Binary Matrix Factorization with Applications

An interesting problem in Nonnegative Matrix Factorization (NMF) is to factorize the matrix X which is of some specific class, for example, binary matrix. In this paper, we extend the standard NMF to Binary Matrix Factorization (BMF for short): given a binary matrix X, we want to factorize X into two binary matrices W,H (thus conserving the most important integer property of the objective matrix X ) satisfying X WH. Two algorithms are studied and compared. These methods rely on a fundamental boundedness property of NMF which we propose and prove. This new property also provides a natural normalization scheme that eliminates the bias of factor matrices. Experiments on both synthetic and real world datasets are conducted to show the competency and effectiveness of BMF.