Model order selection for approximate Boolean matrix factorization problem

Abstract

A key step in applying Boolean matrix factorization (BMF) is establishing the correct model order for the data, i.e., decide where the knowledge stops and the noise starts, or simply, decide the proper number of factors that describe the data well. There are two main approaches to BMF, namely, Discrete Basis Problem (DBP) and Approximation Factorization Problem (AFP). Although the model order selection technique for DBP exists, there is no technique tailored for AFP. We show that the number of factors for DBP cannot be used in AFP, and we present a novel way, reflecting the nature of AFP, how to establish the proper number of factors. Moreover, we show that the number of factors established for AFP is – from a knowledge-representation viewpoint – better than that for DBP.