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(1b.#E7eX~s[V>vn1*. Chapter 5: Mining Frequent Patterns, Association and Correlations. > `!V1 }Ed:5j & x q $1 x}xT9gs=FbZ0mXE+RXZRG Q(j&kBb+DAi5F6;Y@lV#3ys9# > m o d e f g h i n n{t nDy` L|&Ov%j,A7#h!iK3v;Ogck7/ef =l7' [&x^iB#PF!eUPuQ Second, a pattern-growth algorithm, Finding patterns, correlations and descriptors in Finding patterns, correlations and descriptors, Frequent Pattern Queries: Language and Optimizations 1.1.
IHDR & sRGB t$IDATx^]w@iR! s({Bread, Milk, Diaper}) = 2/5Frequent ItemsetAn itemset whose support is greater than or equal to a min_sup threshold, Association Rule Mining TaskAn association rule r is strong ifSupport(r) min_sup Confidence(r) min_conf Given a transactions database D, the goal of association rule mining is to find all strong rules Two-step approach: 1. Pattern Mining Important?Discloses an intrinsic and important property of data setsForms the foundation for many essential data mining tasksAssociation, correlation, and causality analysisSequential, structural (e.g., sub-graph) patternsPattern analysis in spatiotemporal, multimedia, time-series, and stream data Classification: associative classificationCluster analysis: frequent pattern-based clusteringData warehousing: iceberg cube and cube-gradient Semantic data compression: fasciclesBroad applications, Basic Concepts: Frequent Patterns and Association RulesItemset X = {x1, , xk}Find all the rules X Y with minimum support and confidencesupport, s, probability that a transaction contains X Yconfidence, c, conditional probability that a transaction having X also contains YLet supmin = 50%, confmin = 50%Freq. > Frequent pattern : a pattern (a set of items, subsequences, substructures, etc.) Why Is Freq. ({Bread, Milk, Diaper}) = 2 Support (s)Fraction of transactions containing an itemsetE.g. $ @ KDD 94)Method: Initially, scan DB once to get frequent 1-itemsetGenerate length (k+1) candidate itemsets from length k frequent itemsetsTest the candidates against DBTerminate when no frequent or candidate set can be generated, Intro of Apriori AlgorithmBasic idea of AprioriUsing anti-monotone property to reduce candidate itemsetsAny subset of a frequent itemset must be also frequentIn other words, any superset of an infrequent itemset must also be infrequent Basic operations of AprioriCandidate generationCandidate countingHow to generate the candidate itemsets?Self-joiningPruning infrequent candidates, The Apriori AlgorithmCk: Candidate itemset of size kLk : frequent itemset of size k. L1 = {frequent items};for (k = 1; Lk !=; k++) doCandidate Generation: Ck+1 = candidates generated from Lk;Candidate Counting: for each transaction t in database do increment the count of all candidates in Ck+1 that are contained in tLk+1 = candidates in Ck+1 with min_supreturn k Lk; Candidate-generation: Self-joiningGiven Lk, how to generate Ck+1?Step 1: self-joining Lk INSERT INTO Ck+1SELECT p.item1, p.item2, , p.itemk, q.itemkFROM Lk p, Lk qWHERE p.item1=q.item1, , p.itemk-1=q.itemk-1, p.itemk < q.itemkExampleL3={abc, abd, acd, ace, bcd}Self-joining: L3*L3abcd abc * abdacde acd * aceC4={abcd, acde}, Candidate Generation: Pruning Can we further reduce the candidates in Ck+1? 9EDr>eAxP~E=*C[i)S `&(~.#!AhzQ8D88#pJ>bPX*,?>(^EnMp`OOOq0"t{Zsyntp9,U&YGj-\~s. nK
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confidence 50%. Mining Frequent Itemsets: the Key StepFind the frequent itemsets: the sets of items that have minimum supportA subset of a frequent itemset must also be a frequent itemseti.e., if {AB} is a frequent itemset, both {A} and {B} should be frequent itemsetsIteratively find frequent itemsets with cardinality from 1 to k (k-itemset)Use the frequent itemsets to generate association rules. Association Rule Mining Finding frequent patterns, associations, correlations, A Fast Parallel Algorithm for Discovering Frequent Patterns, Mining Periodic Frequent Patterns Common to Multiple Periodic pattern mining: Discover frequent patterns, From Frequent Itemsets to Semantically Meaningful Visual Patterns, Semantic Annotation of Frequent hcheng/paper/ Semantic Annotation of Frequent Patterns , Chapter 4: Mining Frequent Patterns, Associations and 4: Mining Frequent Patterns, Associations and Correlations `4.1 Basic Concepts `4.2 Frequent Itemset Mining Methods `4.3 Which, Computing frequent patterns from semi-structured data - Computing frequent patterns from semi-structured, Mining Frequent Patterns Without Candidate Generation, Comparison of void fraction correlations for different flow patterns in, Discovering Emerging Graph Patterns from Chemicals frequent emerging graph patterns, given a frequency, Lecture for Chapter 5 Mining Frequent Patterns, Associations, Advantages: Very efficient for data sets with small numbers of attributes (.
Moreover, a, Constraint Mining of Frequent Patterns in Long Sequences, Chapter V: Mining Frequent Patterns, Associations and Chapter V: Mining Frequent Patterns, Associations, Parallel Mining Frequent Patterns: A Sampling-based Approach, Mining Frequent Patterns II: Mining Sequential & Navigational Patterns. Syp A01 _z]j4b rR8aRXH i@af[F! 583G=@U ,b Found to be InfrequentIllustrating Apriori PrinciplePruned SupersetsLevel 0Level 1, An ExampleFor rule A C:support = support({A C}) = 50%confidence = support({A C})/support({A}) = 66.6%The Apriori principle:Any subset of a frequent itemset must be frequentMin. What is association rule mining?To find all the strong association rulesAn association rule r is strong ifSupport(r) min_sup Confidence(r) min_conf Rule Evaluation MetricsSupport (s): Fraction of transactions that contain both X and Y, Confidence (c): Measures how often items in Y appear in transactions that contain X, Example of Support and ConfidenceTo calculate the support and confidence of rule {Milk, Diaper} {Beer} # of transactions: 5 # of transactions containing {Milk, Diaper, Beer}: 2 Support: 2/5=0.4 # of transactions containing {Milk, Diaper}: 3 Confidence: 2/3=0.67, Definition: Frequent ItemsetItemsetA collection of one or more itemsExample: {Bread, Milk, Diaper}k-itemsetAn itemset that contains k itemsSupport count ()# transactions containing an itemsetE.g. BS @jPCmLn' WCN.mg% C4g1{M7*t\:v3"Uw?\;b}.cbln. U#bfw+$m G#V!4b5lX B#V!4u5\ YZ`7Is]8F%#aYkN#U;a~uD)3[]53HNr .,0@5aXkQYFob?u~Clktk #" qn:yFm,T)gUntehZg]m&D a:Q>\ !L)Z&Ldt-+K)mjV ?hnh6F aChj6F )*J What Is Association Mining? What Is Frequent Pattern Analysis?.
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!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?ApplicationsBasket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis. support 50%Min. : {A:3, B:3, D:4, E:3, AD:3}Association rules:A D (60%, 100%)D A (60%, 75%), Transaction-idItems bought10A, B, D20A, C, D30A, D, E40B, E, F50B, C, D, E, F, Association RuleWhat is an association rule?An implication expression of the form X Y, where X and Y are itemsets and XY=Example: {Milk, Diaper} {Beer}, 2. Frequents Sets (F):ab(3) ac(3) bc(3) ad(3) bd(3) cd(3)ae(3) be(3) ce(3)de(3)Rules:ab conf=3/6=50%ba conf=3/6=50%Etc. Frequent Itemset IdentificationFind all itemsets whose support min_sup2. IbPNG
Beer and diapers? 02% B"\lJMCHo" Z d))1H 06yuuu|~S>nLp06%bi%H)*"uwE~g}'g'~n{L98Ud9 ,uTO?BZAo1+x/?4x9tT
v0U_{Wyp Q\Z?7xgoP{2) F +pC}|Bd;`QZgqKsc/}xK0TsRM#-\\eWE&Bs `wa6yn6@D"h5{K0F aehU For each itemset c in Ck+1 do For each k-subsets s of c do I, Chapter 5: Mining Frequent Patterns, Association and Correlations. U ' e# x\mlE~v-"*.Z? that occurs frequently in a data set First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule miningMotivation: Finding inherent regularities in dataWhat products were often purchased together? How to Get an Efficient Method?The complexity of a brute-force method is O(MNw) M=2I-1, I is the number of itemsHow to get an efficient method?Reduce the number of candidate itemsetsCheck the supports of candidate itemsets efficiently.
{gExk{e-B"TRQ'usWwt?{3>(6"PDEDPGE"PP(5@h-vj(Jpt P(Z %8Z:0 E]"@ Nk"@m>%%]tJpZ>=_rWeWYBW8. > Anti-Monotone PropertyAny subset of a frequent itemset must be also frequent an anti-monotone propertyAny transaction containing {beer, diaper, milk} also contains {beer, diaper}{beer, diaper, milk} is frequent {beer, diaper} must also be frequentIn other words, any superset of an infrequent itemset must also be infrequent No superset of any infrequent itemset should be generated or testedMany item combinations can be pruned! (Agrawal & Srikant @VLDB94, Mannila, et al. [Aq` ) P)@~%@(z@ c{*S4 T SB
Discovering Stable Periodic-Frequent Patterns in of patterns. Output the itemsets with a counter (min_sup*N)Complexity ~ O(NMw) Expensive since M = 2I-1 !!! &( QV @= G)2w5F/@S " t h IHDR i gAMA pHYs + IDATxu}yER2%F v.P01$ $A^zAn%1JdE6-KddF$E-)Zr:'3M0\r{`jfz>utu5 $3X|7j[33oO'rP9A 8)o=MGl 'wZI0Uq' 5nk5qRc/P ;H1D0@"p*8nkFU6$#h23 @ 8rzCnaj"VF#@ fGt%3 1JT53S.SUX[bf@N What Is Frequent Pattern Analysis?Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) Apriori: A Candidate Generation-and-Test ApproachApriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! *i[)$RC jGH&ACWbLhD4IQ37qd6wggv^P `= ASSOCIATION RULES AND FREQUENT PATTERNS 9. n z@R#$bAMFf[Ok4b j Rule GenerationFrom each frequent itemset, generate all confident rules whose confidence min_conf, Rule GenerationAll candidate rules: {Beer} {Diaper, Milk} (s=0.4, c=0.67){Diaper} {Beer, Milk} (s=0.4, c=0.5){Milk} {Beer, Diaper} (s=0.4, c=0.5){Beer, Diaper} {Milk} (s=0.4, c=0.67) {Beer, Milk} {Diaper} (s=0.4, c=0.67) {Diaper, Milk} {Beer} (s=0.4, c=0.67), Suppose min_sup=0.3, min_conf=0.6, Support({Beer, Diaper, Milk})=0.4Strong rules: {Beer} {Diaper, Milk} (s=0.4, c=0.67){Beer, Diaper} {Milk} (s=0.4, c=0.67) {Beer, Milk} {Diaper} (s=0.4, c=0.67) {Diaper, Milk} {Beer} (s=0.4, c=0.67), {Beer} , {Diaper} , {Milk}, {Beer, Diaper}, {Beer, Milk} , {Diaper, Milk}, Frequent Itemset Indentification: the Itemset LatticeGiven I items, there are 2I-1 candidate itemsets!Level 0Level 1Level 2Level 3Level 4Level 5, Frequent Itemset Identification: Brute-Force ApproachBrute-force approach: Set up a counter for each itemset in the latticeScan the database once, for each transaction T, check for each itemset S whether T S if yes, increase the counter of S by 1. Data Mining Techniques Association Rule. Pat. that occurs frequently in a data set - PowerPoint PPT Presentation, Discovering Frequent Tree Patterns over Data candidate tree patterns without duplicates.