Boolean Matrix Factorization for Data with Symmetric Variables.

Boolean matrix factorization (BMF), a popular methodology of preprocessing and analyzing 1/0 tabular data, generally handles 0s and 1s differently. It aims to explain 1s in the data by factors, while 0s are just left unexplained. This difference is mainly given by the usual data character, where 1s carry much more important information (and are much scarcer) than 0s. However, in some datasets, the 1s and 0s are equally important. Such datasets require symmetrical handling of 1s and 0s. We propose a novel factorization of such data and its algorithm. Unlike usual BMF methods, factors are linearly ordered by priority in our factorization, and factors can contradict each other - meaning that one factor can put 1 where the other puts 0. In such a case, the factor with higher priority is right. We show that the proposed factorization provides a more compact data description than a straightforward application of the usual BMF methods.