Basic Consideration of Co-Clustering Based on Rough Set Theory

In the field of clustering, rough clustering, which is clustering based on rough set theory, is a promising approach for dealing with the certainty, possibility, and uncertainty of belonging of object to clusters. Generalized rough C-means (GRCM), which is a rough set-based extension of hard C-means (HCM; k-means), can extract the overlapped cluster structure by assigning objects to the upper areas of their relatively near clusters. Co-clustering is a useful technique for summarizing co-occurrence information between objects and items such as the frequency of keywords in documents and the purchase history of users. Fuzzy co-clustering induced by multinomial mixture models (FCCMM) is a statistical model-based co-clustering method and introduces a mechanism for adjusting the fuzziness degrees of both objects and items. In this paper, we propose a novel rough co-clustering method, rough co-clustering induced by multinomial mixture models (RCCMM), with reference to GRCM and FCCMM. RCCMM aims to appropriately extract the overlapped co-cluster structure inherent in co-occurrence information by considering the certainty, possibility, and uncertainty. Through numerical experiments, we verified whether the proposed method can appropriately extract the overlapped co-cluster structure.