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A line symmetry based genetic clustering technique: encoding lines in chromosomes

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Abstract

The current paper proposes a new genetic clustering technique using the concepts of line symmetry for assigning points to different clusters. The symmetrical line of a particular cluster is determined automatically using the search capability of genetic algorithms. This line is then used to compute the amount of symmetry of any point within a given cluster. The lines are encoded in the form of a chromosome. Mutation and crossover operations are modified in such a way so that those can help the GA to search for the symmetrical line efficiently. A way of measuring the amount of line symmetry of a given point with respect to a symmetrical line is also thoroughly described which is used further to assign points to different clusters. This in turn produces the partitioning corresponding to a particular chromosome. The compactness of this obtained partitioning is calculated using the line symmetry based measurement and is further used as the objective function of the chromosome. The proposed method is able to detect clusters having line symmetry property. The effectiveness of the proposed technique (LSGA) is shown for 12 artificial and two real-life data sets. Results are compared with those obtained by existing genetic algorithm with line symmetry based clustering technique (GALS), genetic algorithm based K-means clustering technique (GAK-means), average linkage clustering technique, spectral clustering technique, expectation maximization based clustering technique, fuzzy-GA and point-GA clustering techniques.

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Notes

  1. http://bioinformatics.oxfordjournals.org/cgi/content/abstract.

  2. http://www.cs.ucsb.edu/~wychen/download/.

References

  1. Everitt BS (1993) Cluster analysis, 3rd edn. Halsted Press, New York

    MATH  Google Scholar 

  2. Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323. doi:10.1145/331499.331504

    Article  Google Scholar 

  3. Gan G, Ma C, Wu J (2007) Data clustering: theory, algorithms, and applications (ASA-SIAM Series on Statistics and Applied Probability). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA

  4. Xu R, Wunsch D II (2005) Survey of clustering algorithms. Trans Neur Netw 16(3):645–678

    Article  Google Scholar 

  5. Borgelt C (2005/2006) Prototype-based classification and clustering. PhD thesis, University of Magdeburg, Germany

  6. Zabrodsky H, Peleg S, Avnir D (1995) Symmetry as a continuous feature. IEEE Trans Pattern Anal Mach Intell 17(12):1154–1166

    Article  Google Scholar 

  7. Attneave F (1995) Symmetry information and memory for pattern. Am J Psychol 68:209–222

    Article  Google Scholar 

  8. Bandyopadhyay S, Saha S (2013) Unsupervised classification—similarity measures, classical and metaheuristic approaches, and applications. Springer, Berlin

    MATH  Google Scholar 

  9. Jolliffe I (1986) Principal component analysis. Springer, Berlin

    Book  Google Scholar 

  10. Bandyopadhyay S, Saha S (2007) GAPS: a clustering method using a new point symmetry based distance measure. Pattern Recognit 40:3430–3451

    Article  Google Scholar 

  11. Saha S, Spandana R, Ekbal A, Bandyopadhyay S (2015) Simultaneous feature selection and symmetry based clustering using multiobjective framework. Appl Soft Comput 29:479–486

    Article  Google Scholar 

  12. Saha S, Bandyopadhyay S (2010) A symmetry based multiobjective clustering technique for automatic evolution of clusters. Pattern Recognit 43(3):738–751

    Article  Google Scholar 

  13. Saha S, Ekbal A, Gupta K, Bandyopadhyay S (2013) Gene expression data clustering using a multiobjective symmetry based clustering technique. Comput Biol Med 43(11):1965–1977

    Article  Google Scholar 

  14. Saha S, Bandyopadhyay S (2011) On principle axis based line symmetry clustering techniques. Memet Comput 3(2):129–144

    Article  Google Scholar 

  15. Saha S, Bandyopadhyay S (2009) A new line symmetry distance and its application to data clustering. J Comput Sci Technol 24(3):544–556

    Article  Google Scholar 

  16. Chung KL, Lin KS (2006) An efficient line symmetry-based k-means algorithm. Pattern Recognit Lett 27(7):765–772

    Article  Google Scholar 

  17. Chung KL, Lin JS (2007) Faster and more robust point symmetry-based k-means algorithm. Pattern Recognit 40(2):410–422

    Article  Google Scholar 

  18. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor

    Google Scholar 

  19. Hruschka ER, Campello RJGB, Freitas AA, De Carvalho ACPLF (2009) A survey of evolutionary algorithms for clustering. Trans Syst Man Cybern Part C 39(2):133–155

    Article  Google Scholar 

  20. Campello R, Hruschka E, Alves V (2009) On the efficiency of evolutionary fuzzy clustering. J Heuristics 15(1):43–75

    Article  Google Scholar 

  21. Krishna K, Narasimha Murty M (1999) Genetic k-means algorithm. Trans Syst Man Cyber Part B 29(3):433–439

    Article  Google Scholar 

  22. Murthy C, Chowdhury N (1996) In search of optimal clusters using genetic algorithms. Pattern Recognit Lett 17(8):825–832

    Article  Google Scholar 

  23. Krovi R (1992) Genetic algorithms for clustering: a preliminary investigation, vol 4. In: Proceedings of the 25th Hawaii Int. Conference on System Sciences, pp 540–544

  24. Sheikh RH, Raghuwanshi M, Jaiswal AN (2008) Genetic algorithm based clustering: a survey. In: International conference on emerging trends in engineering and technology, pp 314–319

  25. Bandyopadhyay S, Maulik U (2002) An evolutionary technique based on k-means algorithm for optimal clustering in RN. Inf Sci Appl 146(1–4):221–237

    Article  Google Scholar 

  26. Pakhira MK, Bandyopadhyay S, Maulik U (2005) A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification. Fuzzy Sets Syst 155(2):191–214

    Article  MathSciNet  Google Scholar 

  27. Scheunders P (1997) A genetic c-means clustering algorithm applied to color image quantization. Pattern Recognit 30(6):859–866

    Article  Google Scholar 

  28. Lucasius CB, Dane AD, Kateman G (1993) On k-medoid clustering of large data sets with the aid of a genetic algorithm: background, feasibility and comparison. Anal Chim Acta 287:647–669

    Article  Google Scholar 

  29. Sheng W, Liu X (2004) A hybrid algorithm for k-medoid clustering of large data sets. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, Portland, 19–23 June 2004, pp 77–82

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

    Article  Google Scholar 

  31. Chen WY, Song Y, Bai H, Lin CJ, Chang EY (2008) PSC: parallel spectral clustering. http://www.cs.ucsb.edu/~wychen/sc

  32. Bandyopadhyay S (2012) Genetic algorithms for clustering and fuzzy clustering. Wiley Interdisc Rev Data Min Knowl Discov 2(3):285

    Article  Google Scholar 

  33. Bandyopadhyay S, Murthy CA, Pal SK (1995) Pattern classification using genetic algorithms. Pattern Recognit Lett 16:801–808

    Article  Google Scholar 

  34. Srinivas M, Patnaik L (1994) Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans Syst Man Cybern 24(4):656–667

    Article  Google Scholar 

  35. Ben-Hur A, Guyon I (2003) Detecting stable clusters using principal component analysis in methods in molecular biology. Humana Press, New York

    Google Scholar 

  36. Bandyopadhyay S, Maulik U (2002) Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognit 2:1197–1208

    Article  Google Scholar 

  37. Gonzalez RC, Woods RE (1992) Digital image processing. Addison-Wesley, Massachusetts

    Google Scholar 

  38. Bandyopadhyay S, Saha S (2008) A point symmetry based clustering technique for automatic evolution of clusters. IEEE Trans Knowl Data Eng 20(11):1–17

    Article  Google Scholar 

  39. Handl J, Knowles J (2007) An evolutionary approach to multiobjective clustering. IEEE Trans Evol Comput 11(1):56–76

    Article  Google Scholar 

  40. Bandyopadhyay S, Pal SK (2007) Classification and learning using genetic algorithms: applications in bioinformatics and web intelligence. Natural computing series. Springer, Berlin

    MATH  Google Scholar 

  41. Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  42. García S, Herrera F (2008) An extension on “statistical comparisons of classifiers over multiple data sets” for all pairwise comparisons. J Mach Learn Res 9:2677–2694

    MATH  Google Scholar 

  43. Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32:675–701

    Article  Google Scholar 

  44. Nemenyi PB (1963) Distribution-free multiple comparisons. PhD thesis

  45. Saha S, Bandyopadhyay S (2008) Application of a new symmetry based cluster validity index for satellite image segmentation. IEEE Geosci Rem Sens Lett 5(2):166–170

    Article  Google Scholar 

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  1. Department of Computer Science and Engineering, Indian Institute of Technology Patna, Patna, India

    Sriparna Saha

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  1. Sriparna Saha
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Correspondence to Sriparna Saha.

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Saha, S. A line symmetry based genetic clustering technique: encoding lines in chromosomes. Int. J. Mach. Learn. & Cyber. 9, 1963–1986 (2018). https://doi.org/10.1007/s13042-017-0680-x

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