Collaborative Fuzzy Clustering of Variational Bayesian Generative Topographic Mapping

Abstract

In this paper, we propose a Collaborative Clustering method based on Variational Bayesian Generative Topographic Mapping (VBGTM). To do so, we first propose a method that combines VBGTM and Fuzzy c-means (FCM). Collaborative clustering is useful to achieve interaction between different sources of information for the purpose of revealing underlying structures and regularities within data sets. It can be treated as a process of consensus building where we attempt to reveal a structure that is common across all sets of data. VBGTM was introduced as a variational approximation of Generative Topographic Mapping (GTM) to control data overfitting. It provides an analytical approximation to the posterior probability of the latent variables and the distribution of the input data in the latent space. It can be effectively applied to visualize and explore properties of the data. But when the number of latent points is large, similar units need to be grouped (i.e., clustered) to facilitate quantitative analysis of the map and the data. We use FCM to determine the prototypes as well as the resultant clusters and the corresponding membership functions of the input data, based on the latent variables obtained from VBGTM. So, by combining the two algorithms, we develop a method that can do visualization and clustering at the same time. We observe that the hybrid method (F-VBGTM) performs very well in terms of many cluster-validity indexes.