LI Kai, GAO Yan. Fuzzy Clustering with the Structural α-Entropy[J]. Chinese Journal of Electronics, 2018, 27(6): 1118-1125. doi: 10.1049/cje.2018.04.004
Citation: LI Kai, GAO Yan. Fuzzy Clustering with the Structural α-Entropy[J]. Chinese Journal of Electronics, 2018, 27(6): 1118-1125. doi: 10.1049/cje.2018.04.004

Fuzzy Clustering with the Structural α-Entropy

doi: 10.1049/cje.2018.04.004
Funds:  This work is support by the National Natural Science Foundation of China (No.61375075), the Natural Science Foundation of Hebei Province (No.F2018201060), and the Natural Science Foundation of Hebei University (No.799207217074).
  • Received Date: 2017-03-30
  • Rev Recd Date: 2017-10-24
  • Publish Date: 2018-11-10
  • We study fuzzy clustering with the structural α-entropy and present a unified framework for fuzzy clustering with fuzzy entropy, which can be regarded fuzzy clustering with fuzzy entropy as its special case. Then, aiming at weighting exponent m equal to the structural α-entropy index α in the presented unified framework, we obtain the fuzzy membership degrees and cluster centers using Lagrange method. Further, we propose the Structural α-entropy based fuzzy c-means (SEFCM) algorithm. Moreover, to solve clustering of the complicated data, we also present the Structural α-entropy based kernel fuzzy c-means (SEKFCM) algorithm. In experiment, some University of California Irvine (UCI) data sets and synthetic data sets are used to test the performance of the presented algorithms and the role of the structural α-entropy. The experimental results show that the presented algorithms obtain better clustering result.
  • loading
  • K.A. Jain, “Data clustering: 50 years beyond k-means”, Pattern Recognition Letters, Vol.31, No.8, pp.651-666, 2010.
    H.J. Jia, S.F. Ding, M.J. Du, et al., “Approximate normalized cuts without eigen-decomposition”, Information Sciences, Vol.374, pp.135-150, 2016.
    S.F. Ding, J. Zhang, H.J. Jia, et al., “An adaptive density data stream clustering algorithm”, Cognitive Computation, Vol.8, No.1, pp.30-38, 2016.
    J. Zhou, L. Chen, C.L.P. Chen, et al., “Fuzzy clustering with the entropy of attribute weights”, Neurocomputing, Vol.198, pp.125-34, 2016.
    M.J. Du, S.F. Ding and Y. Xue, “A robust density peaks clustering algorithm using fuzzy neighborhood”, International Journal of Machine Learning and Cybernetics, DOI: 10.1007/s13042-017-0636-1, 2017.
    J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, USA, pp.65-80, 1981.
    S.F. Ding, M.J. Du and H. Zhu, “Survey on granularity clustering”, Cognitive Neurodynamics, Vol.9, No.6, pp.561-572, 2015.
    N.B. Karayiannis, “MECA: Maximum entropy clustering algorithm”, Proc. of IEEE World Congress on Computational Intelligence, Orlando, USA, pp.630-635, 1994.
    R.P. Li and M. Mukaidon, “A maximum entropy approach to fuzzy clustering”, Proc. of IEEE International Conference on Fuzzy System, Yokohama, Japan, Vol.4, pp.2227-2232, 1995.
    D. Tran and M. Wagner, “Fuzzy entropy clustering”, Proc. of The Ninth IEEE International Conference on Fuzzy Systems, San Antonio, USA, Vol.1, pp.152-157, 2000.
    S.F. Ding, M.J. Du, T.F. Sun, et al., “An entropy-based density peaks clustering algorithm for mixed type data employing fuzzy neighborhood”, Knowledge-Based Systems, Vol.133, No.1, pp.294-313, 2017.
    J. Yu, Q.S. Cheng and H.K. Huang, “Analysis of the weighting exponent in the FCM”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.34, No.1, pp.634-639, 2004.
    W. Pedrycz, A. Amato, V.D. Lecce, et al., “Fuzzy clustering with partial supervision in organization and classification of digital images”, IEEE Transactions on Fuzzy Systems, Vol.16, No.4, pp.1008-1026, 2008.
    C. Wei and C. Fahn, “The multisynapse neural network and its application to fuzzy clustering”, IEEE Transactions on Neural Networks, Vol.13, No.3, pp.600-618, 2002.
    J. Yu and P.W. Hao, “Comments on the multisynapse neural network and its application to fuzzy clustering”, IEEE Transaction on Neural Networks, Vol.16, No.3, pp.777-778, 2005.
    K. Mizutani and S. Miyamoto, “Possibilistic approach to kernelbased fuzzy c-means clustering with entropy regularization”, Second International Conference on Modeling Decisions for Artificial Intelligence, Tsukuba, Japan, Vol.3558, pp.144-155, 2005.
    D. Graves and W. Pedrycz, “Kernel-based fuzzy clustering and fuzzy clustering: A comparative experimental study”, Fuzzy Sets and Systems, Vol.161, No.4, pp.522-543, 2010.
    D. Swagatam and S. Sudeshna, “Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm”, Information Sciences, Vol.180, pp.1237-1256, 2010.
    S.R. Kannan, S. Ramathilagam, A. Stthya, et al., “Effective fuzzy c-means based kernel function in segmenting medical images”, Computers in Biology and Medicine, Vol.40, No.6, pp.572-579, 2010.
    R.P.F. Marcelo and D.A.T. Francisco, “Kernel-based hard clustering methods in the feature space with automatic variable weighting”, Pattern Recognition, Vol.47, No.9, pp.3082-3095, 2014.
    R.P.F. Marcelo, D.A.T. Francisco and C.S. Eduardo, “Kernelbased hard clustering methods with kernelization of the metric and automatic weighting of the variables”, Pattern Recognition, Vol.51, pp.310-321, 2016.
    A. Renyi, “On measures of entropy and information”, Proc. of the Fourth Berkeley Symposium on Mathematics Statistics and Probability, Berkeley, USA, Vol.1, pp.547-561, 1961.
    J.N. Kapur, “Generalised entropy of order α and β”, The Mathematics Seminar, Vol.4, pp.78-94, 1967.
    J. Havrda and F. Charvat, “Quantification method of classification processes: Concept of structural α-entropy”, Kybernetika, Vol.3, No.4, pp.30-35, 1967.
    D. Dua and E. Karra Taniskidou, “UCI Machine Learning Repository”,, Irvine, School of Information and Computer Science, CA: University of California, 2017-2-20.
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (142) PDF downloads(270) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint