A method for extension of generative topographic mapping for fuzzy clustering

Abstract

In this paper, a new method for fuzzy clustering is proposed that combines generative topographic mapping (GTM) and Fuzzy c-means (FCM) clustering. GTM is used to generate latent variables and their posterior probabilities. These two provide the distribution of the input data in the latent space. FCM determines the seeds of clusters, as well as the resultant clusters and the corresponding membership functions of the input data, based on the latent variables obtained from GTM. Experiments are conducted to compare the results obtained using FCM and the Gustafson-Kessel (GK) algorithm with the proposed method in terms of four cluster-validity indexes. Using simulated and benchmark data sets, it is observed that the hybrid method (GTMFCM) performs better than FCM and GK algorithms in terms of these indexes. It is also found that the superiority of GTMFCM over FCM and GK algorithms becomes more pronounced with the increase in the dimensionality of the input data set.