1. 1 Association Rule Mining Instructor Qiang Yang Slides from Jiawei Han and Jian Pei And from Introduction to Data Mining By Tan, Steinbach, Kumar

2. Frequent-pattern mining methods2 What Is Frequent Pattern Mining? Frequent patterns: pattern (set of items, sequence, etc.) that occurs frequently in a database [AIS93] Frequent pattern mining: finding regularities in data What products were often purchased together? What are the subsequent purchases after buying a PC?

3. Frequent-pattern mining methods3 Why Is Frequent Pattern Mining an Essential Task in Data Mining? Foundation for many essential data mining tasks Association, correlation, causality Sequential patterns, temporal or cyclic association, partial periodicity, spatial and multimedia association Associative classification, cluster analysis, iceberg cube, fascicles (semantic data compression) Broad applications Basket data analysis, cross-marketing, catalog design, sale campaign analysis Web log (click stream) analysis, DNA sequence analysis, etc.

4. Frequent-pattern mining methods4 Basic Concepts: Frequent Patterns and Association Rules Itemset X={x 1, …, x k } Find all the rules X  Y with min confidence and support support, s, probability that a transaction contains X  Y confidence, c, conditional probability that a transaction having X also contains Y. Let min_support = 50%, min_conf = 50%: A  C (50%, 66.7%) C  A (50%, 100%) Customer buys diaper Customer buys both Customer buys beer Transaction-idItems bought 10A, B, C 20A, C 30A, D 40B, E, F

5. Frequent-pattern mining methods5 Concept: Frequent Itemsets OutlookTemperatureHumidityPlay sunnyhothighno sunnyhothighno overcasthothighyes rainymildhighyes rainycoolnormalyes rainycoolnormalno overcastcoolnormalyes sunnymildhighno sunnycoolnormalyes rainymildnormalyes sunnymildnormalyes overcastmildhighyes overcasthotnormalyes rainymildhighno Minimum support=2 {sunny, hot, no} {sunny, hot, high, no} {rainy, normal} Min Support =3 ? How strong is {sunny, no}? Count = Percentage =

6. Frequent-pattern mining methods6 Concept: Itemset  Rules {sunny, hot, no} = {Outlook=Sunny, Temp=hot, Play=no} Generate a rule: Outlook=sunny and Temp=hot  Play=no How strong is this rule? Support of the rule = support of the itemset {sunny, hot, no} = 2 = Pr({sunny, hot, no}) Either expressed in count form or percentage form Confidence = Pr(Play=no | {Outlook=sunny, Temp=hot}) In general LHS  RHS, Confidence = Pr(RHS|LHS) Confidence =Pr(RHS|LHS) =count(LHS and RHS) / count(LHS) What is the confidence of Outlook=sunny  Play=no?

7. Frequent-pattern mining methods7 Frequent Patterns Patterns = Item Sets {i1, i2, … in}, where each item is a pair: (Attribute=value) Frequent Patterns Itemsets whose support >= minimum support Support count(itemset)/count(database)

8. Frequent-pattern mining methods8 Frequent Itemset Generation Given d items, there are 2 d possible candidate itemsets

9. Frequent-pattern mining methods9 Max-patterns Max-pattern: frequent patterns without proper frequent super pattern BCDE, ACD are max-patterns BCD is not a max-pattern TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F Min_sup=2

10. Frequent-pattern mining methods10 Maximal Frequent Itemset Border Infrequent Itemsets Maximal Itemsets An itemset is maximal frequent if none of its immediate supersets is frequent

11. Frequent-pattern mining methods11 Frequent Max Patterns Succinct Expression of frequent patterns Let {a, b, c} be frequent Then, {a, b}, {b, c}, {a, c} must also be frequent Then {a}, {b}, {c}, must also be frequent By writing down {a, b, c} once, we save lots of computation Max Pattern If {a, b, c} is a frequent max pattern, then {a, b, c, x} is NOT a frequent pattern, for any other item x.

12. Frequent-pattern mining methods12 Find Frequent Max Patterns OutlookTemperatureHumidityPlay sunnyhothighno sunnyhothighno overcasthothighyes rainymildhighyes rainycoolnormalyes rainycoolnormalno overcastcoolnormalyes sunnymildhighno sunnycoolnormalyes rainymildnormalyes sunnymildnormalyes overcastmildhighyes overcasthotnormalyes rainymildhighno Minimum support=2 {sunny, hot, no} ??

13. Frequent-pattern mining methods13 Closed Patterns An itemset is closed if none of its immediate supersets has the same support as the itemset {a, b}, {a, b, d}, {a, b, c} are closed patterns But, {a, b} is not a max pattern See where changes happen Reduce # of patterns and rules N. Pasquier et al. In ICDT’99 TIDItems 10a, b, c 20a, b, c 30a, b, d 40a, b, d, 50c, e, f

14. Frequent-pattern mining methods14 Maximal vs Closed Itemsets Transaction Ids Not supported by any transactions indexes beside an item set is the transaction #s.

15. Frequent-pattern mining methods15 Maximal vs Closed Frequent Itemsets Minimum support = 2 # Closed = 9 # Maximal = 4 Closed and maximal Closed but not maximal

16. Frequent-pattern mining methods16 Note on Closed Patterns Closed patterns have no need to specify the minimum support Given dataset, we can find a set of closed patterns from it, so that for any minimum support values, we can immediately find the set of patterns (a subset of the closed patterns). Closed frequent patterns Both closed and above the min support

17. Frequent-pattern mining methods17 Maximal vs Closed Itemsets

18. Frequent-pattern mining methods18 Mining Association Rules—an Example For rule A  C: support = support({A}  {C}) = 50% confidence = support({A}  {C})/support({A}) = 66.6% Min. support 50% Min. confidence 50% Transaction-idItems bought 10A, B, C 20A, C 30A, D 40B, E, F Frequent patternSupport {A}75% {B}50% {C}50% {A, C}50%

19. Frequent-pattern mining methods19 Method 1: Apriori: A Candidate Generation-and-test Approach Any subset of a frequent itemset must be frequent if {beer, diaper, nuts} is frequent, so is {beer, diaper} Every transaction having {beer, diaper, nuts} also contains {beer, diaper} Apriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! Method: generate length (k+1) candidate itemsets from length k frequent itemsets, and test the candidates against DB The performance studies show its efficiency and scalability Agrawal & Srikant 1994, Mannila, et al. 1994

20. Frequent-pattern mining methods20 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

21. 21 Speeding up Association rules Dynamic Hashing and Pruning technique Thanks to Cheng Hong & Hu Haibo

22. Frequent-pattern mining methods22 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 effective hash-based algorithm for mining association rules. In SIGMOD’95

23. Frequent-pattern mining methods23 Still challenging, the niche for DHP DHP ( Park ’95 ): Dynamic Hashing and Pruning Candidate large 2-itemsets are huge. DHP: trim them using hashing Transaction database is huge that one scan per iteration is costly DHP: prune both number of transactions and number of items in each transaction after each iteration

24. Frequent-pattern mining methods24 Hash Table Construction Consider two items sets, all itesms are numbered as i1, i2, …in. For any any pair (x, y), has according to Hash function bucket #= h({x y}) = ((order of x)*10+(order of y)) % 7 Example: Items = A, B, C, D, E, Order = 1, 2, 3 4, 5, H({C, E})= (3*10 + 5)% 7 = 0 Thus, {C, E} belong to bucket 0.

25. Frequent-pattern mining methods25 How to trim candidate itemsets In k-iteration, hash all candidate k+1 itemsets in a hash table, and count all the itemsets in each bucket. In k+1 iteration, examine each of the candidate itemset to see if its correspondent bucket value is above the support ( necessary condition )

26. Frequent-pattern mining methods26 Example TIDItems 100A C D 200B C E 300A B C E 400B E Figure1. An example transaction database

27. Frequent-pattern mining methods27 Generation of C1 & L1(1st iteration) C1 L1 ItemsetSup {A}2 {B}3 {C}3 {D}1 {E}3 ItemsetSup {A}2 {B}3 {C}3 {E}3

28. Frequent-pattern mining methods28 Hash Table Construction Find all 2-itemset of each transaction TID2-itemset 100{A C} {A D} {C D} 200{B C} {B E} {C E} 300{A B} {A C} {A E} {B C} {B E} {C E} 400{B E}

29. Frequent-pattern mining methods29 Hash Table Construction (2) Hash function h({x y}) = ((order of x)*10+(order of y)) % 7 Hash table {C E} {A E} {B C} {B E} {A B} {A C} {C E} {B C} {B E} {C D} {A D} {B E} {A C} bucket 0 1 2 3 4 5 6 3120313

30. Frequent-pattern mining methods30 C2 Generation (2nd iteration) L1*L1 # in the bucket {A B}1 {A C}3 {A E}1 {B C}2 {B E}3 {C E}3 Resulted C2 {A C} {B C} {B E} {C E} C2 of Apriori {A B} {A C} {A E} {B C} {B E} {C E}

31. Frequent-pattern mining methods31 Effective Database Pruning Apriori Don’t prune database. Prune C k by support counting on the original database. DHP More efficient support counting can be achieved on pruned database.

32. Frequent-pattern mining methods32 Performance Comparison

33. Frequent-pattern mining methods33 Performance Comparison (2)

34. Frequent-pattern mining methods34 FP-growth Algorithm Use a compressed representation of the database using an FP-tree Once an FP-tree has been constructed, it uses a recursive divide-and-conquer approach to mine the frequent itemsets

35. Frequent-pattern mining methods35 FP-tree construction null A:1 B:1 null A:1 B:1 C:1 D:1 After reading TID=1: After reading TID=2:

36. Frequent-pattern mining methods36 FP-Tree Construction 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

37. Frequent-pattern mining methods37 FP-growth null A:4 B:2 B:1 C:1 D:1 C:1 D:1 C:1 D:1 Conditional Pattern base for D: (PB | D) = {(A:1,B:1,C:1), (A:1,B:1), (A:1,C:1), (A:1), (B:1,C:1)} Recursively apply FP-growth on PB, and then append to D Thus, frequent Itemsets found from PB|D (with min support = 2): AD, BD, CD, ABD, ACD, BCD D:1

38. Frequent-pattern mining methods38 FP-Growth vs. Apriori: Scalability With the Support Threshold Data set T25I20D10K