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A New Line Symmetry Distance and Its Application to Data Clustering

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Abstract

In this paper, at first a new line-symmetry-based distance is proposed. The properties of the proposed distance are then elaborately described. Kd-tree-based nearest neighbor search is used to reduce the complexity of computing the proposed line-symmetry-based distance. Thereafter an evolutionary clustering technique is developed that uses the new line-symmetry-based distance measure for assigning points to different clusters. Adaptive mutation and crossover probabilities are used to accelerate the proposed clustering technique. The proposed GA with line-symmetry-distance-based (GALSD) clustering technique is able to detect any type of clusters, irrespective of their geometrical shape and overlapping nature, as long as they possess the characteristics of line symmetry. GALSD is compared with the existing well-known K-means clustering algorithm and a newly developed genetic point-symmetry-distance-based clustering technique (GAPS) for three artificial and two real-life data sets. The efficacy of the proposed line-symmetry-based distance is then shown in recognizing human face from a given image.

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References

  1. Jain A K, Murthy M N, Flynn P J. Data clustering: A review. ACM Computing Surveys, Nov. 1999, 31(3): 264–323.

    Article  Google Scholar 

  2. Berg M D, Kreveld M V, Overmars M, Schwarzkopf O. Cluster Analysis for Application. Academic Press, 1973.

  3. Duda R O, Hart P E. Pattern Classification and Scene Analysis. New York: Wiley, 1973.

    MATH  Google Scholar 

  4. Tou J T, Gonzalez R C. Pattern Recognition Principles. Reading: Addison-Wesley, 1974.

    MATH  Google Scholar 

  5. Everitt B S, Landau S, Leese M. Cluster Analysis. London: Arnold, 2001.

    Google Scholar 

  6. Jain A K, Dubes R C. Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  7. Kov̈esi B, Boucher J M, Saoodi S. Stochastic k-means algorithm for vector quantization. Pattern Recognition Letters, 2001, 22(6/7): 603–610.

    Article  Google Scholar 

  8. Kanungo T, Mount D, Netanyahu N S, Piatko C, Silverman R, Wu A. An efficient k-means clustering algorithm: Analysis and implementation. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2002, 24(7): 881–892.

    Article  Google Scholar 

  9. Likas A, Vlassis N, Verbeek J J. The global k-means clustering algorithm. Pattern Recognition, 2003, 36(2): 451–461.

    Article  Google Scholar 

  10. Charalampidis D. A modified k-means algorithm for circular invariant clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, December 2005, 27(12): 1856–1865.

    Article  Google Scholar 

  11. Dave R N, Bhaswan K. Adaptive fuzzy c-shells clustering and detection of ellipses. IEEE Transaction on Neural Networks, September 1992, 3(5): 643–662.

    Article  Google Scholar 

  12. Krishnapuram R, Nasraoui O, Frigui H. The fuzzy c-spherical shells algorithm: A new approach. IEEE Transaction on Neural Networks, September 1992, 3(5): 663–671.

    Article  Google Scholar 

  13. Gath I, Gev A B. Unsupervised optimal fuzzy clustering. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1989, 11: 773–780.

    Article  Google Scholar 

  14. Gustafson D E, Kessel W C. Fuzzy clustering with a fuzzy covariance matrix. In Proc. IEEE Conf. Decision Contr., Ft. Lauderdale, USA, December 12–14, 1979, pp.761–766.

  15. Dave R N. Use of the adaptive fuzzy clustering algorithm to detect lines in digital images. Intell. Robots Compt. Vision VIII, 1989, 1192(2): 600–611.

    Google Scholar 

  16. Man Y, Gath I. Detection and separation of ring-shaped clusters using fuzzy clustering. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1994, 16(8): 855–861.

    Article  Google Scholar 

  17. Höppner F. Fuzzy shell clustering algorithms in image processing: Fuzzy c-rectangular and 2-rectangular shells. IEEE Transaction Fuzzy Systems, Nov. 1997, 5(4): 599–613.

    Article  Google Scholar 

  18. Bandyopadhyay S. An automatic shape independent clustering technique. Pattern Recognition, 2004, 37(1): 33–45.

    Article  Google Scholar 

  19. Bandyopadhyay S, Saha S. GAPS: A clustering method using a new point symmetry-based distance measure. Pattern Recog., 2007, 40(12): 3430–3451.

    Article  MATH  Google Scholar 

  20. Attneave F. Symmetry information and memory for pattern. Am. J. Psychology, 1995, 68(2): 209–222.

    Article  Google Scholar 

  21. Su M C, Chou C H. A competitive learning algorithm using symmetry. IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, 1999, E82-A(4): 680–687.

    Google Scholar 

  22. Su M C, Chou C H. A modified version of the k-means algorithm with a distance based on cluster symmetry. IEEE Transactions Pattern Analysis and Machine Intelligence, 2001, 23(6): 674–680.

    Article  Google Scholar 

  23. Chou C H, Su M C, Lai E. Symmetry as a new measure for cluster validity. In Proc. the 2nd WSEAS Int. Conf. Scientific Computation and Soft Computing, Crete, Greece, 2002, pp.209–213.

  24. Chung K L, Lin J S. Faster and more robust point symmetry-based k-means algorithm. Pattern Recogn., 2007, 40(2): 410–422.

    Article  MATH  MathSciNet  Google Scholar 

  25. M de Berg, M van Kreveld, M Overmars, O Schwarzkopf. Computational Geometry: Algorithms and Applications. 2nd Edition, Springer-Verlag, 2000, http://www.cs.uu.nl/geobook/.

  26. Saha S, Bandyopadhyay S. A genetic clustering technique using a new line symmetry based distance measure. In Proc. the Fifth International Conference on Advanced Computing and Communications (ADCOM'07), IEEE Computer Society, Guwahati, India, 2007, pp.365–370.

  27. Maulik U, Bandyopadhyay S. Genetic algorithm based clustering technique. Pattern Recog., 2000, 33(9): 1455–1465.

    Article  Google Scholar 

  28. Holland J H. Adaptation in Natural and Artificial Systems. AnnArbor: The University of Michigan Press, 1975.

    Google Scholar 

  29. Bhuyan J N, Raghavan V V, Venkatesh K E. Genetic algorithm for clustering with an ordered representation. In Proc. Fourth International Conference on Genetic Algorithm, Morgan Kaufmann, San Diego, CA, USA, July 1991, pp.408–415.

  30. Babu G P, Murty M N. A near-optimal initial seed value selection for k-means algorithm using genetic algorithm. Pattern Recognition Letters, 1993, 14(10): 763–769.

    Article  MATH  Google Scholar 

  31. Krishna K, Murty M N. Genetic k-means algorithm. IEEE Transactions on Systems, Man, and Cybernetics — Part B, June 1999, 29(3): 433–439.

    Article  Google Scholar 

  32. Bandyopadhyay S, Maulik U. Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognition, 2002, 35(6): 1197–1208.

    Article  MATH  Google Scholar 

  33. Gonzalez R C, Woods R E. Digital Image Processing. Massachusetts: Addison-Wesley, 1992.

    Google Scholar 

  34. Mount D M, Arya S. ANN: A library for approximate nearest neighbor searching. 2005, http://www.cs.umd.edu/~mount/ANN.

  35. Srinivas M, Patnaik L. Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics, April 1994, 24(4): 656–667.

    Article  Google Scholar 

  36. Bentley J L, Weide B W, Yao A C. Optimal expected-time algorithms for closest point problems. ACM Transactions on Mathematical Software, 1980, 6(4): 563–580.

    Article  MATH  MathSciNet  Google Scholar 

  37. Friedman J H, Bently J L, Finkel R A. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 1977, 3(3): 209–226.

    Article  MATH  Google Scholar 

  38. Harmon L D, Hunt W F. Automatic recognition of human face profiles. Computer Graphics and Image Processing, April 1977, 6(2): 135–156.

    Article  Google Scholar 

  39. Zhao W, Chellappa R, Phillips P J, Rosenfeld A. Face recognition: A literature survey. ACM Computing Surveys, 2003, 35(4): 399–458.

    Article  Google Scholar 

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Authors and Affiliations

  1. Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India

    Sriparna Saha (Student Member, IEEE) & Sanghamitra Bandyopadhyay (Senior Member, IEEE)

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  1. Sriparna Saha
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  2. Sanghamitra Bandyopadhyay
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Correspondence to Sriparna Saha.

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Saha, S., Bandyopadhyay, S. A New Line Symmetry Distance and Its Application to Data Clustering. J. Comput. Sci. Technol. 24, 544–556 (2009). https://doi.org/10.1007/s11390-009-9244-1

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  • DOI: https://doi.org/10.1007/s11390-009-9244-1

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