Clustering Based on Multiple Criteria for LVQ and K-Means Algorithm

Fujiki Morii; Kazuko Kurahashi

doi:10.20965/jaciii.2009.p0360

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JACIII Vol.13 No.4 pp. 360-365

doi: 10.20965/jaciii.2009.p0360

(2009)

Paper:

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Clustering Based on Multiple Criteria for LVQ and K-Means Algorithm

Fujiki Morii^* and Kazuko Kurahashi^**

^*Dept. of Information and Computer Sciences, Nara Women's University, Nara 630-8506, Japan

^**FUJIFILM Corporation, Medical Systems Business DIV., Kanagawa 238-8538, Japan

Received:

November 24, 2008

Accepted:

March 2, 2009

Published:

July 20, 2009

Keywords:

clustering, LVQ, k-means algorithm, multiple criteria, split and merge procedure

Abstract

When classifying linearly separable data by learning vector quantization (LVQ) or K-Means algorithm (KMA), we cannot necessarily obtain satisfactory classification results for bad selections of initial cluster centers and differences among the distributions of class data. In this paper, to realize reliable classification, clustering based on multiple criteria for LVQ and KMA is proposed, and its performance is provided. To obtain suitable cluster centers, KMA with the split and merge procedure proposed by Kaukoranta et al. is introduced to minimize the squared-error distortion. LVQ using those cluster centers as initial ones is applied to the data, and Κ clusters are produced. Introducing a criterion of whether each cluster reveals unimodality, subclusters split by KMA for clusters having no unimodality are merged into appropriate neighboring clusters except one subcluster, and the validity of the classification result is checked.

Cite this article as:

F. Morii and K. Kurahashi, “Clustering Based on Multiple Criteria for LVQ and K-Means Algorithm,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.4, pp. 360-365, 2009.

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References

[1] R. O. Duda, P. E. Hart, and D. G. Stork, “Pattern Classification (2nd edition),” John Wiley & Sons, INC., 2001.
[2] A. K. Jain and R. C. Dubes, “Algorithms for Clustering Data,” Prentice-Hall, Englewood Cliffs, NJ, 1988.
[3] A. D. Gordon, “Classification (2nd Edition),” Chapman & Hall/CRC, 1999.
[4] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, NY, 1981.
[5] J. MacQueen, “Some Methods for Classification and Analysis of X_k Multivariate Observations,” Proc. 5th Berkeley Symp. on Math. Stat. and Prob. 1, Univ. of California Press, Berkeley and Los Angelessplitting measure, pp. 281-297, 1967.
[6] Y. Linde, A. Buzo, and R. M. Gray, “An Algorithm for Vector Quantizer Design,” IEEE Trans. Commun., Vol.28, pp. 84-95, 1980.
[7] T. Kohonen, “Self-Organizing Maps, 2nd Ed.,” Springer, Berlin, 1997.
[8] N. R. Pal, J. C. Bezdek, and C.-K. Tsao, “Generalized Clustering Networks and Kohonen's Self-Organizing Scheme,” IEEE Trans. Neural Network, Vol.4, No.4, pp. 549-557, 1993.
[9] S. Miyamoto, “Introduction of Cluster Analysis:Theory and Applications of Fuzzy Clustering,” Morikita-Syuppan, 1999 (in Japanese).
[10] T. Kaukoranta, P. Franti, and O. Nevalainen, “Iterative split-and-merge algorithm for vector quantization codebook generation,” Optical Engineering Vol.37, No.10, pp. 2726-2732, 1998.
[11] F. Morii and K. Kurahashi, “Clustering by the K-means algorithm using a split and merge procedure,” Proc. of SCIS and ISIS 2006, pp. 1767-1770, 2006.
[12] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Numerical Recipes in C,” Cambridge University Press, 1988.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] R. O. Duda, P. E. Hart, and D. G. Stork, “Pattern Classification (2nd edition),” John Wiley & Sons, INC., 2001.

[2] [2] A. K. Jain and R. C. Dubes, “Algorithms for Clustering Data,” Prentice-Hall, Englewood Cliffs, NJ, 1988.

[3] [3] A. D. Gordon, “Classification (2nd Edition),” Chapman & Hall/CRC, 1999.

[4] [4] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, NY, 1981.

[5] [5] J. MacQueen, “Some Methods for Classification and Analysis of X_k Multivariate Observations,” Proc. 5th Berkeley Symp. on Math. Stat. and Prob. 1, Univ. of California Press, Berkeley and Los Angelessplitting measure, pp. 281-297, 1967.

[6] [6] Y. Linde, A. Buzo, and R. M. Gray, “An Algorithm for Vector Quantizer Design,” IEEE Trans. Commun., Vol.28, pp. 84-95, 1980.

[7] [7] T. Kohonen, “Self-Organizing Maps, 2nd Ed.,” Springer, Berlin, 1997.

[8] [8] N. R. Pal, J. C. Bezdek, and C.-K. Tsao, “Generalized Clustering Networks and Kohonen's Self-Organizing Scheme,” IEEE Trans. Neural Network, Vol.4, No.4, pp. 549-557, 1993.

[9] [9] S. Miyamoto, “Introduction of Cluster Analysis:Theory and Applications of Fuzzy Clustering,” Morikita-Syuppan, 1999 (in Japanese).

[10] [10] T. Kaukoranta, P. Franti, and O. Nevalainen, “Iterative split-and-merge algorithm for vector quantization codebook generation,” Optical Engineering Vol.37, No.10, pp. 2726-2732, 1998.

[11] [11] F. Morii and K. Kurahashi, “Clustering by the K-means algorithm using a split and merge procedure,” Proc. of SCIS and ISIS 2006, pp. 1767-1770, 2006.

[12] [12] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Numerical Recipes in C,” Cambridge University Press, 1988.

Clustering Based on Multiple Criteria for LVQ and K-Means Algorithm

Fujiki Morii* and Kazuko Kurahashi**

Fujiki Morii^* and Kazuko Kurahashi^**