Monographs on statistics and applied probability

Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Especially, in the last years the availability of huge transactional and experimental data sets and the arising requirements for data mining created needs for clustering algorithms that scale and can be applied in diverse domains.

This paper introduces the fundamental concepts of clustering while it surveys the widely known clustering algorithms in a comparative way. Moreover, it addresses an important issue of clustering process regarding the quality assessment of the clustering results. This is also related to the inherent features of the data set under concern. A review of clustering validity measures and approaches available in the literature is presented. Furthermore, the paper illustrates the issues that are under-addressed by the recent algorithms and gives the trends in clustering process.

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On Clustering Validation Techniques

Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni (1991), and extended Xie-Beni indexes, and the Fukuyama-Sugeno index (1989) Limit analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this Of the indexes tested, the Xie-Beni index provided the best response over a wide range of choices for the number of clusters, (2-10), and for m from 101-7 Finally, our calculations suggest that the best choice for m is probably in the interval [15, 25], whose mean and midpoint, m=2, have often been the preferred choice for many users of FCM >

On cluster validity for the fuzzy c-means model

Color image segmentation: advances and prospects

Survey: Graph clustering

The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed. >

X.L. Xie

Papers

A validity measure for fuzzy clustering