Frequent and Sequential Pattern Mining with Multiple Minimum Supports

Transcription

1 Frequent and Sequential Pattern Mining with Multiple Minimum Supports 中正資管胡雅涵 1

2 Outline Brief review on frequent and sequential pattern mining The rare item problem and the concept of multiple minimum supports (MMSs) My previous studies on MMSs Frequent pattern mining with MMSs Sequential pattern mining with MMSs Cyclically repeated pattern mining with MMSs 2

3 Association Rule Mining Given a set of transactions, find rules that will predict the occurrence of an item based on the occurrences of other items in the transaction Market-Basket transactions TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke Example of Association Rules {Diaper} {Beer}, {Milk, Bread} {Eggs,Coke}, {Beer, Bread} {Milk}, 3 資料來源 :Tan et al., Introduction to Data Mining

4 Definition: Frequent Itemset Itemset A collection of one or more items Example: {Milk, Bread, Diaper} k-itemset An itemset that contains k items Support count ( ) Frequency of occurrence of an itemset E.g. ({Milk, Bread,Diaper}) = 2 Support Fraction of transactions that contain an itemset E.g. s({milk, Bread, Diaper}) = 2/5 Frequent Itemset TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke An itemset whose support is greater than or equal to a minsup threshold 4 資料來源 :Tan et al., Introduction to Data Mining

5 Definition: Association Rule Association Rule An implication expression of the form X Y, where X and Y are itemsets Example: {Milk, Diaper} {Beer} Rule Evaluation Metrics Support (s) Fraction of transactions that contain both X and Y Confidence (c) Measures how often items in Y appear in transactions that contain X TID Items 1 Bread, Milk 2 Bread, Diaper, Beer, Eggs 3 Milk, Diaper, Beer, Coke 4 Bread, Milk, Diaper, Beer 5 Bread, Milk, Diaper, Coke Example: { Milk, Diaper} Beer (Milk, Diaper, Beer) s T (Milk, Diaper, Beer) c (Milk, Diaper) 資料來源 :Tan et al., Introduction to Data Mining

6 Association Rule Mining Task Given a set of transactions T, the goal of association rule mining is to find all rules having support minsup threshold confidence minconf threshold Two-step approach: 1. Frequent Itemset Generation Generate all itemsets whose support minsup 2. Rule Generation Generate high confidence rules from each frequent itemset, where each rule is a binary partitioning of a frequent itemset Frequent itemset generation is still computationally expensive 6 資料來源 :Tan et al., Introduction to Data Mining

7 Frequent Itemset Generation null A B C D E AB AC AD AE BC BD BE CD CE DE ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE 7 ABCD ABCE ABDE ACDE BCDE ABCDE 資料來源 :Tan et al., Introduction to Data Mining Given d items, there are 2 d -1 possible candidate itemsets

8 Reducing Number of Candidates Apriori principle: If an itemset is frequent, then all of its subsets must also be frequent Apriori principle holds due to the following property of the support measure: X, Y : ( X Y ) s( X ) s( Y ) Support of an itemset never exceeds the support of its subsets This is known as the downward closure property 8 資料來源 :Tan et al., Introduction to Data Mining

9 Illustrating Apriori Principle null A B C D E AB AC AD AE BC BD BE CD CE DE Found to be Infrequent ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE ABCD ABCE ABDE ACDE BCDE Pruned supersets ABCDE 9 資料來源 :Tan et al., Introduction to Data Mining

10 Sequential Pattern Mining Sequential pattern mining To find the relationships between occurrences of sequential events To find if there exist any specific order of the occurrences. Example Every time Microsoft stock drops 5%, IBM stock will also drops at least 4% within three days. 10 資料來源 :Tan et al., Introduction to Data Mining

11 Sequential Patterns v.s. Association Rules Correlation between transactions Relationships intra transaction Which items are bought in a certain order? <, > CID Purchased Items Which items are bought together? (, ) 11 資料來源 :Han and Kamber, Data Mining: Concepts and Techniques

12 Applications of sequential pattern mining Customer shopping sequences: First buy computer, then CD-ROM, and then digital camera, within 3 months. Medical treatments, natural disasters (e.g., earthquakes), science & eng. processes, stocks and markets, etc. Telephone calling patterns, Weblog click streams DNA sequences and gene structures 12 資料來源 :Tan et al., Introduction to Data Mining

13 What is Sequential Pattern Mining? Given a set of sequences, find the complete set of frequent subsequences A sequence database SID sequence 10 <a(abc)(ac)d(cf)> 20 <(ad)c(bc)(ae)> 30 <(ef)(ab)(df)cb> 40 <eg(af)cbc> A sequence : < (ef) (ab) (df) c b > An element may contain a set of items. Items within an element are unordered and we list them alphabetically. <a(bc)dc> is a subsequence of <a(abc)(ac)d(cf)> Given support threshold min_sup =2, <(ab)c> is a sequential pattern Downward closure property also holds in SPM 13 資料來源 :Tan et al., Introduction to Data Mining

14 Outline Brief review on frequent and sequential pattern mining The rare item problem and the concept of multiple minimum supports (MMSs) My previous studies on MMSs Frequent pattern mining with MMSs (DSS 06 ) Sequential pattern mining with MMSs (JSS 13 ) Cyclically repeated pattern mining with MMSs (FSKD 11 ) 14

15 Rare item problem The key element that makes ARM and SPM practical is minsup The problem of using single minsup Implicitly assumes that all items in the database are of the same nature or of similar frequencies in the database If minsup is set too high Items with low occurrence cannot appear in the patterns If minsup is set too low Generate too many meaningless patterns 15

16 Multiple minimum supports Examples SARS fever, cough v.s. flu fever, cough LCD TV Blu-ray player v.s. milk bread Solution Each item has its own threshold Resulting in Multiple minimum supports (MMSs) The threshold of an itemset is defined as the minimum threshold among all items in the itemset Problem in mining for multiple minimum supports Downward closure property no longer holds 16

17 An example Consider four items A, B, C and D in a database. Their MIS values are: MIS(A)=5%, MIS(B)=15%, MIS(C)=30%, MIS(D)=40% If the support of {B, C} is 13% and that of {B, D} is 14%, then both itemsets {B, C} and {B, D} are infrequent; Not satisfy their MIS values MIS(B,C)=min[MIS(B),MIS(C)]=15% MIS(B,D)= min[mis(b),mis(d)] =15% Suppose the support of itemset {A, B, C, D} is 8 Itemset {A, B, C, D} is frequent because MIS(A) is only 5%. 17

18 Sorted closure property Solution Sorted closure property Items are sorted by an increasing order of their MIS values If an itemset A doesn t satisfy the MIS value of the first item in A (i.e., A is an infrequent pattern), then A s superset will no longer to be frequent Example Assume support of itemset (A,B) is 0.3% Itemset (A,B) is not a frequent pattern. The support of (A,B,C) and (A,B,D) will never larger than 0.3% (i.e., Itemsets (A,B,C) and (A,B,D) must be infrequent patterns Item name A B C D MIS value 1% 5% 40% 50% 18

19 Outline Brief review on frequent and sequential pattern mining The rare item problem Multiple minimum supports (MMSs) My previous studies on MMSs Frequent pattern mining with MMSs Sequential pattern mining with MMSs Cyclically repeated pattern mining with MMSs 19

20 Frequent pattern mining with MMSs DSS 06 20

21 Motivation To develop an efficient algorithm for the mining of frequent patterns with MMSs MIS-tree, an FP-tree-based data structure, for storing complete set of transactions CFP-growth, an FP-growth-like mining algorithm for mining frequent patterns with MMSs To provide a maintenance mechanism for support tuning process 21

22 An illustrated example TID Item Bought Item 100 d, c, a, f a, c, d, f Bought(Ordered) 200 g, c, a, f, e a, c, e, f, g 300 b, a, c, f, h a, b, c, f, h 400 g, b, f b, f, g 500 b, c b, c Item a b c d e f g h MIS value

23 An illustrated example - The imcompact MIS-tree MIN_frequent item header table MIS head of Item value nodelink a:3 nul l b:2 a b c d e f g h c:2 d:1 f:1 e:1 f:1 g:1 b:1 c:1 f:1 h:1 f:1 g:1 c:1 23

24 An illustrated example - The complete and compact MIS-tree MIN_frequent item header table null MIS head of Item value nodelink a:3 b:2 a b c f g c:2 f:2 g:1 b:1 c:1 f:1 f:1 g:1 c:1 24

25 An illustrated example CFP-growth a:1 c:1 f:1 root root b:1 f:1 g s conditional MIS-tree (a) ag : 1 bg : 1 cg : 1 fg : 2 g s conditional pattern root a:1 cg s conditional MIS-tree acg : 1 g s conditional pattern root (b) a:1 b:1 a:1 c:1 fg s conditional MIS-tree afg : 1 cfg : 1 bfg : 1 g s conditional pattern (c) cfg s conditional MIS-tree acfg : 1 g s conditional pattern (d) All g s conditional pattern : ag, bg, cg, fg, acg, afg, cfg, bfg, acfg All g s conditional frequent pattern ( MIS(g)=2 ): fg (e) 25

26 An illustrated example support tuning null null null a:3 b:2 a:2 a:1 b:2 c:2 a:1 b:2 c:2 b:1 f:1 c:1 c:2 b:1 f:1 c:1 a:2 b:1 f:1 c:1 f:2 c:1 g:1 f:2 c:1 g:1 f:2 c:1 g:1 g:1 f:1 (a) Move up c g:1 f:1 (b) Move up c g:1 f:1 (c) Move up c null null null c:2 a:1 b:2 c:2 a:1 b:2 c:2 c:1 b:2 a:2 b:1 f:1 c:1 a:2 c:1 f:1 c:1 a:2 a:1 f:1 c:1 f:2 c:1 g:1 f:2 b:1 g:1 f:2 b:1 g:1 g:1 f:1 (d) Move up c g:1 f:1 (e) Move up c g:1 f:1 (f) Move up c 26

27 An illustrated example support tuning null null c:2 c:1 f:1 c:1 c:4 f:1 a:2 a:1 b: 1 b:1 a:3 b:1 b:1 f:2 g:1 f:2 f:1 g:1 g:1 b:1 (a) Merge c g:1 b:1 (c) Merge f null null c:4 f:1 c:4 f:1 a:2 a:1 b:1 b:1 a:3 b:1 b:1 f:2 f:1 g:1 f:3 g:1 g:1 b:1 g:1 b:1 (b) Merge a (d) MIS-tree after support tuning 27

28 Experimental evaluation assign MIS value σ A parameter used to modify the MIS value of each item f(a i ) The frequency of item a i 28

29 Runtime(sec) Runtime(sec) Experimental evaluation 2500 N1000-T10-I4-D0400K(MIN=0.01) SIGMA Apriori FP-growth MSapriori CFP-growth Real-life dataset(bms-pos)(min=0.01) SIGMA Apriori FP-growth MSapriori CFP-growth

30 runtime(sec) Experimental evaluation Scalability with Support Tuning Process K 400K 600K # of transactions MIS-tree maintenance mechanism tree reconstruction 30

31 Sequential pattern mining with MMSs JSS 13 31

32 Motivation Sequential patterns with rare items No previous studies discuss sequential pattern mining with MMSs Traditional sequential pattern mining algorithms cannot deal with this problem Both downward closure and sorted closure properties do not hold in sequential pattern mining with MMSs An example Each item may have its own customer group in a large retail store Video games for teenagers, presbyopic glasses for elders or milk for everyone 32

33 SPM with MMSs This study proposes an efficient sequential pattern mining algorithm with consideration of MMSs Preorder Linked Multiple Supports tree (PLMS-tree) Multiple Supports-Conditional Pattern growth (MSCPgrowth) 33

34 Definitions Itemset minsup MIS(i) denote the MIS value of item i (i I). Given an itemset I q = (i 1 i 2...i m ), For itemset I q, minimum support threshold of I q (MIS(I q )) is defined : MIS(I q ) = min[ MIS(i 1 ), MIS(i 2 ),, MIS(i m )] MIN denotes the minimum threshold among all items in I 34

35 Definitions Sequence minsup For a sequence β (= <IB 1, IB 2,, IB s >), IB q I for, 1 q s minimum support threshold of β (MIS(β )) is defined: MIS(β ) = min[ MIS(IB 1 ), MIS(IB 2 ),, MIS(IB s )] SPM with MMSs Given a sequence database S and a sequence β, we call β is frequent in S or β is a sequential pattern in S if: supp(β ) MIS(β ). 35

36 An example For a sequence database S with six items (a, b, c, d, e, f) Item e f c d a b Minimum item support 30% 40% 40% 65% 70% 80% For sequence β = <(a)(c)(b)>, MIS(β ) = min[mis(a), MIS(c), MIS(b)] = 40% Assume frequency of sequence β is 60% β is a sequential pattern because supp(β ) MIS(β )=40%. 36

37 SPM with MMSs Downward closure and sorted closure do not exist in sequential pattern mining items in a sequence cannot be sorted Example: Assume that the support of sequence <(B)(C)> is 4% sequence <(B)(C)> is not a frequent sequential pattern Assume that the support of sequence <(B)(C)(A)> is 3% sequence <(B)(C)(A)> becomes a frequent sequential pattern Item name A B C D MIS value 1% 5% 40% 50% 37

38 SPM with MMSs Solution to the absence of sorted closure property MPS (minimum possible support) value The minimum threshold between the node and its suffix tree Example of MPS Item name D H I MIS value 50% 30% 20% MIS:50% MPS:50% MPS:20% D B E F G C MIS:30% MPS:30% H I MIS:20% MPS:20% 38

39 Data structure of PLMS-tree Structure name Field name Field description iname Which item this node represent icount The number of sequences represented by the portion of the path reaching this node iflag A flag to recognize the last item of an itemset mps Minimum MIS value between this node and items in Tree node its suffix trees pcode The position code of this node plink A node link to this node s parent node clink A node link to this node s first child node slink A node link to this node s first sibling node nlink A node link to the next node shares the same item name in pre-order linked iname which item this node represents Header table mis MIS value of this item nlink A node link to the first tree node with the same item name 39

40 Tree construction (1/6) Four steps 1. Scan database once, if item i with supp(i) MIN, join it into frequent itemset I Only items with supp(i) MIN might be part of sequential pattern 2. Scan database again to insert items in I into the tree 3. Build linkage between nodes with the same iname in pre-order linked To use the position code to avoid recount 4. Set the MPS value of each node 40

41 Tree construction step 1 Items in an itemset is sorted by MIS value in increasing order Item e f c d a b Minimum item support 30% 40% 40% 65% 70% 80% SID Purchasing sequence 10 <(ac)(ab)(bc)> 20 <(ac)(ab)(c)> 30 <(a)(e)(c)(a)(d)> 40 <(ac)(f)(ab)(d)(e)> 50 <(a)(e)(c)(b)(d)(e)> SID Sorted purchasing sequence 10 <(ca)(ab)(cb)> 20 <(ca)(ab)(c)> 30 <(a)(e)(c)(a)(d)> 40 <(ca)(f)(ab)(d)(e)> 50 <(a)(e)(c)(b)(d)(e)> Support of each item: (a:5), (b:4), (c:5), (d:3), (e:3), (f:1) frequent item set I = (a, b, c, d, e) 41

42 Tree construction step 2 Mark the last item i of each transaction as _i iname:icount pcode Iflag=false Iflag=true 1 11 null c:1 _a:1 null c:2 _a:2 c:2 _a:2 null _a:1 _e:1 SID Sorted purchasing sequence 10 <(ca)(ab)(cb)> 20 <(ca)(ab)(c)> 30 <(a)(e)(c)(a)(b)> 40 <(ca)(f)(ab)(d)(e)> 50 <(a)(e)(c)(b)(d)(e)> c:3 _a:3 null _a:1 _e:1 111 a:1 a:2 a:2 _c:1 a:3 _c: _b: _b:1 _b:2 _b:2 _a:1 _b:3 _a: c: c:1 _c: _b:1 _b:1 c:1 _b:1 _c:1 _b:1 c:1 _b:1 _c:1 _d:1 _e:1 _b:1

43 Tree construction - step 2 1 c:3 11 _a:3 null _a:2 10 _e:2 101 SID Sorted purchasing sequence 10 <(ca)(ab)(cb)> 20 <(ca)(ab)(c)> 30 <(a)(e)(c)(a)(b)> 40 <(ca)(f)(ab)(d)(e)> 50 <(a)(e)(c)(b)(d)(e)> 111 a:3 _c: c:1 _b:1 _b: _a:1 _b: _c:1 _d:1 _b:1 _d: _e:1 _e:

44 Tree construction - step 3 iname mis nlink e 30% c 40% d 65% a 70% b 80% nlink c:3 _a:3 a:3 null nlink _a:2 _e:2 _c:2 _b:3 _a:1 _b:1 c:1 _c:1 _d:1 _b:1 _d:1 _b:1 _e:1 _e:1 44

45 Tree construction - step 4 iname mis nlink e 30% c 40% d 65% a 70% b 80% 45 mps null 1 c:3 _a: % 30% 40% 11 _a:3 _e: % 70% 40% 30% 111 a:3 _c: % 70% 40% 30% 1111 _b: _a:1 _b: % 80% 40% 70% 30% c:1 _c:1 _d:130% _b:1 _d: % 30% % % _b:1 _e:1 80% _e: % 30%

46 Tree construction - step 4 iname mis nlink e 30% c 40% d 65% a 70% b 80% mps null 1 c:3 _a: % 30% 40% 11 _a:3 _e: % 70% 40% 30% 111 a:3 _c: % 70% 40% 30% 1111 _b: _a:1 _b: % 80% 40% 70% 30% c:1 _c:1 _d:130% _b:1 _d: % 30% % % _b:1 _e:1 80% _e: % 30%

47 MSCP-growth (1/3) Pattern (null) growth iname mps nlink e 30% c 40% d 65% a 70% b 80% c:3 _a:3 null _a:2 _e:2 Record (_e:2) as root set of (e) 30% supp(e) MPS(e) a:3 _c:2 Join e into candidate pattern set (to keep growth) supp(e) MIS(e) Join e into sequential pattern set Recursive to growth pattern (e) c:1 _b:1 _b:3 _c:1 _d:1 _e:1 _a:1 _b:1 _b:1 _d:1 _e:1

48 MSCP-growth (2/3) Pattern (e) growth iname mps nlink e 30% c 40% d 65% a 70% b 80% c:3 _a:3 null Record (_c:2) as root set of (e)(c) _a:2 _e:2 Root set of (e) 48 supp(e) < MPS(e) & supp(e)<mis(e) Needn t to keep growth supp(c) MPS(c) Join c into candidate pattern set (to keep growth) supp((e)(c)) MIS(ec), Join (e)(c) into sequential pattern set Recursive to growth pattern (e)(c) 48 c:1 _b:1 a:3 _b:3 _c:1 _d:1 _e:1 _a:1 _b:1 _c:2 _b:1 _d:1 _e:1 30% 30% Record (_e:1) as root set of (e)(e)

49 MSCP-growth (3/3) Pattern (e)(c) growth iname mps nlink e 30% c 40% d 65% a 70% b 80% c:3 _a:3 a:3 null _a:2 _e:2 _c:2 Root set of (e)(c) supp(b) MPS(b) Join b into candidate pattern set (to keep growth) supp((e)(c)(b)) MIS(ecb), Join (e)(c)(b) into sequential pattern set Recursive to growth pattern (e)(c)(b) c:1 _b:1 _b:3 _c:1 _d:1 _e:1 _a:1 _b:1 _b:1 _d:1 _e:1 30% 49 Record (_b:1) as root set of (e)(c)(b)

50 Experimental evaluation (1/3) 50

51 Experimental evaluation (2/3) 51

52 Runtime(sec) Runtime(sec) Experimental evaluation (3/3) DS1-D2.50-C10-T MSCP-growth MS-GSP SC-POS MSCP-growth MS-GSP

53 Cyclically repeated pattern mining with MMSs FSKD 11 53

54 Cyclically repeated pattern mining with MMSs (1/4) Sequential pattern mining analysis of customer purchase behavior, process analysis of scientific experiments, web-log analysis, DNA sequence analysis, medical record analysis A pattern may have periodicity or cyclically occur in a sequence Periodic pattern mining discover complete set of recurring patterns which occur in each regular time period in a time series database assumes the dataset consists of single long sequence data only not suitable for the repeated pattern mining in market basket analysis it considers multiple customer sequences 54

55 Cyclically repeated pattern mining with MMSs (2/4) Cyclic patterns (Toroslu, 2003) Take account of multiple data-sequences Holds the original form of sequential pattern mining Considers additional information: repetition support Apply in purchasing behavior analysis, web usage mining, and DNA sequence analysis Disadvantage Basically assumes all items are of the same nature or have similar repeated purchase frequencies in the sequence database Not the case in a large grocery retailer 55

56 Introduction (3/4) Why cyclic pattern mining is not suitable for mining large grocery retail?? Each product may have different purchase frequency according to number of pieces or capacity in a pack and customer s usage frequency etc. Cyclic pattern mining sets single repetition support only How to set a proper repetition threshold for all products?? Example. If set too high : cannot find cyclic patterns involving products with low purchase <(peanut butter, frequencies toast), toast, toast, toast, (peanut butter, toast), toast, toast> Consider following If set too situation: low : discover too much meaningless cyclic patterns 1. set minimum repetition threshold too high (ex.3): never find the repeated buying relationship between peanut butter and toast 2. set minimum repetition threshold too low (ex.1): combinatorial explosion 56

57 Introduction (4/4) Consider multiple minimum support in this paper specify minimum item repetition supports (MIR) for various products reflect their different natures and frquencies, each sequence has its own minimum sequence repetition support (MSR) while counting repetition supports for various sequences, the proposed method can retrieve cyclic patterns based on MSRs of the corresponded sequences. Consider the compactness constraint ensure that the pattern would occur in a reasonable period In a pattern, (the timestamp of the last item) (the timestamp of first item) given threshold 57

58 Problem definition Example 1. an itemset time stamp for a 1 Given a data-sequence and t-length=7. b b,..., ( a : t ),( a : t ),...,( a : t a : 1,( b : 2),( bcd : 3),( a : 5),( d : 6),( bc :10),( a :11),( b :12),( b :13),( bcd :15) ) n n 1, 2 b n The sequence ( a),( bc) is a com-subsequence of α (1) itemset (a) and (bc) occur in α ; (2) the difference between itemsets (a) and (bc) is 2 t_length. The sequence b b,..., 1, 2 b n ( bc),( bcd ) is not a com-subsequence in α (1) the the time stamp distance between them is 12 t_length. 58

59 Problem definition Example 2. (continue ex. 1) Given a : 1,( b : 2),( bcd : 3),( a : 5),( d : 6),( bc :10),( a :11),( b :12),( b :13),( bcd :15) and com-subsequence ( a),( bc) We can say the repetition support of β = 3 59

60 Problem definition Example 3. (for MIR, MSR) (continue) Following ex. 3, we have com-subsequence The user-specified MIR values are as follow: MIR(a)=3, MIR(b)=4, MIR(c)=2, and MIR(d)=4. MIR(bc) = 2 min MIR( a), MIR( bc) MSR (β)= =2 ( a),( bc) (for rep_subsequence) From ex 2. we know that The rep_support of com-subsequence ( a= ),( 3. bc) min MIR( b1 ), MIR( b2 ),...,MIR( bm ) β s rep_support MSR(β), β is rep_subsequence b b,..., 1, 2 b m 60

61 Problem definition Example 4. (cyclic sequential pattern)(continue) sid, s Assume cus_suppor that cus_minsupport=3 t SDB sid, s ( sid, s) SDB is a rep_subsequence in s ( a),( bc) is a rep_subsequence of sid 10,30,40,50 cus_minsup port cus_suppor cussup_cou t SDB ( ( a),( ntbc SDB ) ( ) ) 4 cus_minsupport <(a),(bc)> is a cyclic sequential pattern 61

62 Problem Definition Example 5. Let t-length=7, MIR(a)=3, MIR(b)=4, MIR(c)=2, and MIR(d)=4., and cus_minsupport= 3 We have MSR( ( a),( d) )=3, ( a),( d) is not a cyclic sequential pattern and MSR( ( a),( cd ))=2 62 ( a),( cd ) is a cyclic sequential pattern

63 Experiment Compare with prefixspan cyclic pattern mining (Toroslu et al., 2003) Environment In Java language tested on an Intel Core 2 Q GHz Windows XP system with 4 gigabyte of main memory 63

64 Experimental setup set MIR value of each item f(a i ): the average number of occurrence of a i in SDB, MIN: the smallest MIR value of all items σ (0 σ 1) : control how MIR value related to theirs frequencies if σ = 0 conventional cyclical patterns. 64

65 Experiment real-life TEJ finance stock database Recorded between 2009/04/15 and 2011/04/15 Include the 33 finance stocks recorded historical weekly stock price and volume The categorization of the stock data Volume: average and standard deviation z-score Event type rule (volume, v) Event type rule (price, p) 1 v<0 6 P<-25% 2 0 v<2 7-25% p<0 3 2 v<4 8 p=0 4 4 v<6 9 0<p 25% 5 v 6 10 p>25% 65

66 Experimental evaluation Evaluate how the σ value affects the efficiency cus_minsupport is set to 0.5, t_length is set to 200, and MIN is set to 1 66

67 Real-data result cus_minsupport = 0.3, t_length = 8 MIN=15 (denoted as cyclic pattern_h) MIN=1 (denoted as cyclic pattern_l) 67

68 Scalability test 68

69 Example for the rare item problem If we use conventional cyclic pattern mining with higher repetition threshold (i.e. 15) event types 6 (i.e. p -25%) and 10 (i.e. p>25%), would never be discovered. IF lower repetition threshold (i.e. 1) is considered almost all the combinations of items would be sequential patterns The MIR value of each event type (σ =0.4,MIN=1) Event type MIR Event type MIR