Validity Measure For Fuzzy Clustering Research Articles

Fuzzy clustering algorithms incorporating local information for change detection in remotely sensed images

In this paper we have used two fuzzy clustering algorithms, namely fuzzy c-means (FCM) and Gustafson–Kessel clustering (GKC) along with local information for unsupervised change detection in multitemporal remote sensing images. In conventional FCM and GKC no spatio-contextual information is taken into account and thus the result is not so much robust to small changes. Since the pixels are highly correlated with their neighbors in image space (spatial domain), incorporation of local information enhances the performance of the algorithms. In this work we have introduced a new technique for incorporation of local information. Change detection maps are obtained by separating the pixel-patterns of the difference image into two groups. Hybridization of FCM and GKC with two other optimization techniques, genetic algorithm (GA) and simulated annealing (SA), is made to further enhance the performance. To show the effectiveness of the proposed technique, experiments are conducted on two multispectral and multitemporal remote sensing images. Two fuzzy cluster validity measures (Xie–Beni and fuzzy hypervolume) have been used to quantitatively evaluate the performance. Results are compared with those of existing state of the art Markov random field (MRF) and neural network based algorithms and found to be superior. The proposed technique is less time consuming and unlike MRF does not require any a priori knowledge of distributions of changed and unchanged pixels.

Fuzzy Bayesian validation for cluster analysis of yeast cell-cycle data

Clustering for the analysis of the genes organizes the patterns into groups by the similarity of the dataset and has been used for identifying the functions of the genes in the cluster and analyzing the functions of unknown genes. Since the genes usually belong to multiple functional families, fuzzy clustering methods are more appropriate than the conventional hard clustering methods which assign a sample to only one group. In this paper, a Bayesian-like validation method selecting a fuzzy partition is proposed to evaluate the fuzzy partitions effectively. The theoretical interpretation of the obtained memberships is beyond the scope of this paper, and an empirical evaluation of the proposed method is conducted by comparing to the four representative conventional fuzzy cluster validity measures in four well-known datasets. Analysis of yeast cell-cycle data follows to evaluate the proposed method.

Fuzzy clustering as a means of selecting representative conformers and molecular alignments.

This paper describes the first application of fuzzy c-means clustering for the selection of representatives from assemblies of conformations or alignments. In case of alignments, their quality is taken into account using a weighted c-means scheme, developed in this work. The performance of fuzzy cluster validity measures, such as compactness, partition function, and entropy, are studied on several examples, but the visual 3D representation of data points is shown to be most beneficial in determining the optimum number of clusters. Fuzzy clustering is expected to perform better than crisp clustering methods in cases where there are a significant number of "outliers", such as in molecular dynamics simulations and molecular alignments.

A validity measure for fuzzy 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>