Boolean matrix factorization meets consecutive ones property

Nikolaj Tatti, Pauli Miettinen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive ones property (OBMF). A major application of this optimization problem comes from graph visualization: standard techniques for visualizing graphs are circular or linear layout, where nodes are ordered in circle or on a line. A common problem with visualizing graphs is clutter due to too many edges. The standard approach to deal with this is to bundle edges together and represent them as ribbon. We also show that we can use OBMF for edge bundling combined with circular or linear layout techniques.
We demonstrate that not only this problem is NP-hard but we cannot have a polynomial-time algorithm that yields a multiplicative approximation guarantee (unless P = NP). On the positive side, we develop a greedy algorithm where at each step we look for the best 1-rank factorization. Since even obtaining 1-rank factorization is NP-hard, we propose an iterative algorithm where we fix one side and and find the other, reverse the roles, and repeat. We show that this step can be done in linear time using pq-trees. We also extend the problem to cyclic ones property and symmetric factorizations. Our experiments show that our algorithms find high-quality factorizations and scale well.
Original languageEnglish
Title of host publicationProceedings of the 2019 SIAM International Conference on Data Mining
EditorsTanya Berger-Wolf, Nitesh Chawla
Number of pages9
PublisherSociety for Industrial and Applied Mathematics
Publication date2019
Pages729-737
ISBN (Electronic)978-1-61197-567-3
DOIs
Publication statusPublished - 2019
MoE publication typeA4 Article in conference proceedings
EventSIAM International Conference on Data Mining (SDM19) - Hyatt Regency Calgary, Calgary, Canada
Duration: 2 May 20194 May 2019

Fields of Science

  • 113 Computer and information sciences

Cite this

Tatti, N., & Miettinen, P. (2019). Boolean matrix factorization meets consecutive ones property. In T. Berger-Wolf, & N. Chawla (Eds.), Proceedings of the 2019 SIAM International Conference on Data Mining (pp. 729-737). Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611975673.82