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Counterexamples to convergence theorem of maximum-entropy clustering algorithm 被引量：6

Counterexamples to convergence theorem of maximum-entropy clustering algorithm
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摘要 In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases. In this paper, we surveyed the development of maximum-entropy clustering algorithm, pointed out that the maximum-entropy clustering algorithm is not new in essence, and constructed two examples to show that the iterative sequence given by the maximum-entropy clustering algorithm may not converge to a local minimum of its objective function, but a saddle point. Based on these results, our paper shows that the convergence theorem of maximum-entropy clustering algorithm put forward by Kenneth Rose et al. does not hold in general cases.
作者 于剑 石洪波 黄厚宽 孙喜晨 程乾生
机构地区 School of Computer and Information Technology Department of Information Science
出处 《Science in China(Series F)》 2003年第5期321-326,共6页 中国科学（F辑英文版）
关键词 ENTROPY fixed point clustering algorithm convergence. entropy, fixed point, clustering algorithm, convergence.
分类号 TP18 [自动化与计算机技术—控制理论与控制工程]
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参考文献9

  • 1[1]Rose, K., Gurewtiz, E., Fox, G., A deterministic annealing approach to clustering, Pattern Recognition Letters, 1990, 11: 589-594.
  • 2[2]Karayiannis, N. B., MECA: Maximum entropy clustering algorithm, in Proc. IEEE Int. Conf. Fuzzy Syst., Orlando, FL, June 26-29, 1994, 630-635.
  • 3[3]Li, R._P., Mukaidono, M., A maximum entropy approach to fuzzy clustering, Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems, Yokohama, Japan, March 20-24, 1995, 2227-2232.
  • 4[4]Karayiannis, N. B., Fuzzy partition entropies and entropy constrained fuzzy clustering algorithms, J. Intell. Fuzzy Syst., 1997, 5(2): 103-111.
  • 5[5]Miyamoto, S., Mukaidono, M., Fuzzy c-means as a regularization and maximum entropy approach, Proc. of the 7th International Fuzzy Systems Association World Congress, Vol. II, June 25-30, Prague, Chech, 1997, 86-92.
  • 6[6]Karayiannis, N. B., An axiomatic approach to soft learning vector quantization and clustering, IEEE Trans. on Neural Networks, 1999, 10(5): 1153-1165.
  • 7[7]Miyamoto, S., Umayahara, K., Two methods of fuzzy c-means and classification functions, Proc. of 6th Conf. of the International Federation of Classification Societies, July 21-24, Roma, Italy, 1998, 105-110.
  • 8[8]Zhang Zhihua, Zheng Nanning, Shi Gang, Maximum-entropy clustering algorithm and its global convergence analysis, Science in China, Ser. E, 2001, 44(1): 89-101.
  • 9[9]Rose, K., Deterministic annealing for clustering, compression, classification, regression, and related optimization problems, Proceedings of the IEEE, 1998, 86(11): 2210-2239.

同被引文献30

  • 1张志华,郑南宁,史罡.Maximum-entropy clustering algorithm and its global convergence analysis[J].Science China(Technological Sciences),2001,44(1):89-101. 被引量：3
  • 2张敏,于剑.基于划分的模糊聚类算法[J].软件学报,2004,15(6):858-868. 被引量：179
  • 3彭宁嵩,杨杰,刘志,张风超.Mean-Shift跟踪算法中核函数窗宽的自动选取[J].软件学报,2005,16(9):1542-1550. 被引量：165
  • 4Rose K,Gurewtiz E,Fox G.A deterministic annealing approach to clustering. Pattern Recognition . 1990
  • 5Karayiannis N B.An axiomatic approach to soft learn ingvector quantization and clustering. IEEE ACM Transactions on Networking . 1999
  • 6Karayiannis N,B Meca.Maximum entropy clustering algorithm. Proc IEEE Conf Fuzzy Syst . 1994
  • 7Li R P,Mukaidon M.A maximum entropy approach to fuzzy clustering. Proceedings of the 4th IEEE International Conference onFuzzy System . 1995
  • 8Karayiannis N B.Fuzzy partition entropies and entropy constrained fuzzy clustering algorithms. J Intell Fuzzy Syst . 1997
  • 9Miyamoto S,Mukaidono M.Fuzzy c-means as aregularization and maximum entropy approach. Proceedings of the 7th International Fuzzy SystemsAssociation World Congress (IFSA’97), Prague: Chech . 1997
  • 10Miyamoto S,,Umayahara K.Two methods of fuzzy c-meansand classification functions. Proceedings of the 6thConference of the International Federation of ClassificationSocieties . 1998

引证文献6

二级引证文献233

Science in China(Series F)
2003年 第5期

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