On FNM-based and RFCM-based fuzzy co-clustering algorithms

In this paper, some types of fuzzy co-clustering algorithms are proposed. First, it is shown that the common base of the objective function for quadratic-regularized fuzzy co-clustering and entropy-regularized fuzzy co-clustering is very similar to the base for quadratic-regularized fuzzy nonmetric model and entropy-regularized fuzzy nonmetric model, respectively. Next, it is shown that the above mentioned non-sense clustering problem in previously proposed fuzzy co-clustering algorithms is identical to that in fuzzy nonmetric model algorithms, in the case that all dissimilarities among rows and columns are zero. Based on the above discussion, a method is proposed applying fuzzy nonmetric model after all dissimilarities among rows and columns are non-zero. Furthermore, since relational fuzzy c-means is similar to fuzzy nonmetric model, in the sense that both methods are designed for homogenous relational data, a method is proposed applying relational fuzzy c-means after setting all dissimilarities among rows and columns to some non-zero value. An illustrative numerical example is presented for the proposed methods.