1. UNIT 4 December 5, 2015 Data Mining: Concepts and Techniques1

2. December 5, 2015Data 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

3. December 5, 2015Data 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 Applications Basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis.

4. December 5, 2015Data 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 Data warehousing: iceberg cube and cube-gradient Semantic data compression: fascicles Broad applications

5. December 5, 2015Data 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

6. December 5, 2015Data 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

7. December 5, 2015Data Mining: Concepts and Techniques7 Closed Patterns and Max-Patterns Exercise. DB = {, } Min_sup = 1. What is the set of closed itemset? : 1 : 2 What is the set of max-pattern? : 1 What is the set of all patterns? !!

8. December 5, 2015Data Mining: Concepts and Techniques8 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

9. December 5, 2015Data Mining: Concepts and Techniques9 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)

10. Frequent itemsets December 5, 2015Data Mining: Concepts and Techniques10

11. Association rule mining can be viewed as a two step process: 1) Find all frequent pattern 2) Generate strong association rules from frequent itemsets December 5, 2015Data Mining: Concepts and Techniques11

12. December 5, 2015Data Mining: Concepts and Techniques12 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

13. December 5, 2015Data Mining: Concepts and Techniques13 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

14. December 5, 2015Data Mining: Concepts and Techniques14 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 ;

15. December 5, 2015Data Mining: Concepts and Techniques15 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}

16. December 5, 2015Data Mining: Concepts and Techniques16 How to Generate Candidates? Suppose the items in L k-1 are listed in an order Step 1: self-joining L k-1 insert into C k select p.item 1, p.item 2, …, p.item k-1, q.item k-1 from L k-1 p, L k-1 q where p.item 1 =q.item 1, …, p.item k-2 =q.item k-2, p.item k-1 < q.item k-1 Step 2: pruning forall itemsets c in C k do forall (k-1)-subsets s of c do if (s is not in L k-1 ) then delete c from C k

17. December 5, 2015Data Mining: Concepts and Techniques17 Challenges of Frequent Pattern Mining Challenges Multiple scans of transaction database Huge number of candidates Tedious workload of support counting for candidates

18. Improving efficiency of apriori Variations of apriori to improve efficiency  Hash based technique  Transaction reduction  Partitioning  Sampling  Dynamic itemset counting 18

19. Method 1) Hash based technique hashing itemsets into corresponding buckets A hash-based technique can be used to reduce the size of the candidate k-itemsets, Ck, for k > 1. December 5, 2015Data Mining: Concepts and Techniques19

20. Method 2) Transaction reduction (reducing the number of transactions scanned in future iterations) A transaction that does not contain any frequent k- itemsets cannot contain any frequent (k+1)-itemsets. Therefore, such a transaction can be marked or removed from further consideration because subsequent scans of the database for j-itemsets, where j > k, will not require it. December 5, 2015Data Mining: Concepts and Techniques20

21. Method 3 ) partitioning (partitioning the data to find candidate itemsets) 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 minimum support count for each partition= min_support * number of transactions in that partition. Scan 2: consolidate global frequent patterns December 5, 2015Data Mining: Concepts and Techniques21

22. December 5, 2015Data Mining: Concepts and Techniques22

23. Method 4) Sampling (mining on a subset of the given data) The basic idea of the sampling approach is to pick a random sample S of the given data D, and then search for frequent itemsets in S instead of D. The sample size of S is such that the search for frequent itemsets in S can be done in main memory, and so only one scan of the transactions in S is required overall. Because we are searching for frequent itemsets in S rather than in D, it is possible that we will miss some of the global frequent itemsets. To lessen this possibility, we use a lower support threshold than minimum support to find the frequent itemsets local to S (denoted LS). The rest of the database is then used to compute the actual frequencies of each itemset in LS. 23

24. Method 5) dynamic itemset counting (adding candidate itemsets at different points during a scan) A dynamic itemset counting technique was proposed in which the database is partitioned into blocks marked by start points. In this variation, new candidate itemsets can be added at any start point, unlike in Apriori, which determines new candidate itemsets only immediately before each complete database scan. 24

25. December 5, 2015Data Mining: Concepts and Techniques25 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?

26. mining frequent itemset without generating candidate 1) Vertical data format 2) FP growth December 5, 2015 Data Mining: Concepts and Techniques26

27. Mining frequent itemsets using vertical data format Question Answer 27

28. Minimum support = 2 28

29. Question) Find frequent itemsets using vertical data format. December 5, 2015Data Mining: Concepts and Techniques29

30. December 5, 2015Data Mining: Concepts and Techniques30 Mining Various Kinds of Association Rules Mining multilevel association Mining multidimensional association Mining quantitative association

31. 31 Mining Multiple-Level Association Rules Items often form concept hierarchies Flexible support settings Items at the lower level are expected to have lower support

32. December 5, 2015Data Mining: Concepts and Techniques32

33. Association rules generated from mining data at multiple levels of abstraction are called multiple- level or multilevel association rules. Various ways: 1) Using uniform support for all levels 2) Using reduced support at lower level 3) Using items or group-based minimum support (referred as group based support) – because users or experts often have insight as to which groups are more important than others. 33

34. 34

35. 35 Mining Multi-Dimensional Association Single-dimensional rules: buys(X, “milk”)  buys(X, “bread”) Multi-dimensional rules:  2 dimensions or predicates Inter-dimension assoc. rules (no repeated predicates) age(X,”19-25”)  occupation(X,“student”)  buys(X, “coke”) hybrid-dimension assoc. rules (repeated predicates) age(X,”19-25”)  buys(X, “popcorn”)  buys(X, “coke”) Categorical Attributes: finite number of possible values, no ordering among values (occupation, color ) Quantitative Attributes: numeric, implicit ordering among values(income, age, price)—discretization, clustering, and gradient approaches

36. December 5, 2015Data Mining: Concepts and Techniques36 Mining Quantitative Associations Techniques can be categorized by how numerical attributes, such as age or salary are treated 1.Static discretization based on predefined concept hierarchies (data cube methods). This decritization occurs before mining. 2.Dynamic discretization or clustered into bins based on the distribution of the data. K-predicate set searching for frequent itemsets. A k-predicate set is a set containing k conjunctive predicates.{age,occupation,buys} is a 3 predicate set.

37. December 5, 2015Data Mining: Concepts and Techniques37 Static Discretization of Quantitative Attributes Discretized prior to mining using concept hierarchy. Numeric values are replaced by ranges. In relational database, finding all frequent k-predicate sets will require k or k+1 table scans. Data cube is well suited for mining. The cells of an n-dimensional cuboid correspond to the predicate sets. Mining from data cubes can be much faster. (income)(age) () (buys) (age, income)(age,buys)(income,buys) (age,income,buys)

38. December 5, 2015Data Mining: Concepts and Techniques38 Mining Quantitative Association Rules age(X,”34-35”)  income(X,”30-50K”)  buys(X,”high resolution TV”) Numeric attributes are dynamically discretized during mining process so as to satisfy some mining criteria, such as maximizing the confidence or compactness of the rules. 2-D quantitative association rules: A quan1  A quan2  A cat Cluster adjacent association rules to form general rules using a 2-D grid Example

39. Discretization Finding frequent predicate sets: Once the 2-D array containing the count distribution for each category is set up, it can be scanned to find the frequent predicate sets (those satisfying minimum support) that also satisfy minimum confidence. Strong association rules can then be generated from these predicate sets, using a rule generation algorithm. December 5, 2015Data Mining: Concepts and Techniques39

40. Clustering the association rules: “Can we find a simpler rule to replace the above four rules?” Notice that these rules are quite “close” to one another, forming a rule cluster on the grid. Indeed, the four rules can be combined or “clustered” together to form the following simpler rule, which subsumes and replaces the above four rules: December 5, 2015Data Mining: Concepts and Techniques40

41. December 5, 2015Data Mining: Concepts and Techniques41

42. December 5, 2015Data Mining: Concepts and Techniques42

43. December 5, 2015Data Mining: Concepts and Techniques43 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

44. December 5, 2015Data Mining: Concepts and Techniques44 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

45. December 5, 2015Data Mining: Concepts and Techniques45 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 Never be larger than the original database (not count node-links and the count field) For Connect-4 DB, compression ratio could be over 100

46. December 5, 2015Data Mining: Concepts and Techniques46 Partition Patterns and Databases Frequent patterns can be partitioned into subsets according to f-list F-list=f-c-a-b-m-p Patterns containing p Patterns having m but no p … Patterns having c but no a nor b, m, p Pattern f Completeness and non-redundency

47. December 5, 2015Data Mining: Concepts and Techniques47 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

48. December 5, 2015Data Mining: Concepts and Techniques48 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

49. December 5, 2015Data Mining: Concepts and Techniques49 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

50. December 5, 2015Data Mining: Concepts and Techniques50 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 =

51. December 5, 2015Data Mining: Concepts and Techniques51 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

52. December 5, 2015Data Mining: Concepts and Techniques52 Scaling FP-growth by DB Projection FP-tree cannot fit in memory?—DB projection First partition a database into a set of projected DBs Then construct and mine FP-tree for each projected DB Parallel projection vs. Partition projection techniques Parallel projection is space costly

53. December 5, 2015Data Mining: Concepts and Techniques53 Partition-based Projection Parallel projection needs a lot of disk space Partition projection saves it Tran. DB fcamp fcabm fb cbp fcamp p-proj DB fcam cb fcam m-proj DB fcab fca b-proj DB f cb … a-proj DB fc … c-proj DB f … f-proj DB … am-proj DB fc cm-proj DB f …

54. December 5, 2015Data Mining: Concepts and Techniques54 FP-Growth vs. Apriori: Scalability With the Support Threshold Data set T25I20D10K

55. December 5, 2015Data Mining: Concepts and Techniques55 FP-Growth vs. Tree-Projection: Scalability with the Support Threshold Data set T25I20D100K

56. December 5, 2015Data Mining: Concepts and Techniques56 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

57. December 5, 2015Data Mining: Concepts and Techniques57 Implications of the Methodology Mining closed frequent itemsets and max-patterns CLOSET (DMKD’00) Mining sequential patterns FreeSpan (KDD’00), PrefixSpan (ICDE’01) Constraint-based mining of frequent patterns Convertible constraints (KDD’00, ICDE’01) Computing iceberg data cubes with complex measures H-tree and H-cubing algorithm (SIGMOD’01)

58. December 5, 2015Data Mining: Concepts and Techniques58 MaxMiner: Mining Max-patterns 1 st scan: find frequent items A, B, C, D, E 2 nd scan: find support for AB, AC, AD, AE, ABCDE BC, BD, BE, BCDE CD, CE, CDE, DE, Since BCDE is a max-pattern, no need to check BCD, BDE, CDE in later scan R. Bayardo. Efficiently mining long patterns from databases. In SIGMOD’98 TidItems 10A,B,C,D,E 20B,C,D,E, 30A,C,D,F Potential max-patterns

59. December 5, 2015Data Mining: Concepts and Techniques59 Mining Frequent Closed Patterns: CLOSET Flist: list of all frequent items in support ascending order Flist: d-a-f-e-c Divide search space Patterns having d Patterns having d but no a, etc. Find frequent closed pattern recursively Every transaction having d also has cfa  cfad is a frequent closed pattern J. Pei, J. Han & R. Mao. CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets", DMKD'00. TIDItems 10a, c, d, e, f 20a, b, e 30c, e, f 40a, c, d, f 50c, e, f Min_sup=2

60. December 5, 2015Data Mining: Concepts and Techniques60 CLOSET+: Mining Closed Itemsets by Pattern-Growth Itemset merging: if Y appears in every occurrence of X, then Y is merged with X Sub-itemset pruning: if Y כ X, and sup(X) = sup(Y), X and all of X’s descendants in the set enumeration tree can be pruned Hybrid tree projection Bottom-up physical tree-projection Top-down pseudo tree-projection Item skipping: if a local frequent item has the same support in several header tables at different levels, one can prune it from the header table at higher levels Efficient subset checking

61. December 5, 2015Data Mining: Concepts and Techniques61 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

62. December 5, 2015Data Mining: Concepts and Techniques62 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

63. December 5, 2015Data Mining: Concepts and Techniques63 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

64. December 5, 2015Data Mining: Concepts and Techniques64 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 22 A11000100 10,0009.260.910.839055 A21001000 100,0008.440.090.05670 A3100010010000100,0009.180.09 8172 A41000 10.50.330

65. December 5, 2015Data Mining: Concepts and Techniques65 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)