A new multiobjective clustering technique based on the concepts of stability and symmetry

Knowledge and Information Systems

Volumn 23, Issue 1, 2010, Pages 1-27

  Saha, Sriparna ^a   Bandyopadhyay, Sanghamitra ^a  

^a INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Clustering; Multiobjective optimization (MOO); Stability; Symmetry

Indexed keywords

CLUSTER ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; CRYSTAL SYMMETRY; GENETIC ALGORITHMS; MULTIOBJECTIVE OPTIMIZATION; SIMULATED ANNEALING;

AUTOMATIC CLUSTERING TECHNIQUES; CLUSTERING; EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION; MULTI-OBJECTIVE CLUSTERING; MULTI-OBJECTIVE OPTIMIZATION TECHNIQUES; OPTIMIZATION STRATEGY; OPTIMIZATION TECHNIQUES; SINGLE-OBJECTIVE GENETIC ALGORITHMS;

CLUSTERING ALGORITHMS;

EID: 77950689680     PISSN: 02191377     EISSN: 02193116     Source Type: Journal    
DOI: 10.1007/s10115-009-0204-4     Document Type: Article

References (47)

1. Anderberg MR (2000) Computational geometry: algorithms and applications. Springer, Berlin
2. Assent I, Krieger R, Glavic B, Seidli T (2008) Clustering multidimensional sequences in spatial and temporal databases. Knowl Inf Syst 16(1):1-27
3. Attneave F (1995) Symmetry information and memory for pattern. Am J Psychol 68:209-222
4. Bandyopadhyay S, Maulik U (2001) Nonparametric genetic clustering: comparison of validity indices. IEEE Trans Syst Man Cybernet C 31(1):120-125
5. Bandyopadhyay S, Maulik U (2002) Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognit 35(6):1197-1208
6. Bandyopadhyay S, Pal SK (2007) Classification and learning using genetic algorithms: applications in bioinformatics and web intelligence. Springer, Heidelberg
7. Bandyopadhyay S, Saha S (2007) GAPS: A clustering method using a new point symmetry based distance measure. Pattern Recognit 40:3430-3451
8. 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 (accepted)
9. Bandyopadhyay S, Saha S, Maulik U, Deb K (2008) A simulated annealing based multi-objective optimization algorithm: AMOSA. IEEE Trans Evol Comput 12(3):269-283
10. Ben-Hur A, Guyon I (2003) Detecting stable clusters using principal component analysis in methods in molecular biology. Humana press, Totowa, NJ
11. Bezdek JC, Pal NR (1998) Some new indexes of cluster validity. IEEE Trans Syst Man Cybernet 28: 301-315
12. Breckenridge J (1989) Replicating cluster analysis: method, consistency and validity. Multivar Behav Res 24:147-161
13. Corne DW, Jerram NR, Knowles JD, Oates MJ (2001) PESA-II: region-based selection in evolutionary multiobjective optimization, In: Spector L, Goodman ED, Wu A, Langdon WB, Voigt H-M, Gen M, Sen S, Dorigo M, Pezeshk S, Garzon MH, Burke E (eds) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001). Morgan Kaufmann, San Francisco, California, USA, pp. 283-290. http://citeseer.ist.psu.edu/corne01pesaii.html
14. Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 1:224-227
15. Deb K (2001) Multi-objective optimization using evolutionary algorithms. John Wiley and Sons, Ltd, England
16. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182-197
17. Denton AM, Besemann CA, Dorr DH (2009) Pattern-based time-series subsequence clustering using radial distribution functions. Knowl Inf Syst 18(1):1-27
18. Dudoit S, Fridlyand J (2002) A prediction-based resampling method for estimating the number of clusters in a data set. Genome Biol 3(7):1299-1323
19. Dunn JC (1974) Well separated clusters and optimal fuzzy partitions. J Cyberns 4:95-104
20. Eduardo RH, Nelson FFE (2003) A genetic algorithm for cluster analysis. Intell Data Anal 7:15-25
21. Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugenics 3:179-188
22. Fukuyama Y, Sugeno M (1989) A new method of choosing the number of clusters for the fuzzy c-means method. In: Proceedings of the fifth fuzzy systems symposium, pp. 247-250
23. Geman S, Geman D (1984) Stochastic relaxation, gibbs distributions and the Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell 6(6):721-741
24. Handl J, Knowles J (2007) An evolutionary approach to multiobjective clustering. IEEE Trans Evol Com-put 11(1):56-76
25. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, AnnArbor
26. Jain AK, Duin P, Jianchang M (2000) Statistical pattern recognition: a review. IEEE Trans Pattern Anal Mach Intell 22(1):4-37
27. Kim DJ, Park YW, Park DJ (2001) A novel validity index for determination of the optimal number of clusters. IEICE Trans Inf Syst D-E84(2):281-285
28. Kwon SH (1998) Cluster validity index for fuzzy clustering. Electron Lett 34(22):2176-2177
29. Lange T, Roth V, Braun ML, Buhmann JM (2004) Stability-based validation of clustering solutions. Neural Comput 16:1299-1323
30. Le T (2007) Multiobjective clustering with automatic determination of the number of clusters. http://dbkgroup.org/handl/mock/
31. Li T (2008) Clustering based on matrix approximation: a unifying view. Knowl Inf Syst 17(1):1-15
32. Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Trans Pattern Anal Mach Intell 24(12):1650-1654
33. Moise G, Sander J, Ester M (2008) Robust projected clustering. Knowl Inf Syst 14(3):273-298
34. Mount DM, Arya S (2005) ANN: A library for approximate nearest neighbor searching. http://www.cs.umd.edu/mount/ANN
35. Nayak R (2008) Fast and effective clustering of xml data using structural information. Knowl Inf Syst 14(2):197-215
36. Ohsawa Y, Sakauchi M (1983) BD-Tree: A new n-dimensional data structure with efficient dynamic characteristics. In: Proceedings of the 9th world computer congress, IFIP83', pp. 539-544
37. Pakhira MK, Maulik U, Bandyopadhyay S (2004) Validity index for crisp and fuzzy clusters. Pattern Recognit 37(3):487-501
38. Saha S, Bandyopadhyay S (2008) Application of a new symmetry based cluster validity index for satellite image segmentation. IEEE Geosci Remote Sens Lett 5(2):166-170
39. Sheng W, Swift S, Zhang L, Liu X (2005) A weighted sum validity function for clustering with a hybrid niching genetic algorithm. IEEE Trans Syst Man Cybernet B Cybernet 35(6):1156-1167
40. Srinivas M, Patnaik L (1994) Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Trans Syst Man Cybernet 24(4):656-667
41. Su M-C, Chou C-H (2001) A modified version of the k-means algorithm with a distance based on cluster symmetry. IEEE Trans Pattern Anal Mach Intell 23(6):674-680
42. Tibshirani R, Walther G, Botstein D, Brown P (2001) Cluster validation by prediction strength, Technical report, Statistics Department, Stanford University, Stanford, CA
43. Tibshirani R, Walther G, Hastie T (2000) Estimating the number of clusters in a dataset via the gap statistic, Technical report
44. van Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. Kluwer Academic Publisher, Dordrecht
45. Veldhuizen DV, Lamont G (2000) Multiobjective evolutionary algorithms: analyzing the state-of-the-art. Evol Comput 2:125-147
46. Wu X, Kumar V, Quinlan JR, Ghosh J, Yang Q, Motoda H, McLachlan GJ, Ng A, Liu B, Yu PS, Zhou Z-H, Steinbach M, Hand DJ, Steinberg D (2008) Top 10 algorithms in data mining. Knowl Inf Syst 14(1):1-37
47. Xie XL, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841-847