From-Below Approximations in Boolean Matrix Factorization: Geometry and New Algorithm

TL;DR

This paper introduces a new Boolean matrix factorization algorithm emphasizing from-below approximations, which considers entry significance, and demonstrates superior performance over existing methods on synthetic and real data.

Contribution

The paper presents a novel algorithm for Boolean matrix factorization that incorporates entry significance and from-below approximations, improving coverage and efficiency.

Findings

The new algorithm achieves better coverage with fewer factors.

It outperforms existing algorithms in exact decomposition tasks.

Experimental results confirm its effectiveness on synthetic and real datasets.

Abstract

We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously proposed algorithms do not consider the possibly different significance of different matrix entries, our results help measure such significance and suggest where to focus when computing factors. An experimental evaluation of the new algorithm on both synthetic and real data demonstrates its good performance in terms of good coverage by the first k factors as well as a small number of factors needed for exact decomposition and indicates that the algorithm outperforms the available ones in these terms. We also propose future research topics.