Aggregation of multi-objective fuzzy symmetry-based clustering techniques for improving gene and cancer classification

Focus
  • 56 Downloads

Abstract

The current work reports about the application of a cluster ensemble approach in combining results produced by some multiobjective-based clustering techniques. Firstly, some multiobjective-based fuzzy clustering techniques are developed using the search capabilities of differential evolution and particle swarm optimization. Both these clustering techniques utilize a recently developed point symmetry-based distance for allocation of points to different clusters. The appropriate partitioning from a data set is identified by optimizing simultaneously two cluster quality measures, namely Xie–Beni index and FSym-index. First objective function uses Euclidean distance as a similarity measure, and the second objective function uses point symmetry-based distance in its computation. A set of trade-off solutions are produced by each of these clustering techniques on the final Pareto optimal front. Finally, this set of solutions are combined using a link-based cluster ensemble technique. The effectiveness of ensemble techniques is illustrated on partitioning some real-life gene expression and cancer data sets where automatic identification of set of genes or set of cancer tissues is a pressing issue. The potency of the ensemble techniques applied on both the multi-objective DE- and PSO-based clustering approaches is shown in comparison with several state-of-the-art techniques.

Keywords

Unsupervised classification Cluster ensemble Multi-objective particle swarm optimization Multi-objective differential evolution Symmetry Gene expression data Cancer data classification 

Notes

Acknowledgements

Authors would like to acknowledge the help from Indian Institute of Technology Patna and National Institute of Technology Mizoram to conduct this research.

Compliance with ethical standards

Conflict of interest

All the authors declare that they do not have any conflict of interest.

Human and animal rights

We have not performed any experiments which involve animals or humans.

References

  1. Acharya S, Saha S, Thadisina Y (2016) Multiobjective simulated annealing-based clustering of tissue samples for cancer diagnosis. IEEE J Biomed Health Inform 20(2):691–698CrossRefGoogle Scholar
  2. Alaei HK, Salahshoor K, Alaei HK (2013) A new integrated on-line fuzzy clustering and segmentation methodology with adaptive PCA approach for process monitoring and fault detection and diagnosis. Soft Comput 17(3):345–362CrossRefGoogle Scholar
  3. Alizadeh AA, Eisen MB, Davis RE, Ma C, Lossos IS, Rosenwald A, Boldrick JC, Sabet H, Tran T, Yu X, Powell JI, Yang L, Marti GE, Moore T, Hudson JJ, Lu L, Lewis DB, Tibshirani R, Sherlock G, Chan WC, Greiner TC, Weisenburger DD, Armitage JO, Warnke R, Levy R, Wilson W, Grever MR, Byrd JC, Botstein D, Brown PO, Staudt LM (2000) Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature 403(6769):503–511CrossRefGoogle Scholar
  4. Alon U, Barkai N, Notterman DA, Gish K, Ybarra S, Mack D, Levine AJ (1999) Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc Natl Acad Sci 96(12):6745–6750CrossRefGoogle Scholar
  5. Bakhshali M (2017) Segmentation and enhancement of brain mr images using fuzzy clustering based on information theory. Soft Comput. https://doi.org/10.1007/s00500-016-2210-2
  6. Bandyopadhyay S, Saha S (2007) GAPS: a clustering method using a new point symmetry based distance measure. Pattern Recognit 40(12):3430–3451CrossRefMATHGoogle Scholar
  7. Bandyopadhyay S, Saha S (2013) Unsupervised classification—similarity measures, classical and metaheuristic approaches, and applications. Springer, BerlinMATHGoogle Scholar
  8. Bandyopadhyay S, Maulik U, Wang JT (eds) (2007a) Analysis of biological data: a soft computing approach. Volume 3 of science, engineering, and biology informatics. World Scientific, SingaporeGoogle Scholar
  9. Bandyopadhyay S, Maulik U, Mukhopadhyay A (2007b) Multiobjective genetic clustering for pixel classification in remote sensing imagery. IEEE Trans Geosci Remote Sens 45(5–2):1506–1511CrossRefGoogle Scholar
  10. Bandyopadhyay S, Mukhopadhyay A, Maulik U (2007c) An improved algorithm for clustering gene expression data. Bioinformatics 23(21):2859–2865CrossRefGoogle Scholar
  11. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum, New YorkCrossRefMATHGoogle Scholar
  12. Brunet JP, Tamayo P, Golub TR, Mesirov JP (2004) Metagenes and molecular pattern discovery using matrix factorization. Proc Natl Acad Sci 101(12):4164–4169CrossRefGoogle Scholar
  13. Calado P, Cristo M, Gonçalves MA, de Moura ES, Ribeiro-Neto BA, Ziviani N (2006) Link-based similarity measures for the classification of web documents. JASIST 57(2):208–221CrossRefGoogle Scholar
  14. Chen Y, Li K, Chen Z, Wang J (2017) Restricted gene expression programming: a new approach for parameter identification inverse problems of partial differential equation. Soft Comput 21(10):2651–2663CrossRefGoogle Scholar
  15. Cherkassky V (1997) The nature of statistical learning theory. IEEE Trans Neural Netw 8(6):1564CrossRefGoogle Scholar
  16. Chitsaz E, Jahromi MZ (2016) A novel soft subspace clustering algorithm with noise detection for high dimensional datasets. Soft Comput 20(11):4463–4472CrossRefMATHGoogle Scholar
  17. Das S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. In: Genetic and evolutionary computation conference, GECCO 2005, proceedings, Washington DC, USA, June 25–29, pp 991–998Google Scholar
  18. Das S, Abraham A, Konar A (2008) Automatic clustering using an improved differential evolution algorithm. IEEE Trans Syst Man Cybern Part A 38(1):218–237CrossRefGoogle Scholar
  19. de Souto MCP, Costa IG, de Araujo DSA, Ludermir TB, Schliep A (2008) Clustering cancer gene expression data: a comparative study. BMC Bioinform 9:497CrossRefGoogle Scholar
  20. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  21. Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MATHMathSciNetGoogle Scholar
  22. Dorigo M, Stützle T (2004) Ant colony optimization. Bradford Company, ScituateMATHGoogle Scholar
  23. Du X, Ni Y, Xie D, Yao X, Ye P, Xiao R (2015) The time complexity analysis of a class of gene expression programming. Soft Comput 19(6):1611–1625CrossRefMATHGoogle Scholar
  24. Eisen M, Spellman P, Brown P, Botstein D (1998a) Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad Sci 85:14863–14868CrossRefGoogle Scholar
  25. Eisen MB, Spellman PT, Brown PO, Botstein D (1998b) Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad Sci USA 95(25):14863–8CrossRefGoogle Scholar
  26. Fern XZ, Brodley CE (2004) Solving cluster ensemble problems by bipartite graph partitioning. In: Machine learning, proceedings of the twenty-first international conference (ICML 2004), Banff, Alberta, Canada, July 4–8Google Scholar
  27. Fraley C, Raftery AE (1998) How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput J 41(8):578–588CrossRefMATHGoogle Scholar
  28. Fred ALN, Jain AK (2005) Combining multiple clusterings using evidence accumulation. IEEE Trans Pattern Anal Mach Intell 27(6):835–850CrossRefGoogle Scholar
  29. Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675–701CrossRefMATHGoogle Scholar
  30. Ghosh D, Chinnaiyan AM (2002) Mixture modelling of gene expression data from microarray experiments. Bioinformatics 18(2):275–286CrossRefGoogle Scholar
  31. Handl J, Knowles J (2007) An evolutionary approach to multiobjective clustering. IEEE Trans Evol Comput 11(1):56–76CrossRefGoogle Scholar
  32. Herwig R, Poustka AJ, Mller C, Bull C, Lehrach H, O’Brien J (1999) Large-scale clustering of cdna-fingerprinting data. Genome Res 9(11):1093–105CrossRefGoogle Scholar
  33. Heyer LJ, Kruglyak S, Yooseph S (1999) Exploring expression data: identification and analysis of coexpressed genes. Genome Res 9(11):1106–1115CrossRefGoogle Scholar
  34. Iam-on N, Boongoen T, Garrett SM (2008) Refining pairwise similarity matrix for cluster ensemble problem with cluster relations. In: Discovery science, 11th international conference, DS 2008, Budapest, Hungary, October 13–16, 2008. Proceedings, pp 222–233Google Scholar
  35. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  36. Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323CrossRefGoogle Scholar
  37. Jarman IH, Etchells TA, Bacciu D, Garibaldi JM, Ellis IO, Lisboa PJG (2011) Clustering of protein expression data: a benchmark of statistical and neural approaches. Soft Comput 15(8):1459–1469CrossRefGoogle Scholar
  38. Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697CrossRefGoogle Scholar
  39. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, pp 1942–1948Google Scholar
  40. Kittler J, Hatef M, Duin RPW, Matas J (1998) On combining classifiers. IEEE Trans Pattern Anal Mach Intell 20(3):226–239CrossRefGoogle Scholar
  41. Klink S, Reuther P, Weber A, Walter B, Ley M (2006) Analysing social networks within bibliographical data. In: Database and expert systems applications, 17th international conference, DEXA 2006, Kraków, Poland, September 4–8, 2006, Proceedings, pp 234–243Google Scholar
  42. Kuo RJ, Wang MJ, Huang TW (2011) An application of particle swarm optimization algorithm to clustering analysis. Soft Comput 15(3):533–542CrossRefGoogle Scholar
  43. Li D (2011) Gene expression studies with DGL global optimization for the molecular classification of cancer. Soft Comput 15(1):111–129CrossRefGoogle Scholar
  44. Li Y, Yang G, He H, Jiao L, Shang R (2016) A study of large-scale data clustering based on fuzzy clustering. Soft Comput 20(8):3231–3242CrossRefGoogle Scholar
  45. Liu L, Hawkins D, Ghosh S, Young S (2003) Robust singular value decomposition analysis of microarray data. Proc Natl Acad Sci 100:13167–13172CrossRefMATHMathSciNetGoogle Scholar
  46. Lockhart DJ, Winzeler EA (2000) Genomics, gene expression and DNA arrays. Nature 405(6788):827–36CrossRefGoogle Scholar
  47. Lu Y, Liang M, Ye Z, Cao L (2015) Improved particle swarm optimization algorithm and its application in text feature selection. Appl Soft Comput 35:629–636CrossRefGoogle Scholar
  48. Maulik U, Saha I (2010) Automatic fuzzy clustering using modified differential evolution for image classification. IEEE Trans Geosci Remote Sens 48(9):3503–3510CrossRefGoogle Scholar
  49. Maulik U, Mukhopadhyay A, Bandyopadhyay S (2009) Combining pareto-optimal clusters using supervised learning for identifying co-expressed genes. BMC Bioinform 10(27):1197–1208Google Scholar
  50. Nemenyi P (1963) Distribution-free multiple comparisons. Ph.D. thesis, New Jersey, USAGoogle Scholar
  51. Ni Q, Pan Q, Du H, Cao C, Zhai Y (2017) A novel cluster head selection algorithm based on fuzzy clustering and particle swarm optimization. IEEE/ACM Trans Comput Biol Bioinform 14(1):76–84CrossRefGoogle Scholar
  52. Noorbehbahani F, Mousavi SR, Mirzaei A (2015) An incremental mixed data clustering method using a new distance measure. Soft Comput 19(3):731–743CrossRefGoogle Scholar
  53. Pakhira MK, Maulik U, Bandyopadhyay S (2004) Validity index for crisp and fuzzy clusters. Pattern Recognit 37(3):487–501CrossRefMATHGoogle Scholar
  54. Re M (2011) Comparing early and late data fusion methods for gene expression prediction. Soft Comput 15(8):1497–1504CrossRefMathSciNetGoogle Scholar
  55. Rousseeuw P (1987) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20(1):53–65Google Scholar
  56. Saha S (2017) Enhancing point symmetry-based distance for data clustering. Soft Comput. https://doi.org/10.1007/s00500-016-2477-3
  57. Saha S, Bandyopadhyay S (2009) A new point symmetry based fuzzy genetic clustering technique for automatic evolution of clusters. Inf Sci 179(19):3230–3246CrossRefMATHGoogle Scholar
  58. 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):1965–1977CrossRefGoogle Scholar
  59. Saha S, Kaushik K, Alok AK, Acharya S (2016) Multi-objective semi-supervised clustering of tissue samples for cancer diagnosis. Soft Comput 20(9):3381–3392CrossRefGoogle Scholar
  60. Sharan R, Shamir R (2000) Center CLICK: a clustering algorithm with applications to gene expression analysis. In: Proceedings of the eighth international conference on intelligent systems for molecular biology, August 19–23, 2000, La Jolla/San Diego, CA, USA, pp 307–316Google Scholar
  61. Sherlock G (2000) Analysis of large-scale gene expression data. Curr Opin Immunol 12(2):201–205CrossRefMathSciNetGoogle Scholar
  62. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359CrossRefMATHMathSciNetGoogle Scholar
  63. Strehl A, Ghosh J (2002) Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3:583–617MATHMathSciNetGoogle Scholar
  64. Tamayo P, Slonim D, Mesirov J, Zhu Q, Kitareewan S, Dmitrovsky E, Lander ES, Golub TR (1999) Interpreting patterns of gene expression with self-organizing maps: methods and application to hematopoietic differentiation. Proc Natl Acad Sci 96(6):2907–2912CrossRefGoogle Scholar
  65. Xie XL, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13(8):841–847CrossRefGoogle Scholar
  66. Yang X, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24(1):169–174CrossRefGoogle Scholar
  67. Yin C, Xia L, Zhang S et al (2017) Improved clustering algorithm based on high-speed network data stream. Soft Comput. https://doi.org/10.1007/s00500-017-2708-2
  68. Yue S, Wang P, Wang J, Huang T (2013) Extension of the gap statistics index to fuzzy clustering. Soft Comput 17(10):1833–1846CrossRefGoogle Scholar
  69. Yue S, Wang J, Wang J, Bao X (2016) A new validity index for evaluating the clustering results by partitional clustering algorithms. Soft Comput 20(3):1127–1138CrossRefGoogle Scholar
  70. Zăvoianu AC, Lughofer E, Bramerdorfer G, Amrhein W, Klement EP (2015) DECMO2: a robust hybrid and adaptive multi-objective evolutionary algorithm. Soft Comput 19(12):3551–3569CrossRefGoogle Scholar
  71. Zhou Z, Zhu S (2017) Kernel-based multiobjective clustering algorithm with automatic attribute weighting. Soft Comput. https://doi.org/10.1007/s00500-017-2590-y

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology PatnaPatnaIndia
  2. 2.Department of Computer Science and EngineeringNational Institute of Technology MizoramAizawlIndia

Personalised recommendations