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Prefix-projection global constraint and top-k approach for sequential pattern mining

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Abstract

Sequential pattern mining (SPM) is an important data mining problem with broad applications. SPM is a hard problem due to the huge number of intermediate subsequences to be considered. State of the art approaches for SPM (e.g., PrefixSpan Pei et al. 2001) are largely based on the pattern-growth approach, where for each frequent prefix subsequence, only its related suffix subsequences need to be considered, and the database is recursively projected into smaller ones. Many authors have promoted the use of constraints to focus on the most promising patterns according to the interests of the end user. The top-k SPM problem is also used to cope with the difficulty of thresholding and to control the number of solutions. State of the art methods developed for SPM and top-k SPM, though efficient, are locked into a rather rigid search strategy, and suffer from the lack of declarativity and flexibility. Indeed, adding new constraints usually amounts to changing the data-structures used in the core of the algorithm, and combining these new constraints often require new developments. Recent works (e.g. Kemmar et al. 2014; Négrevergne and Guns 2015) have investigated the use of Constraint Programming (CP) for SPM. However, despite their nice declarative aspects, all these modelings have scaling problems, due to the huge size of their constraint networks. To address this issue, we propose the Prefix-Projection global constraint, which encapsulates both the subsequence relation as well as the frequency constraint. Its filtering algorithm relies on the principle of projected databases which allows to keep in the variables domain, only values leading to a frequent pattern in the database. Prefix-Projection filtering algorithm enforces domain consistency on the variable succeeding the current frequent prefix in polynomial time. This global constraint also allows for a straightforward implementation of additional constraints such as size, item membership, regular expressions and any combination of them. Experimental results show that our approach clearly outperforms existing CP approaches and competes well with the state-of-the-art methods on large datasets for mining frequent sequential patterns, sequential patterns under various constraints, and top-k sequential patterns. Unlike existing CP methods, our approach achieves a better scalability.

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Notes

  1. 〈A C〉 appears respectively in the first sequence 〈A B C B C〉 (i.e., two positions (1, 3) at 〈A B C B C〉 and (1, 5) at 〈A BCB C〉) and in the second sequence 〈B A B C〉 (i.e., one position (2, 4) at 〈B A B C〉); thus it is a frequent pattern. Notice that when some sequential pattern appears many times in some sequence (e.g., 〈A C〉 in 〈A B C B C〉), it is considered a single occurrence.

  2. We say that a pattern is non-contiguous if it contains at least one wildcard before the last item.

  3. A sequential pattern p is maximal if there is no sequential pattern q such that p ≼ q.

  4. We indifferently denote σ by 〈d 1 ,…,d i 〉 or by 〈σ(P 1 ),…,σ(P i )〉.

  5. We note by top-k-PP-BL the top-k algorithm using as first step the top-k-init-BL strategy.

  6. We note by top-k-PP-IPL the top-k algorithm using as first step the top-k-init-IPL strategy.

  7. www.genenames.org

  8. http://www.gecode.org

  9. https://sites.google.com/site/prefixprojection4cp/

  10. http://www.cs.rpi.edu/zaki/www-new/pmwiki.php/Software/

  11. http://illimine.cs.uiuc.edu/software/prefixspan-mining-sequential-patterns-efficiently-prefix-projected-pattern-growth/

  12. http://www-kdd.isti.cnr.it/SMA/

  13. http://www.philippe-fournier-viger.com/spmf/

  14. https://dtai.cs.kuleuven.be/CP4IM/cpsm/

  15. Recall that in all experiments, ℓ was fixed to the maximum size of sequences in the database.

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Authors and Affiliations

  1. LITIO, University of Oran 1 Ahmed Ben Bella, Oran, Algeria

    Amina Kemmar & Yahia Lebbah

  2. GREYC (CNRS UMR 6072), University of Caen, Caen, France

    Samir Loudni & Patrice Boizumault

  3. LIPN (CNRS UMR 7030), University PARIS 13, Paris, France

    Thierry Charnois

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Correspondence to Yahia Lebbah.

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Kemmar, A., Lebbah, Y., Loudni, S. et al. Prefix-projection global constraint and top-k approach for sequential pattern mining. Constraints 22, 265–306 (2017). https://doi.org/10.1007/s10601-016-9252-z

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