An Algorithm for the Multi-Relational Boolean Factor Analysis based on Essential Elements

The Multi-Relational Boolean factor analysis is a method from the family of matrix decomposition methods which enables us an- alyze binary multi-relational data, i.e. binary data which are composed from many binary data tables interconnected via relation. In this paper we present a new Boolean matrix factorization algorithm for this kind of data, which use the new knowledge from the theory of the Boolean factor analysis, so-called essential elements. We show on real dataset that uti- lizing essential elements in the algorithm leads to better results in terms of quality and the number of obtained multi-relational factors.