A Fully-Unsupervised Possibilistic C-Means Clustering Algorithm

Abstract

In 1993, Krishnapuram and Keller first proposed possibilistic C-means (PCM) clustering by relaxing the constraint in fuzzy C-means of which memberships for a data point across classes sum to 1. The PCM algorithm tends to produce coincident clusters that can be a merit of PCM as a good mode-seeking algorithm, and so various extensions of PCM had been proposed in the literature. However, the performance of PCM and its extensions heavily depends on initializations and parameters selection with a number of clusters to be given a priori. In this paper, we propose a novel PCM algorithm, termed a fully unsupervised PCM (FU-PCM), without any initialization and parameter selection that can automatically find a good number of clusters. We start by constructing a generalized framework for PCM clustering that can be a generalization of most existing PCM algorithms. Based on the generalized PCM framework, we propose the new type FU-PCM so that the proposed FU-PCM algorithm is free of parameter selection and initializations without a given number of clusters. That is, the FU-PCM becomes a FU-PCM clustering algorithm. Comparisons between the proposed FU-PCM and other existing methods are made. The computational complexity of the FU-PCM algorithm is also analyzed. Some numerical data and real data sets are used to show these good aspects of FU-PCM. Experimental results and comparisons actually demonstrate the proposed FU-PCM is an effective parameter-free clustering algorithm that can also automatically find the optimal number of clusters.

Keywords

• Clustering
• fuzzy clustering
• possibilistic clustering
• fuzzy C-means (FCM)
• possibilistic C-means (PCM)
• fully-unsupervised PCM (FU-PCM)