Local convergence analysis of a grouped variable version of coordinate descent
Journal of Optimization Theory and Applications
A valuation of state of object based on weighted Mahalanobis distance
Pattern Recognition
Unsupervised Optimal Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Computing Surveys (CSUR)
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
A Similarity-Based Robust Clustering Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering Using a Similarity Measure Based on Shared Near Neighbors
IEEE Transactions on Computers
Similarity measures in fuzzy rule base simplification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Robust clustering methods: a unified view
IEEE Transactions on Fuzzy Systems
A class of constrained clustering algorithms for object boundary extraction
IEEE Transactions on Image Processing
A self-organizing network for hyperellipsoidal clustering (HEC)
IEEE Transactions on Neural Networks
Using the clustering coefficient to guide a genetic-based communities finding algorithm
IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
On the convergence of some possibilistic clustering algorithms
Fuzzy Optimization and Decision Making
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Clustering algorithms divide up a dataset into a set of classes/clusters, where similar data objects are assigned to the same cluster. When the boundary between clusters is ill defined, which yields situations where the same data object belongs to more than one class, the notion of fuzzy clustering becomes relevant. In this course, each datum belongs to a given class with some membership grade, between 0 and 1. The most prominent fuzzy clustering algorithm is the fuzzy c-means introduced by Bezdek (Pattern recognition with fuzzy objective function algorithms, 1981), a fuzzification of the k-means or ISODATA algorithm. On the other hand, several research issues have been raised regarding both the objective function to be minimized and the optimization constraints, which help to identify proper cluster shape (Jain et al., ACM Computing Survey 31(3):264---323, 1999). This paper addresses the issue of clustering by evaluating the distance of fuzzy sets in a feature space. Especially, the fuzzy clustering optimization problem is reformulated when the distance is rather given in terms of divergence distance, which builds a bridge to the notion of probabilistic distance. This leads to a modified fuzzy clustering, which implicitly involves the variance---covariance of input terms. The solution of the underlying optimization problem in terms of optimal solution is determined while the existence and uniqueness of the solution are demonstrated. The performances of the algorithm are assessed through two numerical applications. The former involves clustering of Gaussian membership functions and the latter tackles the well-known Iris dataset. Comparisons with standard fuzzy c-means (FCM) are evaluated and discussed.