Mining discrete patterns via binary matrix factorization

Bao Hong Shen, Shuiwang Ji, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

34 Scopus citations

Abstract

Mining discrete patterns in binary data is important for sub- sampling, compression, and clustering. We consider rank- one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds.

Original languageEnglish (US)
Title of host publicationKDD '09
Subtitle of host publicationProceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Pages757-765
Number of pages9
DOIs
StatePublished - Nov 9 2009
Event15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '09 - Paris, France
Duration: Jun 28 2009Jul 1 2009

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Conference

Conference15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '09
CountryFrance
CityParis
Period6/28/097/1/09

Keywords

  • Binary matrix factorization
  • Integer linear program
  • Maximum flow
  • Minimum cut
  • Rank-one
  • Regularization

ASJC Scopus subject areas

  • Software
  • Information Systems

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  • Cite this

    Shen, B. H., Ji, S., & Ye, J. (2009). Mining discrete patterns via binary matrix factorization. In KDD '09: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 757-765). (Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining). https://doi.org/10.1145/1557019.1557103