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Keywords
(6)
Competitive Learning
Fuzzy C Mean
Fuzzy C Means Clustering
Learning Vector Quantization
Stochastic Approximation
Gradient Descent
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(1)
Pattern recognition with fuzzy objective function algorithms
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Sequential Competitive Learning and the Fuzzy cMeans Clustering Algorithms
Sequential Competitive Learning and the Fuzzy cMeans Clustering Algorithms,10.1016/08936080(95)000941,Neural Networks,Nikhil R. Pal,James C. Bezdek
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Sequential Competitive Learning and the Fuzzy cMeans Clustering Algorithms
(
Citations: 28
)
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Nikhil R. Pal
,
James C. Bezdek
,
Richard J. Hathaway
Several recent papers have described sequential
competitive learning
algorithms that are curious hybrids of algorithms used to optimize the fuzzy cmeans (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. 787796, 1996
DOI:
10.1016/08936080(95)000941
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Citation Context
(9)
...Selforganization mapping and competitive learning are a class of efficient algorithms and there have been some famous algorithms, such as Sequential Hard Cmeans(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 Guan
,
et 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 Szilágyi
,
et al.
Analytical and numerical evaluation of the suppressed fuzzy cmeans al...
...VQ algorithms [13, 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. Tsekouras
,
et al.
Fast fuzzy vector quantization
...Sequential hard Cmeans(SHCM) is an earlier CL model in pattern clustering and the online version of hard Cmeans (HCM)[5], [
6
], [7]...
...For example, in the unsupervised competitive learning algo rithm [
6
], [Pj(l) = 1 if Dij = Ilxi Pjl12 = min k Ilx iPkI1 2, and ° otherwise...
Tao Guan
,
et al.
SelfBranching Competitive Learning for image segmentation
...Table 2 reveals that averagely, both fuzzy SOM and fuzzy ART2 can provide more adequate recognition than fuzzy cmeans [
40
]...
R. J. Kuo
,
et al.
Part family formation through fuzzy ART2 neural network
References
(11)
Optimization of clustering criteria by reformulation
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Citations: 104
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R. J. Hathaway
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J. C. Bezdek
Journal:
IEEE Transactions on Fuzzy Systems  TFS
, vol. 3, no. 2, pp. 241245, 1995
Differential competitive learning for centroid estimation and phoneme recognition
(
Citations: 40
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SeongGon Kong
,
Bart Kosko
Journal:
IEEE Transactions on Neural Networks
, vol. 2, no. 1, pp. 118124, 1991
The irises of the gaspe peninsula
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E. Anderson
Local convergence analysis of a grouped variable version of coordinate descent
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J. C. Bezdek
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R. J. Hathaway
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Journal:
Journal of Optimization Theory and Applications  J OPTIMIZ THEOR APPL
, vol. 54, no. 3, pp. 471477, 1987
Fuzzy competitive learning
(
Citations: 73
)
Fulai Chung
,
Tong Lee
Journal:
Neural Networks
, vol. 7, no. 3, pp. 539551, 1994
Sort by:
Citations
(28)
An Online Multiscale Clustering Algorithm for Irregular Data Sets
Tao Guan
,
Yongling Yu
,
Tao Xue
Conference:
International Conference on Future Computer Sciences and Application  ICFCSA
, 2011
Analytical and numerical evaluation of the suppressed fuzzy cmeans algorithm: a study on the competition in cmeans clustering models
(
Citations: 1
)
László Szilágyi
,
Sándor M. Szilágyi
,
Zoltán Benyó
Journal:
Soft Computing  SOCO
, vol. 14, no. 5, pp. 495505, 2010
Fast fuzzy vector quantization
George E. Tsekouras
,
Dimitrios Darzentas
,
Ioanna Drakoulaki
,
Antonios D. Niros
Conference:
IEEE International Conference on Fuzzy Systems
, pp. 18, 2010
SelfBranching Competitive Learning for image segmentation
Tao Guan
,
Ling Ling Li
Published in 2010.
A new segmentation system for brain MR images based on fuzzy techniques
(
Citations: 22
)
S. R. Kannan
Journal:
Applied Soft Computing  ASC
, vol. 8, no. 4, pp. 15991606, 2008