Sparse Boolean Matrix Factorizations

Abstract

Matrix factorizations are commonly used methods in data mining. When the input data is Boolean, replacing the standard matrix multiplication with Boolean matrix multiplication can yield more intuitive results. Unfortunately, finding a good Boolean decomposition is known to be computationally hard, with even many sub-problems being hard to approximate. Many real-world data sets are sparse, and it is often required that also the factor matrices are sparse. This requirement has motivated many new matrix decomposition methods and many modifications of the existing methods. This paper studies how Boolean matrix factorizations behave with sparse data: can we assume some sparsity on the factor matrices, and does the sparsity help with the computationally hard problems. The answer to these problems is shown to be positive.