This Article 
 Bibliographic References 
 Add to: 
A Modified Version of the K-Means Algorithm with a Distance Based on Cluster Symmetry
June 2001 (vol. 23 no. 6)
pp. 674-680

Abstract—In this paper, we propose a modified version of the K-means algorithm to cluster data. The proposed algorithm adopts a novel nonmetric distance measure based on the idea of “point symmetry.” This kind of “point symmetry distance” can be applied in data clustering and human face detection. Several data sets are used to illustrate its effectiveness.

[1] A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Englewood Cliffs, N.J.: Prentice Hall, 1988.
[2] R.O. Duda and P.E. Hart, Pattern Classification and Scene Analysis. New York: Wiley, 1973.
[3] J. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum, 1981.
[4] J.A Hartigan,Clustering Algorithms, John Wiley and Sons, New York, N.Y., 1975.
[5] J. Tou and R. Gonzalez, Pattern Recognition Principles. Reading, Mass.: Addison-Wesley, 1974.
[6] E. Ruspini, “A New Approach to Clustering,” Information Control, vol. 15, no. 1, pp. 22-32, July 1969.
[7] G.H. Ball and D.I. Hall, “Some Fundamental Concepts and Synthesis Procedures for Pattern Recognition Preprocessors,” Proc. Int'l Conf. Microwaves, Circuit Theory, and Information Theory, pp. 281-297, Sept. 1964.
[8] T. Kohonen, “The“Neural”Phonetic Typewriter,” IEEE Computer, vol. 27, no. 3, pp. 11-12, Mar. 1988.
[9] T. Kohonen, "Self-Organization and Associated Memory," Berlin Heidelberg. New York: Springer-Verlag, 1988.
[10] J. Mao and A.K. Jain, “A Self-Organizing Network for Hyperellipsoidal Clustering,” IEEE Trans. Neural Networks, vol. 7, pp. 16-29, Jan. 1996.
[11] G. Carpenter and S. Grossberg, “A Massively Parallel Architecture for a Self-Organizing Neural Pattern Recognition Machine,” Computer Vision, Graphics and Image Understanding, vol. 37, pp. 54–115, 1987.
[12] G.A. Carpenter and S. Grossberg, “ART2: Self-Organization of Stable Category Recognition Codes for Analog Input Patterns,” Application Optics, vol. 26, no. 23, pp. 4919-4930, Dec. 1987.
[13] C.T. Zahn, “Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters,” IEEE Trans. Computer, vol. 20, pp. 68-86, Jan. 1971.
[14] D. Blostein and N. Ahuja, “Shape From Texture: Integrating Texture-Element Extraction and Surface Estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1233-1251, Dec. 1989.
[15] M.C. Su, N. DeClaris, and T.K. Liu, “Application of Neural Networks in Cluster Analysis,” Proc. IEEE Int'l Conf. System, Man, and Cybernetics, pp. 1-6, 1997.
[16] M.C. Su and H.T. Chang, “Self-Organizing Neural Networks for Data Projection,” Proc. Fifth Int'l Computer Science Conf., pp. 206-215, Dec. 1999.
[17] F. Attneave, “Symmetry Information and Memory for Pattern,” Am. J. Psychology, vol. 68, pp. 209-222, 1995.
[18] W. Miller, Symmetry Groups and Their Applications. London: Academic Press, 1972.
[19] H. Weyl, Symmetry. Princeton, NJ.: Princeton Univ. Press, 1952.
[20] D. Reisfeld, H. Wolfsow, and Y. Yeshurun, “Context-Free Attentional Operators: the Generalized Symmetry Transform,” Int'l J. Computer Vision, vol. 14, pp. 119-130, 1995.
[21] H. Zabrodsky, S. Peleg, and D. Avnir, "Symmetry as a Continuous Feature," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 1,154-1,166, 1995.
[22] K. Kanatani, “Comments on“Symmetry as a Continuous Feature”,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 3, pp. 246-247, Mar. 1997.
[23] M.C. Su and C.H. Chou, “A Competitive Learning Algorithm Using Symmetry,” IEICE Trans. Fundamentals of Electronics, Communications, and Computer Sciences, vol. E82-A, no. 4, pp. 680-687, Apr. 1999.
[24] R.C. Gonzalez and R.E. Woods, Digital Image Processing, Addison-Wesley, New York, 1993.

Index Terms:
Data clustering, pattern recognition, k-means algorithm, face detection.
Mu-Chun Su, Chien-Hsing Chou, "A Modified Version of the K-Means Algorithm with a Distance Based on Cluster Symmetry," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 674-680, June 2001, doi:10.1109/34.927466
Usage of this product signifies your acceptance of the Terms of Use.