  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.
