Benchmarking validity procedures for unsupervised fuzzy pattern classification

In this paper, we present some numerical results of an experimental study of the problem of automatic determination of the number of clusters in unsupervised fuzzy clustering. The study was conducted using the well-known fuzzy c-means algorithm and four associated validity criteria that we applied to illustrative examples of artificial and real data sets. We will mainly focus on the risk of validating bad solutions or rejecting good ones. This risk is inherent to traditional validity procedures, which generally make use of a single criterion, and a multi-criteria procedure is proposed in order to avoid it in real-world applications.