A New Boolean Matrix Factorization Algorithm Based on Cardano's Method

Han Xiao, Tsuyoshi Migita, Norikazu Takahashi

Abstract: A two-phase Boolean matrix factorization algorithm was recently developed by other authors. In the first phase of their algorithm, a nonnegative optimization problem is solved using an iterative method like the well-known multiplicative update rule for nonnegative matrix factorization. In the second phase, the nonnegative solution obtained in the first phase is thresholded to generate a binary solution. In this paper, we present a new update rule for the first phase, which makes use of Cardano’s method for solving cubic equations. We then prove that the update rule has the global convergence property in the sense of Zangwill. We also show through experiments using some benchmark datasets that the new algorithm is superior to the original one in terms of the number of iterations in the first phase and the quality of binary solutions.