Fuzzy Co-Clustering Algorithms Based on Fuzzy Relational Clustering and TIBA Imputation

Abstract

In this paper, two types of fuzzy co-clustering algorithms are proposed. First, it is shown that the base of the objective function for the conventional fuzzy co-clustering method is very similar to the base for entropy-regularized fuzzy nonmetric model. Next, it is shown that the non-sense clustering problem in the conventional 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 this discussion, a method is proposed applying entropy-regularized fuzzy nonmetric model after all dissimilarities among rows and columns are set to some values using a TIBA imputation technique. Furthermore, since relational fuzzy c-means is similar to fuzzy nonmetric model, in the sense that both methods are designed for homogeneous relational data, a method is proposed applying entropy-regularized relational fuzzy c-means after imputing all dissimilarities among rows and columns with TIBA. Some numerical examples are presented for the proposed methods.