Chapter 13, Sequence Data Mining
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1 CSI 4352, Introduction to Data Mining Chapter 13, Sequence Data Mining Young-Rae Cho Associate Professor Department of Computer Science Baylor University Topics Single Sequence Mining Frequent sequence pattern mining Finding sub-sequences that frequently occur in a sequence ACTTCGATGGAGCCAGTCGCGAAATTCGACTAGATCG Sequence Dataset Mining Frequent sequence pattern mining Finding sub-sequences that frequently occur among sequences Sequence data clustering Grouping similar sequences Sequence data classification Classifying a new sequence id sequence 1 ACTTCG 2 GGAGC 3 CGTCGAT 4 ATCGATCGC 5 TCGACT 6 AGATCGC 1
2 Applications Examples Customer shopping sequential patterns e.g., First buy a computer, then a CD-ROM, and then a printer within 3 months Stock market changes Web-log patterns Medical treatment records Gene or protein sequences Natural disaster records Challenges Finding the complete set satisfying the minimum support threshold Developing efficient and scalable algorithms Incorporating various kinds of user-specific constraints Problem Definition Scope Transaction data Sequential transaction data Frequent itemset patterns (Frequent) Sequential patterns Definitions Sequence: an ordered list of items, e.g., x = <a c f e c d> Sub-sequence of x: an ordered sequence of items from x Not necessarily consecutive (different from a substring) <a e c> <c f d> <a c> <c e c> <a f c d> <c f c e> Frequent sequence pattern s 10 <acadcf> < a c d > is a frequent sequence 20 <abcaed> pattern with 75% minimum support 30 <efadfcb> 40 <egafcbd> 2
3 Extended Problem Definition Extended Definitions Consider or at a single position Sequence: an ordered list of elements and each element is a set of items, e.g., x = <(ab) c (df) (ef) d> Sub-sequence of x <(ab) d> <a c (ef)> <a f e> <(ab) e f> <b f d> <c d f> Frequent sequence pattern s <(ab) c> is a frequent sequence pattern with 75% minimum support Properties of Sequence Patterns Properties Anti-monotonic property Apriori algorithm If a sequence S is not frequent, then none of the super-sequences of S are frequent Example If <(ab)d> is infrequent, so do <(ab)de> and <(abc)d> and <a(ab)d> min_sup = 75% 3
4 GSP Algorithm GSP Generalized Sequential Pattern mining Algorithm (1) Initially, find all frequent length-1 sequences ( = frequent 1-itemset ) (2) Generate candidate length-(k+1) sequences from frequent length-k sequences (3) Count support for each candidate sequence to select frequent sequences (4) Repeat (2) and (3) until no frequent sequence or no candidate is found Length-1 Sequences Example min_sup = 75% Candidate Length-1 Sequences <a>, <b>, <c>, <d>, <e>, <f>, <g> Frequent Length-1 Sequences <a>, <b>, <c>, <e>, <f> 4
5 Length-2 Sequences Candidate & Frequent Length-2 Sequences <a> <b> <c> <e> <f> <a> <aa> <ab> <ba> <ac> <ca> <ae> <ea> <af> <fa> <b> <bb> <bc> <cb> <be> <eb> <bf> <fb> <c> <cc> <ce> <ec> <cf> <fc> <e> <ee> <ef> <fe> <f> <ff> <a> <b> <c> <e> <f> <a> <(ab)> <(ac)> <(ae)> <(af)> <b> <(bc)> <(be)> <(bf)> <c> <(ce)> <(cf)> <e> <(ef)> <f> Length-3 Sequences Candidate & Frequent Length-3 Sequences <ab> <ac> <bc> <(ab)> <ab> <aab> <abb> <abc> <acb> <abc> <(ab)b> <a(ab)> <ac> <aac> <acc> <abc> <bac> <(ab)c> <bc> <bbc> <bcc> <(ab)c> <(ab)> <(ab)(ab)> 5
6 Summary of GSP Algorithm Strength Apriori pruning Weakness Generates a huge set of candidate sequences Requires multiple scans of database Inefficient for mining long sequential patterns References Agrawal, R. and Srikant, R., Mining sequential patterns. In Proceedings of ICDE (1995) Srikant, R. and Agrawal, R., Mining sequential patterns: Generalizations and performance improvements. In Proceedings of EDBT (1996) PrefixSpan Algorithm PrefixSpan Prefix-projected sequential pattern mining Prefix Suppose all items in an element are listed alphabetically. Given x=<e 1, e 2,, e m >, y=<e 1, e 2,, e m > (m n) is a prefix of x if and only if (1) e i = e i for (i m 1) (2) e m e m (3) all items in (e m e m ) are alphabetically after those in e m <a>, <aa>, <a(ab)> and <a(abc)> are prefixes of <a(abc)(ac)d(cf)> Main Idea Keep track of prefixes (instead of all candidate sequences) from the sequence database Project their suffixes into projected databases 6
7 Projected Database Definition A set of maximal suffixes of substrings with a given prefix Example <a>-projected database includes <(abc)(ac)d(cf)> <(_b)a(bc)(ae)> <(_b)(df)cb> <(_f)cbc> PrefixSpan Algorithm Algorithm (1) Find all frequent length-1 sequences <a>, <b>, <c>, <e>, <f> (2) Divide search space to Maximal substrings having prefix <a> Maximal substrings having prefix <b> Maximal substrings having prefix <c> Maximal substrings having prefix <e> Maximal substrings having prefix <f> (3) Construct a projected database for each search space (4) Find subsets of sequential patterns recursively 7
8 PrefixSpan Algorithm Example min_sup = 75% pattern <a> <b> <c> <e> <f> projected database <(abc)(ac)d(cf)>, <(_b)a(bc)(ae)>, <(_b)(df)cb>, <(_f)cbc> <(_c)(ac)d(cf)>, <a(bc)(ae)>, <(df)cb>, <c> <(ac)d(cf)>, <(ae)>, <b>, <bc> <(_f)(ab)(df)cb>, <g(af)cbc> <(ab)(df)cb>, <cbc> PrefixSpan Algorithm Example (continued) pattern <a> <b> <c> <e> <f> projected database <(abc)(ac)d(cf)>, <(_b)a(bc)(ae)>, <(_b)(df)cb>, <(_f)cbc> <(_c)(ac)d(cf)>, <a(bc)(ae)>, <(df)cb>, <c> <(ac)d(cf)>, <(ae)>, <b>, <bc> <(_f)(ab)(df)cb>, <g(af)cbc> <(ab)(df)cb>, <cbc> recursion pattern <ab> <ac> <(ab)> projected database <(_c)(ac)d(cf)>, <(_c)(ae)>, <c> <(ac)d(cf)>, <(ae)>, <b>, <bc> <(_c)(ac)d(cf)>, <a(bc)(ae)>, <(df)cb> 8
9 PrefixSpan Algorithm Example (continued) pattern <ab> <ac> <(ab)> projected database <(_c)(ac)d(cf)>, <(_c)(ae)>, <c> <(ac)d(cf)>, <(ae)>, <b>, <bc> <(_c)(ac)d(cf)>, <a(bc)(ae)>, <(df)cb> recursion pattern <(ab)c> projected database <d(cf)>, <(ae)>, <b> Summary of PrefixSpan Algorithm Strength Efficient (major cost is to construct projected databases) Project databases keep shrinking rapidly Weakness Searching frequency redundantly References Pei, J., et al., PrefixSpan: Mining sequential patterns efficiently by prefix-projected pattern growth. In Proceedings of ICDE (2001) 9
10 Constraint-Based Sequence Mining Constraint Types Prefix anti-monotonic If a sequence s violates the constraint C, then so does any sequence having s as a prefix Prefix monotonic If a sequence s satisfies the constraint C, then so does any sequence having s as a prefix Application Push prefix anti-monotonic constraints for early pruning Reference Pei, J., Han, J. and Wang, W, Mining sequential patterns with constraints in large databases. In Proceedings of CIKM (2002) Questions? Lecture Slides on the Course Website, 10
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