Decomposition of Boolean multi-relational data with graded relations

Decomposition (or factorization) of Boolean multi-relation data, i.e. data in the form of Boolean matrices, together with relation between them, containing zeros and ones only, received a considerable attention in data mining research. The main aim is to find new variables-factors-hidden in data that explain data. The main advantage of Boolean data is interpretability. In this paper we argue that considering only Boolean data can be limiting. Especially the relation between input matrices is not necessarily of a Boolean nature. Usually this relation represents linkages to some degree, e.g. how much a user likes or dislikes a movie. Using Boolean method for such data-data must be somehow binarized first-leads to a loss of information. First, we reformulate decomposition problem for multi-relational data with ordinal relations. Then we propose a new algorithm for such data along with an experimental evaluation.