A survey of fuzzy clustering algorithms for pattern recognition. I

Abstract

Clustering algorithms aim at modeling fuzzy (i.e., ambiguous) unlabeled patterns efficiently. Our goal is to propose a theoretical framework where the expressive power of clustering systems can be compared on the basis of a meaningful set of common functional features. Part I of this paper reviews the following issues related to clustering approaches found in the literature: relative (probabilistic) and absolute (possibilistic) fuzzy membership functions and their relationships to the Bayes rule, batch and on-line learning, prototype editing schemes, growing and pruning networks, modular network architectures, topologically perfect mapping, ecological nets and neuro-fuzziness. From this discussion an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed as a unifying framework in the comparison of clustering systems. Moreover, a set of functional attributes is selected for use as dictionary entries in the comparison of clustering algorithms, which is the subject of part II of this paper.

GeCiM: A Novel Generalized Approach to C-Means Clustering

“…2. The other key thing that deserves a remark is the fact, that pure PCM (β = 0) is quite unstable, which means in most cases it leads to poor quality partitions (as indicated in [2]), but sometimes it finds a set of prototypes offering 149 correct decisions. One such case is depicted in eq.…”

“…The influence of fuzzy logic also reached the theory of clustering, causing a division between crisp and fuzzy partitioning. The relaxation of the probabilistic constraint in fuzzy clustering techniques gave birth to the absolute or possibilistic fuzzy clustering [2]. The most popular (in the sense of most frequently used) examples for these c-means clustering categories are the kmeans or hard c-means (in the followings: HCM), fuzzy c-means (FCM) [6], and possibilistic c-means (PCM) [15] algorithms, probably because of their easily understandable and implementable alternating optimization (AO) solution.…”

“…PCM emerged by the relaxation of the constraint that normalizes the degrees of membership, which caused several differences. Possibilistic memberships are context-insensitive, that is, they are only influenced by the distance of the given input vector from the given cluster prototype, and is not influenced by other clusters [2]. PCM reportedly tends to produce coincident clusters [3], as its objective function treats each cluster independently.…”

Fuzzy Clustering Algorithms and Validity Indices for Distributed Data

“…The literature on fuzzy clustering is extensive and several studies have been carried out with different characteristics and for different purposes during the past years [2,[6][7][8][9]. One of the most used fuzzy clustering algorithms is the Fuzzy c-Means (FCM) [5,10].…”

Color Reduction Using the Combination of the Kohonen Self-Organized Feature Map and the Gustafson-Kessel Fuzzy Algorithm

“…Techniques in this category attempt to find the optimal palette using vector classifiers like the Growing Neural Gas (GNG) [6], Adaptive Color Reduction [7], FOSART [8][9][10][11], Fuzzy ART [12,13] and FCM [14].…”