) Projection-based (FPgrowth, CLOSET+,...) Vertical format approach (CHARM,...) Mining a variety of rules and interesting patterns Constraint-based mining Mining sequential and structured patterns Extensions and applications

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September 2, 2014Data Mining: Concepts and Techniques51 Frequent-Pattern Mining: Research Problems Mining fault-tolerant frequent, sequential and structured patterns Patterns allows limited faults (insertion, deletion, mutation) Mining truly interesting patterns Surprising, novel, concise, … Application exploration E.g., DNA sequence analysis and bio-pattern classification “Invisible” data mining

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September 2, 2014Data Mining: Concepts and Techniques52 Ref: Basic Concepts of Frequent Pattern Mining (Association Rules) R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. SIGMOD'93. (Max-pattern) R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD'98. (Closed-pattern) N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association rules. ICDT'99. (Sequential pattern) R. Agrawal and R. Srikant. Mining sequential patterns. ICDE'95

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September 2, 2014Data Mining: Concepts and Techniques53 Ref: Apriori and Its Improvements R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB'94. H. Mannila, H. Toivonen, and A. I. Verkamo. Efficient algorithms for discovering association rules. KDD'94. A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association rules in large databases. VLDB'95. J. S. Park, M. S. Chen, and P. S. Yu. An effective hash-based algorithm for mining association rules. SIGMOD'95. H. Toivonen. Sampling large databases for association rules. VLDB'96. S. Brin, R. Motwani, J. D. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket analysis. SIGMOD'97. S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database systems: Alternatives and implications. SIGMOD'98.

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September 2, 2014Data Mining: Concepts and Techniques54 Ref: Depth-First, Projection-Based FP Mining R. Agarwal, C. Aggarwal, and V. V. V. Prasad. A tree projection algorithm for generation of frequent itemsets. J. Parallel and Distributed Computing:02. J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. SIGMOD’ 00. J. Pei, J. Han, and R. Mao. CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets. DMKD'00. J. Liu, Y. Pan, K. Wang, and J. Han. Mining Frequent Item Sets by Opportunistic Projection. KDD'02. J. Han, J. Wang, Y. Lu, and P. Tzvetkov. Mining Top-K Frequent Closed Patterns without Minimum Support. ICDM'02. J. Wang, J. Han, and J. Pei. CLOSET+: Searching for the Best Strategies for Mining Frequent Closed Itemsets. KDD'03. G. Liu, H. Lu, W. Lou, J. X. Yu. On Computing, Storing and Querying Frequent Patterns. KDD'03.

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September 2, 2014Data Mining: Concepts and Techniques55 Ref: Vertical Format and Row Enumeration Methods M. J. Zaki, S. Parthasarathy, M. Ogihara, and W. Li. Parallel algorithm for discovery of association rules. DAMI:97. Zaki and Hsiao. CHARM: An Efficient Algorithm for Closed Itemset Mining, SDM'02. C. Bucila, J. Gehrke, D. Kifer, and W. White. DualMiner: A Dual- Pruning Algorithm for Itemsets with Constraints. KDD’02. F. Pan, G. Cong, A. K. H. Tung, J. Yang, and M. Zaki, CARPENTER: Finding Closed Patterns in Long Biological Datasets. KDD'03.

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September 2, 2014Data Mining: Concepts and Techniques56 Ref: Mining Multi-Level and Quantitative Rules R. Srikant and R. Agrawal. Mining generalized association rules. VLDB'95. J. Han and Y. Fu. Discovery of multiple-level association rules from large databases. VLDB'95. R. Srikant and R. Agrawal. Mining quantitative association rules in large relational tables. SIGMOD'96. T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Data mining using two-dimensional optimized association rules: Scheme, algorithms, and visualization. SIGMOD'96. K. Yoda, T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Computing optimized rectilinear regions for association rules. KDD'97. R.J. Miller and Y. Yang. Association rules over interval data. SIGMOD'97. Y. Aumann and Y. Lindell. A Statistical Theory for Quantitative Association Rules KDD'99.

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September 2, 2014Data Mining: Concepts and Techniques57 Ref: Mining Correlations and Interesting Rules M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A. I. Verkamo. Finding interesting rules from large sets of discovered association rules. CIKM'94. S. Brin, R. Motwani, and C. Silverstein. Beyond market basket: Generalizing association rules to correlations. SIGMOD'97. C. Silverstein, S. Brin, R. Motwani, and J. Ullman. Scalable techniques for mining causal structures. VLDB'98. P.-N. Tan, V. Kumar, and J. Srivastava. Selecting the Right Interestingness Measure for Association Patterns. KDD'02. E. Omiecinski. Alternative Interest Measures for Mining Associations. TKDE’03. Y. K. Lee, W.Y. Kim, Y. D. Cai, and J. Han. CoMine: Efficient Mining of Correlated Patterns. ICDM’03.

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September 2, 2014Data Mining: Concepts and Techniques58 Ref: Mining Other Kinds of Rules R. Meo, G. Psaila, and S. Ceri. A new SQL-like operator for mining association rules. VLDB'96. B. Lent, A. Swami, and J. Widom. Clustering association rules. ICDE'97. A. Savasere, E. Omiecinski, and S. Navathe. Mining for strong negative associations in a large database of customer transactions. ICDE'98. D. Tsur, J. D. Ullman, S. Abitboul, C. Clifton, R. Motwani, and S. Nestorov. Query flocks: A generalization of association-rule mining. SIGMOD'98. F. Korn, A. Labrinidis, Y. Kotidis, and C. Faloutsos. Ratio rules: A new paradigm for fast, quantifiable data mining. VLDB'98. K. Wang, S. Zhou, J. Han. Profit Mining: From Patterns to Actions. EDBT’02.

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September 2, 2014Data Mining: Concepts and Techniques59 Ref: Constraint-Based Pattern Mining R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item constraints. KDD'97. R. Ng, L.V.S. Lakshmanan, J. Han & A. Pang. Exploratory mining and pruning optimizations of constrained association rules. SIGMOD’98. M.N. Garofalakis, R. Rastogi, K. Shim: SPIRIT: Sequential Pattern Mining with Regular Expression Constraints. VLDB’99. G. Grahne, L. Lakshmanan, and X. Wang. Efficient mining of constrained correlated sets. ICDE'00. J. Pei, J. Han, and L. V. S. Lakshmanan. Mining Frequent Itemsets with Convertible Constraints. ICDE'01. J. Pei, J. Han, and W. Wang, Mining Sequential Patterns with Constraints in Large Databases, CIKM'02.

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September 2, 2014Data Mining: Concepts and Techniques60 Ref: Mining Sequential and Structured Patterns R. Srikant and R. Agrawal. Mining sequential patterns: Generalizations and performance improvements. EDBT’96. H. Mannila, H Toivonen, and A. I. Verkamo. Discovery of frequent episodes in event sequences. DAMI:97. M. Zaki. SPADE: An Efficient Algorithm for Mining Frequent Sequences. Machine Learning:01. J. Pei, J. Han, H. Pinto, Q. Chen, U. Dayal, and M.-C. Hsu. PrefixSpan: Mining Sequential Patterns Efficiently by Prefix-Projected Pattern Growth. ICDE'01. M. Kuramochi and G. Karypis. Frequent Subgraph Discovery. ICDM'01. X. Yan, J. Han, and R. Afshar. CloSpan: Mining Closed Sequential Patterns in Large Datasets. SDM'03. X. Yan and J. Han. CloseGraph: Mining Closed Frequent Graph Patterns. KDD'03.

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September 2, 2014Data Mining: Concepts and Techniques61 Ref: Mining Spatial, Multimedia, and Web Data K. Koperski and J. Han, Discovery of Spatial Association Rules in Geographic Information Databases, SSD’95. O. R. Zaiane, M. Xin, J. Han, Discovering Web Access Patterns and Trends by Applying OLAP and Data Mining Technology on Web Logs. ADL'98. O. R. Zaiane, J. Han, and H. Zhu, Mining Recurrent Items in Multimedia with Progressive Resolution Refinement. ICDE'00. D. Gunopulos and I. Tsoukatos. Efficient Mining of Spatiotemporal Patterns. SSTD'01.

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September 2, 2014Data Mining: Concepts and Techniques62 Ref: Mining Frequent Patterns in Time-Series Data B. Ozden, S. Ramaswamy, and A. Silberschatz. Cyclic association rules. ICDE'98. J. Han, G. Dong and Y. Yin, Efficient Mining of Partial Periodic Patterns in Time Series Database, ICDE'99. H. Lu, L. Feng, and J. Han. Beyond Intra-Transaction Association Analysis: Mining Multi-Dimensional Inter-Transaction Association Rules. TOIS:00. B.-K. Yi, N. Sidiropoulos, T. Johnson, H. V. Jagadish, C. Faloutsos, and A. Biliris. Online Data Mining for Co-Evolving Time Sequences. ICDE'00. W. Wang, J. Yang, R. Muntz. TAR: Temporal Association Rules on Evolving Numerical Attributes. ICDE’01. J. Yang, W. Wang, P. S. Yu. Mining Asynchronous Periodic Patterns in Time Series Data. TKDE’03.

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September 2, 2014Data Mining: Concepts and Techniques63 Ref: Iceberg Cube and Cube Computation S. Agarwal, R. Agrawal, P. M. Deshpande, A. Gupta, J. F. Naughton, R. Ramakrishnan, and S. Sarawagi. On the computation of multidimensional aggregates. VLDB'96. Y. Zhao, P. M. Deshpande, and J. F. Naughton. An array-based algorithm for simultaneous multidi-mensional aggregates. SIGMOD'97. J. Gray, et al. Data cube: A relational aggregation operator generalizing group-by, cross-tab and sub-totals. DAMI: 97. M. Fang, N. Shivakumar, H. Garcia-Molina, R. Motwani, and J. D. Ullman. Computing iceberg queries efficiently. VLDB'98. S. Sarawagi, R. Agrawal, and N. Megiddo. Discovery-driven exploration of OLAP data cubes. EDBT'98. K. Beyer and R. Ramakrishnan. Bottom-up computation of sparse and iceberg cubes. SIGMOD'99.

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September 2, 2014Data Mining: Concepts and Techniques64 Ref: Iceberg Cube and Cube Exploration J. Han, J. Pei, G. Dong, and K. Wang, Computing Iceberg Data Cubes with Complex Measures. SIGMOD’ 01. W. Wang, H. Lu, J. Feng, and J. X. Yu. Condensed Cube: An Effective Approach to Reducing Data Cube Size. ICDE'02. G. Dong, J. Han, J. Lam, J. Pei, and K. Wang. Mining Multi- Dimensional Constrained Gradients in Data Cubes. VLDB'01. T. Imielinski, L. Khachiyan, and A. Abdulghani. Cubegrades: Generalizing association rules. DAMI:02. L. V. S. Lakshmanan, J. Pei, and J. Han. Quotient Cube: How to Summarize the Semantics of a Data Cube. VLDB'02. D. Xin, J. Han, X. Li, B. W. Wah. Star-Cubing: Computing Iceberg Cubes by Top-Down and Bottom-Up Integration. VLDB'03.

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September 2, 2014Data Mining: Concepts and Techniques65 Ref: FP for Classification and Clustering G. Dong and J. Li. Efficient mining of emerging patterns: Discovering trends and differences. KDD'99. B. Liu, W. Hsu, Y. Ma. Integrating Classification and Association Rule Mining. KDD’98. W. Li, J. Han, and J. Pei. CMAR: Accurate and Efficient Classification Based on Multiple Class-Association Rules. ICDM'01. H. Wang, W. Wang, J. Yang, and P.S. Yu. Clustering by pattern similarity in large data sets. SIGMOD’ 02. J. Yang and W. Wang. CLUSEQ: efficient and effective sequence clustering. ICDE’03. B. Fung, K. Wang, and M. Ester. Large Hierarchical Document Clustering Using Frequent Itemset. SDM’03. X. Yin and J. Han. CPAR: Classification based on Predictive Association Rules. SDM'03.

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September 2, 2014Data Mining: Concepts and Techniques66 Ref: Stream and Privacy-Preserving FP Mining A. Evfimievski, R. Srikant, R. Agrawal, J. Gehrke. Privacy Preserving Mining of Association Rules. KDD’02. J. Vaidya and C. Clifton. Privacy Preserving Association Rule Mining in Vertically Partitioned Data. KDD’02. G. Manku and R. Motwani. Approximate Frequency Counts over Data Streams. VLDB’02. Y. Chen, G. Dong, J. Han, B. W. Wah, and J. Wang. Multi- Dimensional Regression Analysis of Time-Series Data Streams. VLDB'02. C. Giannella, J. Han, J. Pei, X. Yan and P. S. Yu. Mining Frequent Patterns in Data Streams at Multiple Time Granularities, Next Generation Data Mining:03. A. Evfimievski, J. Gehrke, and R. Srikant. Limiting Privacy Breaches in Privacy Preserving Data Mining. PODS’03.

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September 2, 2014Data Mining: Concepts and Techniques67 Ref: Other Freq. Pattern Mining Applications Y. Huhtala, J. Kärkkäinen, P. Porkka, H. Toivonen. Efficient Discovery of Functional and Approximate Dependencies Using Partitions. ICDE’98. H. V. Jagadish, J. Madar, and R. Ng. Semantic Compression and Pattern Extraction with Fascicles. VLDB'99. T. Dasu, T. Johnson, S. Muthukrishnan, and V. Shkapenyuk. Mining Database Structure; or How to Build a Data Quality Browser. SIGMOD'02.

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