Journal ArticleDOI
Recent convergence results for the fuzzy c-means clustering algorithms
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TLDR
The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FCM in a brief and unified way.Abstract:
One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FCM) have often been used to solve certain types of clustering problems. During the last two years several new local results concerning both numerical and stochastic convergence of FCM have been found. Numerical results describe how the algorithms behave when evaluated as optimization algorithms for finding minima of the corresponding family of fuzzy c-means functionals. Stochastic properties refer to the accuracy of minima of FCM functionals as approximations to parameters of statistical populations which are sometimes assumed to be associated with the data. The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FCM in a brief and unified way.read more
Citations
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Journal ArticleDOI
Segmentation of brain electrical activity into microstates: model estimation and validation
TL;DR: A precise mathematical formulation of the model for evoked potential recordings is presented, where the microstates are represented as normalized vectors constituted by scalp electric potentials due to the underlying generators.
Journal ArticleDOI
A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain
Lawrence O. Hall,A. Bensaid,Laurence P. Clarke,R.P. Velthuizen,Martin S. Silbiger,James C. Bezdek +5 more
TL;DR: For a more complex segmentation problem with tumor/edema or cerebrospinal fluid boundary, inconsistency in rating among experts was observed, with fuzzy c-means approaches being slightly preferred over feedforward cascade correlation results.
Journal ArticleDOI
Fuzzy clustering with partial supervision
Witold Pedrycz,J. Waletzky +1 more
TL;DR: This paper presents a problem of fuzzy clustering with partial supervision, i.e., unsupervised learning completed in the presence of some labeled patterns, and proposes two specific learning scenarios of complete and incomplete class assignment of the labeled patterns.
References
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Book
Pattern Recognition with Fuzzy Objective Function Algorithms
TL;DR: Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with, becomes what you need to get.
Journal ArticleDOI
A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters
TL;DR: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space; in both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squarederror criterion function.
A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters
TL;DR: In this paper, two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space, and the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the LSE criterion function.