Binary Matrix Factorization via Dictionary Learning

TL;DR

This paper introduces two scalable, fast binary matrix factorization methods based on dictionary learning, suitable for online applications, with an effective model selection approach, demonstrating interpretability across diverse data types.

Contribution

It presents novel binary matrix factorization algorithms leveraging dictionary learning adapted for binary data, emphasizing speed, scalability, and online applicability.

Findings

Effective at producing interpretable factorizations

Suitable for online binary matrix factorization

Addresses model selection with MDL principle

Abstract

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for over thirty years, especially within the field of data mining. Dictionary learning refers to a family of methods for learning overcomplete basis (also called frames) in order to efficiently encode samples of a given type; this area, now also about twenty years old, was mostly developed within the signal processing field. In this work we propose two binary matrix factorization methods based on a binary adaptation of the dictionary learning paradigm to binary matrices. The proposed algorithms focus on speed and scalability; they work with binary factors combined with bit-wise operations and a few auxiliary integer ones. Furthermore, the methods are readily applicable to online binary matrix factorization. Another important issue in matrix factorization is the choice of rank for the factors; we address this model selection problem with an efficient method based on the Minimum Description Length principle. Our preliminary results show that the proposed methods are effective at producing interpretable factorizations of various data types of different nature.