Convergence of alternating optimization
Neural, Parallel & Scientific Computations
New modifications and applications of fuzzy C-means methodology
Computational Statistics & Data Analysis
Identification of piecewise affine systems by means of fuzzy clustering and competitive learning
Engineering Applications of Artificial Intelligence
Unsupervised Pixel Classification in Satellite Imagery: A Two-stage Fuzzy Clustering Approach
Fundamenta Informaticae
Dealing with non-metric dissimilarities in fuzzy central clustering algorithms
International Journal of Approximate Reasoning
Generalized fuzzy C-means clustering algorithm with improved fuzzy partitions
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Density-weighted fuzzy c-means clustering
IEEE Transactions on Fuzzy Systems
An information-theoretic fuzzy C-spherical shells clustering algorithm
Fuzzy Sets and Systems
Applying the possibilistic c-means algorithm in kernel-induced spaces
IEEE Transactions on Fuzzy Systems - Special section on computing with words
Image segmentation based on FCM with mahalanobis distance
ICICA'10 Proceedings of the First international conference on Information computing and applications
Link speed estimation and incident detection using clustering and neuro-fuzzy methods
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Estimation of link speed using pattern classification of GPS probe car data
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part II
Unsupervised Pixel Classification in Satellite Imagery: A Two-stage Fuzzy Clustering Approach
Fundamenta Informaticae
Fuzzy partition based soft subspace clustering and its applications in high dimensional data
Information Sciences: an International Journal
Colon cell image segmentation based on level set and kernel-based fuzzy clustering
ICIC'13 Proceedings of the 9th international conference on Intelligent Computing Theories and Technology
On the convergence of some possibilistic clustering algorithms
Fuzzy Optimization and Decision Making
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In this paper, we revisit the convergence and optimization properties of fuzzy clustering algorithms, in general, and the fuzzy c-means (FCM) algorithm, in particular. Our investigation includes probabilistic and (a slightly modified implementation of) possibilistic memberships, which will be discussed under a unified view. We give a convergence proof for the axis-parallel variant of the algorithm by Gustafson and Kessel, that can be generalized to other algorithms more easily than in the usual approach. Using reformulated fuzzy clustering algorithms, we apply Banach's classical contraction principle and establish a relationship between saddle points and attractive fixed points. For the special case of FCM we derive a sufficient condition for fixed points to be attractive, allowing identification of them as (local) minima of the objective function (excluding the possibility of a saddle point).