Unsupervised Optimal Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural networks and the bias/variance dilemma
Neural Computation
A new cluster validity index for the fuzzy c-mean
Pattern Recognition Letters
Minimum-Entropy Data Partitioning Using Reversible Jump Markov Chain Monte Carlo
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Constrained Clustering as an Optimization Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A cluster validity index for fuzzy clustering
Pattern Recognition Letters
Robust clustering methods: a unified view
IEEE Transactions on Fuzzy Systems
On cluster validity for the fuzzy c-means model
IEEE Transactions on Fuzzy Systems
A Modified Deterministic Annealing Algorithm for Robust Image Segmentation
Journal of Mathematical Imaging and Vision
Cancer classification using kernelized fuzzy C-means
FS'08 Proceedings of the 9th WSEAS International Conference on Fuzzy Systems
A comprehensive validity index for clustering
Intelligent Data Analysis
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Cluster validity has been widely used to evaluate the fitness of partitions produced by clustering algorithms. This paper presents a new validity, which is called the Vapnik---Chervonenkis-bound (VB) index, for data clustering. It is estimated based on the structural risk minimization (SRM) principle, which optimizes the bound simultaneously over both the distortion function (empirical risk) and the VC-dimension (model complexity). The smallest bound of the guaranteed risk achieved on some appropriate cluster number validates the best description of the data structure. We use the deterministic annealing (DA) algorithm as the underlying clustering technique to produce the partitions. Five numerical examples and two real data sets are used to illustrate the use of VB as a validity index. Its effectiveness is compared to several popular cluster-validity indexes. The results of comparative study show that the proposed VB index has high ability in producing a good cluster number estimate and in addition, it provides a new approach for cluster validity from the view of statistical learning theory.