J. Blanc-Talon et al. (Eds.): ACIVS 2005, LNCS 3708, pp. 146 – 153, 2005. © Springer-Verlag Berlin Heidelberg 2005 An Alternative Fuzzy Compactness and Separation Clustering Algorithm Miin-Shen Yang 1,* and Hsu-Shen Tsai 2 1 Department of Applied Mathematics, Chung Yuan Christian University Chung-Li 32023, Taiwan msyang@math.cycu.edu.tw 2 Department of Management Information System, Takming College Taipei 11451, Taiwan Abstract. This paper presents a fuzzy clustering algorithm, called an alternative fuzzy compactness & separation (AFCS) algorithm that is based on an exponen- tial-type distance function. The proposed AFCS algorithm is more robust than the fuzzy c-means (FCM) and the fuzzy compactness & separation (FCS) pro- posed by Wu et al. (2005). Some numerical experiments are performed to as- sess the performance of FCM, FCS and AFCS algorithms. Numerical results show that the AFCS has better performance than the FCM and FCS from the robust point of view. Keywords: Fuzzy clustering algorithms; Fuzzy c-means (FCM); Fuzzy com- pactness & separation (FCS); Alternative fuzzy compactness & separation (AFCS); Exponential-type distance; Robust; Noise. 1 Introduction Cluster analysis is a method for clustering a data set into most similar groups in the same cluster and most dissimilar groups in different clusters. It is a branch in statisti- cal multivariate analysis and an unsupervised learning in pattern recognition. Since Zadeh [14] proposed fuzzy sets that produced the idea of partial memberships to clus- ters, fuzzy clustering has been widely studied and applied in a variety of substantive areas (see Baraldi and Blonda [1], Bezdek [2], Hoppner et al. [7] and Yang [12]). In fuzzy clustering literature, the fuzzy c-means (FCM) clustering algorithm and its variations are the most used methods. Because the clustering results obtained using FCM are roughly spherical with simi- lar volumes, many fuzzy clustering algorithms such as the Gustafson-Kessel (G-K) algorithm (Gustafson and Kessel [5]), the minimum scatter volume (MSV) and mini- mum cluster volume (MCV) algorithms (Krishnapuram and Kim [8]), the unsuper- vised fuzzy partition-optimal number of classes (UFP-ONC) algorithm (Gath and Geva [4]), Lp-norm generalization (Hathaway et al. [6]) and more generalized-type FCM (Yu and Yang [13]) were proposed to extend the FCM. However, most of these algorithms are based on a within-cluster scatter matrix with a compactness measure. Recently, Wu et al. [11] proposed a novel fuzzy clustering algorithm, called the fuzzy compactness & separation (FCS) algorithm. The FCS objective function is based on a