Toward quality assessment of Boolean matrix factorizations

Boolean matrix factorization has become an important direction in data analysis. In this paper, we examine the question of how to assess the quality of Boolean matrix factorization algorithms. We critically examine the current approaches, and argue that little attention has been paid to this problem so far and that a systematic approach to it is missing. We regard quality assessment of factorization algorithms as a multifaceted problem, identify major views with respect to which quality needs to be assessed, and present various observations on the available algorithms in this regard. Due to its primary importance, we concentrate on the quality of collections of factors computed from data, present a method to assess this quality, and evaluate this method by experiments.