Intelligent Data Analysis 4 (2000) 241–253 241 IOS Press Unsupervised fuzzy learning and cluster seeking A. Bouroumi ∗ , M. Limouri and A. Essa¨ ıd Laboratoire LCS, Facult´ e des Sciences, Universit ´ e Mohammed V – Agdal, B.P. 1014, Av. Ibn Battouta, Rabat, Morocco Received 1 November 1999 Revised 13 December 1999 Accepted 6 January 2000 Abstract. This paper presents a new approach to unsupervised pattern classification. The classification scheme consists of two main stages. The first one is an unsupervised fuzzy learning procedure, which allows, using a similarity measure and a corresponding threshold, to seek clusters within a set of totally unlabeled samples. It provides, for each detected cluster, a good initial prototype as well as the membership degree of each sample. The second stage is an optimization procedure involving the fuzzy c-means (FCM) algorithm. Both procedures are repeated for different values of the similarity threshold, and three validity criteria are used to assess and rank the quality of all resulting partitions. The effectiveness of this approach is demonstrated, for different parameter values, on both artificial and real test data. Keywords: Unsupervised learning, fuzzy clustering, pattern recognition, cluster validity 1. Introduction Clustering is a very useful tool that has many important applications in a variety of scientific and engineering disciplines such as psychology, biology, medicine, communications, computer vision, and remote sensing [5]. The object of cluster analysis is to organize a set of unlabeled input data into a number of natural groups (clusters) such that elements within each group must be as similar as possible and dissimilar from those of other groups. Various clustering algorithms proposed in the literature [4,9, 14,23] can be classified into two main categories: Hierarchical and Partitional. Hierarchical clustering algorithms provide a sequence of nested partitions. They do not need to specify the number of clusters a priori and problems due to initialization and local minima do not arise in hierarchical clustering. However, these methods cannot always separate overlapping clusters and cannot incorporate a priori knowledge about the global shape or size of clusters. Moreover, hierarchical clustering is static in the sense that objects are definitely assigned to clusters and cannot move to other clusters. On the other hand, partitional clustering algorithms provide a single partition. They are essentially prototype-based and can be divided into two classes: crisp (or hard) and fuzzy. Hard clustering assigns each data point to a unique cluster, assuming well-defined boundaries between the clusters [9,23]. In contrast, fuzzy clustering assigns class-membership degrees to each sample vector rather than assigning * Corresponding author. Tel. and Fax: +212 7 77 39 98; E-mail: bouroumi@ieee.org. 1088-467X/00/$8.00  2000 – IOS Press. All rights reserved