Fuzzy and Crisp Gaussian Kernel-Based Co-Clustering With Automatic Width Computation

Abstract

Co-clustering algorithms separate a data matrix in blocks, by grouping, simultaneously, objects according to variables and variables according to objects, and has gained widespread attention in the last few years. At the same time, kernel-based clustering is a well-developed topic of research. These methods can efficiently group nonlinear clusters through transformations in the data space. The research involving co-clustering and kernel function is still in the initial stage. In this article, we proposed the first kernel-based algorithms that can learn the width hyperparameter of the Gaussian kernel automatically for hard and fuzzy co-clustering. The main advantages of the proposed methods are that there is no need for a previous additional step to tune the width hyperparameter, and we consider width hyperparameters that are the same for all clusters, varying only with respect to objects or variables (global methods), or they can also vary across clusters (local methods). As a consequence, our methods can rescale the objects and variables separately, according to their distribution, and in the local case, also according to the distribution in each variable cluster and object cluster, respectively. Experiments conducted over 14 real datasets, and compared with traditional clustering methods and previous state-of-the-art co-clustering algorithms, showed the efficiency of the proposed algorithms.

Authors

José Nataniel A. de Sá, Centro de Informática, Universidade Federal de Pernambuco, Recife-PE, Brazil

Marcelo R.P. Ferreira, Departamento de Estatistica, Centro de Ciências Exatas e da Natureza, Universidade Federal da Paraiba, João Pessoa – PB, Brazil

Francisco de A.T. de Carvalho, Centro de Informática, Universidade Federal de Pernambuco, Recife-PE, Brazil