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Data Mining: Concepts and Techniques — Chapter 8 — 8. 3 Mining sequence patterns in transactional databases 20 March 2018 Data Mining: Concepts and Techniques 1
Chapter 8. Mining Stream, Time. Series, and Sequence Data Mining data streams Mining time-series data Mining sequence patterns in transactional databases Mining sequence patterns in biological data 20 March 2018 Data Mining: Concepts and Techniques 2
Sequence Databases & Sequential Patterns n Transaction databases, time-series databases vs. sequence databases n Frequent patterns vs. (frequent) sequential patterns n Applications of sequential pattern mining n Customer shopping sequences: n n 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. n Telephone calling patterns, Weblog click streams n DNA sequences and gene structures 20 March 2018 Data Mining: Concepts and Techniques 3
What Is Sequential Pattern Mining? n Given a set of sequences, find the complete set of frequent subsequences A sequence : < (ef) (ab) (df) c b > A sequence database SID 10 20 30 40 sequence
Challenges on Sequential Pattern Mining n n A huge number of possible sequential patterns are hidden in databases A mining algorithm should n n n 20 March 2018 find the complete set of patterns, when possible, satisfying the minimum support (frequency) threshold be highly efficient, scalable, involving only a small number of database scans be able to incorporate various kinds of user-specific constraints Data Mining: Concepts and Techniques 5
Sequential Pattern Mining Algorithms n Concept introduction and an initial Apriori-like algorithm n n Agrawal & Srikant. Mining sequential patterns, ICDE’ 95 Apriori-based method: GSP (Generalized Sequential Patterns: Srikant & Agrawal @ EDBT’ 96) n Pattern-growth methods: Free. Span & Prefix. Span (Han et al. @KDD’ 00; Pei, et al. @ICDE’ 01) n Vertical format-based mining: SPADE (Zaki@Machine Leanining’ 00) n Constraint-based sequential pattern mining (SPIRIT: Garofalakis, Rastogi, Shim@VLDB’ 99; Pei, Han, Wang @ CIKM’ 02) n Mining closed sequential patterns: Clo. Span (Yan, Han & Afshar @SDM’ 03) 20 March 2018 Data Mining: Concepts and Techniques 6
The Apriori Property of Sequential Patterns n A basic property: Apriori (Agrawal & Sirkant’ 94) n If a sequence S is not frequent n Then none of the super-sequences of S is frequent n E. g,
GSP—Generalized Sequential Pattern Mining n n n GSP (Generalized Sequential Pattern) mining algorithm n proposed by Agrawal and Srikant, EDBT’ 96 Outline of the method n Initially, every item in DB is a candidate of length-1 n for each level (i. e. , sequences of length-k) do n scan database to collect support count for each candidate sequence n generate candidate length-(k+1) sequences from length-k frequent sequences using Apriori n repeat until no frequent sequence or no candidate can be found Major strength: Candidate pruning by Apriori 20 March 2018 Data Mining: Concepts and Techniques 8
Finding Length-1 Sequential Patterns n n n Examine GSP using an example Initial candidates: all singleton sequences n , ,
GSP: Generating Length-2 Candidates 51 length-2 Candidates
Candidate Generate-and-test: Drawbacks n A huge set of candidate sequences generated. n n Especially 2 -item candidate sequence. Multiple Scans of database needed. n The length of each candidate grows by one at each database scan. n Inefficient for mining long sequential patterns. n A long pattern grow up from short patterns n The number of short patterns is exponential to the length of mined patterns. 20 March 2018 Data Mining: Concepts and Techniques 11
The SPADE Algorithm n SPADE (Sequential PAttern Discovery using Equivalent Class) developed by Zaki 2001 n A vertical format sequential pattern mining method n A sequence database is mapped to a large set of n n Item:
The SPADE Algorithm 20 March 2018 Data Mining: Concepts and Techniques 13
Bottlenecks of GSP and SPADE n A huge set of candidates could be generated n 1, 000 frequent length-1 sequences generate s huge number of length-2 candidates! n Multiple scans of database in mining n Breadth-first search n Mining long sequential patterns n Needs an exponential number of short candidates n A length-100 sequential pattern needs 1030 candidate sequences! 20 March 2018 Data Mining: Concepts and Techniques 14
Prefix and Suffix (Projection) n ,
Mining Sequential Patterns by Prefix Projections n n Step 1: find length-1 sequential patterns n , ,
Finding Seq. Patterns with Prefix n Only need to consider projections w. r. t. n n -projected database: <(abc)(ac)d(cf)>, <(_d)c(bc)(ae)>, <(_b)(df)cb>, <(_f)cbc> Find all the length-2 seq. pat. Having prefix :
Completeness of Prefix. Span SDB SID 10 <(ad)c(bc)(ae)> 30 <(ef)(ab)(df)cb> 40 -projected database <(abc)(ac)d(cf)> <(_d)c(bc)(ae)> <(_b)(df)cb> <(_f)cbc>
Efficiency of Prefix. Span n No candidate sequence needs to be generated n Projected databases keep shrinking n Major cost of Prefix. Span: constructing projected databases n 20 March 2018 Can be improved by pseudo-projections Data Mining: Concepts and Techniques 19
Speed-up by Pseudo-projection n Major cost of Prefix. Span: projection n Postfixes of sequences often appear repeatedly in recursive projected databases n When (projected) database can be held in main memory, use pointers to form projections n Pointer to the sequence n Offset of the postfix s=
Pseudo-Projection vs. Physical Projection n Pseudo-projection avoids physically copying postfixes n n However, it is not efficient when database cannot fit in main memory n n Efficient in running time and space when database can be held in main memory Disk-based random accessing is very costly Suggested Approach: n n 20 March 2018 Integration of physical and pseudo-projection Swapping to pseudo-projection when the data set fits in memory Data Mining: Concepts and Techniques 21
Performance on Data Set C 10 T 8 S 8 I 8 20 March 2018 Data Mining: Concepts and Techniques 22
Performance on Data Set Gazelle 20 March 2018 Data Mining: Concepts and Techniques 23
Effect of Pseudo-Projection 20 March 2018 Data Mining: Concepts and Techniques 24
Ref: Mining Sequential Patterns n n n n n R. Srikant and R. Agrawal. Mining sequential patterns: Generalizations and performance improvements. EDBT’ 96. H. Mannila, H Toivonen, and A. I. Verkamo. Discovery of frequent episodes in event sequences. DAMI: 97. M. Zaki. SPADE: An Efficient Algorithm for Mining Frequent Sequences. Machine Learning, 2001. J. Pei, J. Han, H. Pinto, Q. Chen, U. Dayal, and M. -C. Hsu. Prefix. Span: Mining Sequential Patterns Efficiently by Prefix-Projected Pattern Growth. ICDE'01 (TKDE’ 04). J. Pei, J. Han and W. Wang, Constraint-Based Sequential Pattern Mining in Large Databases, CIKM'02. X. Yan, J. Han, and R. Afshar. Clo. Span: Mining Closed Sequential Patterns in Large Datasets. SDM'03. J. Wang and J. Han, BIDE: Efficient Mining of Frequent Closed Sequences, ICDE'04. H. Cheng, X. Yan, and J. Han, Inc. Span: Incremental Mining of Sequential Patterns in Large Database, KDD'04. J. Han, G. Dong and Y. Yin, Efficient Mining of Partial Periodic Patterns in Time Series Database, ICDE'99. J. Yang, W. Wang, and P. S. Yu, Mining asynchronous periodic patterns in time series data, KDD'00. 20 March 2018 Data Mining: Concepts and Techniques 25