Clustering Spherical Shells by a Mini-Max Information Algorithm

  • Xulei Yang
  • Qing Song
  • Wenbo Zhang
  • Zhimin Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3852)


We focus on spherical shells clustering by a mini-max information (MMI) clustering algorithm based on mini-max optimization of mutual information (MI). The minimization optimization leads to a mass constrained deterministic annealing (DA) approach, which is independent of the choice of the initial data configuration and has the ability to avoid poor local optima. The maximization optimization provides a robust estimation of probability soft margin to phase out outliers. Furthermore, a novel cluster validity criteria is estimated to determine an optimal cluster number of spherical shells for a given set of data. The effectiveness of MMI algorithm for clustering spherical shells is demonstrated by experimental results.


Cluster Algorithm Mutual Information Spherical Shell Cluster Number Structural Risk Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Blahut, R.E.: Computation of Channel Capacity and Rate-Distortion Functions. IEEE Tran. on Information Theory 18, 460–473 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blahut, R.E.: Princinple and practice of information theory. Addison-Wesley, Reading (1987)Google Scholar
  3. 3.
    Dave, R.N.: Fuzzy shell-clustering and applications to circle detection in digital images. Int. J. General Systems 16, 343–355 (1990)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dave, R.N.: Validating fuzzy partitions obtained through c-shells clustering. Pattern Recognition Letters 17, 613–623 (1996)CrossRefGoogle Scholar
  5. 5.
    Krishnapuram, R., Nasraoui, O., Frigui, H.: The fuzzy c-spherical shells algorithm: a new approach. IEEE Trans. Neural Networks 3, 663–671 (1992)CrossRefGoogle Scholar
  6. 6.
    Man, Y., Gath, I.: Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering. IEEE Trans. Pattern Analysis and Machine Intelligence 16, 855–861 (1994)CrossRefGoogle Scholar
  7. 7.
    Rose, K., Gurewitz, E., Fox, G.C.: Statistical mechanics and phase transitions in clustering. Physical Review letters 65, 945–948 (1990)CrossRefGoogle Scholar
  8. 8.
    Rose, K.: Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc. of IEEE, 86, 2210–2239 (1998)Google Scholar
  9. 9.
    Song, Q.: A robust information clustering algorithm. Neural Computation 17, 2672–2698 (2005)zbMATHCrossRefGoogle Scholar
  10. 10.
    Vapnik, V.N.: Statistical Learning Theory. John Wiley and Sons, NY (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xulei Yang
    • 1
  • Qing Song
    • 1
  • Wenbo Zhang
    • 1
  • Zhimin Wang
    • 1
  1. 1.School of Electrical and Electronics EngineeringNanyang Technological UniversitySingapore

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