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Sequential Competitive Learning and the Fuzzy c-Means Clustering Algorithms

Sequential Competitive Learning and the Fuzzy c-Means Clustering Algorithms,10.1016/0893-6080(95)00094-1,Neural Networks,Nikhil R. Pal,James C. Bezdek

Sequential Competitive Learning and the Fuzzy c-Means Clustering Algorithms   (Citations: 28)
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Several recent papers have described sequential competitive learning algorithms that are curious hybrids of algorithms used to optimize the fuzzy c-means (FCM) and learning vector quantization (LVQ) models. First, we show that these hybrids do not optimize the FCM functional. Then we show that the gradient descent conditions they use are not necessary conditions for optimization of a sequential version of the FCM functional. We give a numerical example that demonstrates some weaknesses of the sequential scheme proposed by Chung and Lee. And finally, we explain why these algorithms may work at times, by exhibiting the stochastic approximation problem that they unknowingly attempt to solve. Copyright © 1996 Published by Elsevier Science Ltd
Journal: Neural Networks , vol. 9, no. 5, pp. 787-796, 1996
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    • ...Self-organization mapping and competitive learning are a class of efficient algorithms and there have been some famous algorithms, such as Sequential Hard C-means(SHCM) [1], Hard Cmeans (HCM), Rival Penalized Competitive Learning (RPCL) [2], Frequency Sensitive Competitive Learning (FSCL), Kohonen’s SOFM [3], FFSCL, Neural Gas Network [4], Learning Vector Quantization(LVQ) [5], Lloyd’s method LGB [6], fuzzy competitive learning [7]...

    Tao Guanet al. An Online Multiscale Clustering Algorithm for Irregular Data Sets

    • ...For the sake of clarity and easy comprehension, we need to remark that although the competition among clusters treated in this paper is the same as in case of traditional competitive algorithms that stand at the basis of Kohonen’s (1990) networks, the algorithms investigated here radically differ from those in the sense that conventional competitive clustering models do not optimize quadratic objective functions (Pal et al. 1996; Bezdek et ...

    László Szilágyiet al. Analytical and numerical evaluation of the suppressed fuzzy c-means al...

    • ...VQ algorithms [1-3, 8, 11, 13, 15, 19, 26], there are relatively few methods that address the issue of fuzzy vector quantization (FVQ) [5, 23] or fuzzy learning vector quantization (FLVQ) [6, 7, 12, 22]...
    • ...First, fuzzy clustering is able to model the uncertainty involved in a training data set [5, 12]...
    • ...representative fuzzy clustering algorithm is the fuzzy cmeans method [12]...

    George E. Tsekouraset al. Fast fuzzy vector quantization

    • ...Sequential hard C-means(SHCM) is an earlier CL model in pattern clustering and the online version of hard C-means (HCM)[5], [6], [7]...
    • ...For example, in the unsupervised competitive learning algo­ rithm [6], [Pj(l) = 1 if Dij = Ilxi -Pjl12 = min k Ilx i-PkI1 2, and ° otherwise...

    Tao Guanet al. Self-Branching Competitive Learning for image segmentation

    • ...Table 2 reveals that averagely, both fuzzy SOM and fuzzy ART2 can provide more adequate recognition than fuzzy c-means [40]...

    R. J. Kuoet al. Part family formation through fuzzy ART2 neural network

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