Interpretable Clustering Ensembles Using Binary Matrix Factorization

Abstract

The combination of multiple clustering solutions used to obtain accurate and novel output has attracted attention in data clustering research. Despite the success of clustering ensembles, there are still several fundamental limiting issues including the lack of a unified formalized problem formulation and an intuitive interpretation of the resulting solution. We formulate the clustering ensemble problem as a binary matrix factorization imposing assumptions of a binary structure on the resulting matrices. In such a framework, every data object is assigned to its representative ensemble centroid allowing for interpretation and validation of the consensus clustering results. We demonstrate that the formulated problem can be efficiently solved by means of iterative rank-one binary matrix approximation and apply the Proximus algorithm proposing an effective initialization scheme. The evaluation of the proposed clustering ensemble method demonstrates its efficacy on synthetic and real problems.