Choosing the number of clusters boris mirkin

Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery

Volumn 1, Issue 3, 2011, Pages 252-260

  Mirkin, Boris ^a,b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

HIERARCHICAL CLUSTERING; HIERARCHICAL SYSTEMS;

FURTHER DEVELOPMENT; MIXTURE OF DISTRIBUTIONS; NUMBER OF CLUSTERS;

K-MEANS CLUSTERING;

EID: 84857058733     PISSN: 19424787     EISSN: 19424795     Source Type: Journal    
DOI: 10.1002/widm.15     Document Type: Article

References (64)

1. Vapnik V. Estimation of Dependences Based on Empirical Data. 2nd ed. New York: Springer Science+ Business Media Inc.; 2006.
2. Biernacki C, Celeux G, Govaert G. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Trans Pattern and Machine Intell 2000, 22:719-725.
3. Bouguila N, Ziou D. High-dimensional unsupervised selection and estimation of a finite generalized Dirichlet mixture model based on minimum message length. IEEE Trans Pattern and Machine Intell 2007, 29:1716-1731.
4. Bock HH. Probability models and hypotheses testing in partitioning cluster analysis. In: Arabie P, Hubert L, de Soete G, eds. Clustering and Classification. River Edge, NJ: World Scientific Publishing; 1996, 377-453.
5. Lo Y, Mendell NR, Rubin DB. Testing the number of components in a normal mixture. Biometrika 2001, 88:767-778.
6. Bozdogan H. Mixture-model cluster analysis and choosing the number of clusters using a new informational complexity ICOMP, AIC, and MDL modelselection criteria. In: Bozdogan H, Sclove S, Gupta A, et al., eds. Multivariate Statistical Modeling. Vol. II. Dordrecht: Kluwer, 1994, 69-113.
7. McLachlan GJ, Peel D. Finite Mixture Models. New York: John Wiley & Sons; 2000. 8. Figueiredo M, Jain AK. Unsupervised learning of finite mixture models. IEEE Trans Pattern andMachine Intell 2002, 24:381-396.
8. Figueiredo M, Jain AK. Unsupervised learning of finite mixture models. IEEE Trans Pattern andMachine Intell 2002, 24:381-396.
9. Yeung KY, Fraley C, Murua A, Raftery AE, Ruzzo WL. Model-based clustering and data transformations for gene expression data. Bioinformatics 2001, 17:977-987.
10. Hu X, Xu L. Investigation of several model selection criteria for determining the number of cluster. Neural Inf Process 2004, 4: 1-10.
11. WindhamMP, Cutler A. Information ratios for validating mixture analyses. J Am Stat Assoc 1992, 87:1188-1192.
12. Celeux G, Soromento M. An entropy criterion for assessing the number of clusters in a mixture model. J Classification 1996, 13:195-212.
13. Cheung Y. Maximum weighted likelihood via rival penalized EM for density mixture clustering with automatic model selection. IEEE Trans Knowledge Data Eng 2005, 17:750-761.
14. Duda RO, Hart PE. Pattern Classification and Scene Analysis. New York: John Wiley & Sons; 1973.
15. Pelleg D, Moore A. X-means: extending k-means with efficient estimation of the number of clusters. Proceedings of 17th International Conference on Machine Learning. San Francisco: Morgan Kaufmann; 2000, 727-734.
16. Ishioka T. An expansion of X-means for automatically determining the optimal number of clusters. Proceedings of International Conference on Computational Intelligence. Calgary, Canada; 2005, 91-96.
17. Feng Y, Hamerly G. PG-means: learning the number of clusters in data. Advances in Neural Information Processing Systems, 19 (NIPS Proceeding). Cambridge MA: MIT Press; 2006, 393-400.
18. Mojena R. Hierarchical grouping methods and stopping rules: an evaluation. Comput J 1977, 20:359-363.
19. Milligan GW. A Monte-Carlo study of thirty internal criterion measures for cluster analysis. Psychometrika 1981, 46:187-199.
20. Fraley C, Raftery AE. How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput J 1988, 41: 578-588.
21. Mirkin B. Mathematical Classification and Clustering. New York: Kluwer; 1996.
22. Newman MEJ, Girvan M. Finding and evaluating community structure in networks. Phys Rev E 2004, 69:026113.
23. Hartigan JA. Clustering Algorithms. New York: John Wiley & Sons.
24. Banfield JD, Raftery AE. Model-based Gaussian and non-Gaussian clustering. Biometrics 1993, 49:803-821.
25. Mirkin B. Sequential fitting procedures for linear data aggregation model. J Classification 1990, 7:167-195.
26. Mirkin B. Clustering for Data Mining: A Data Recovery Approach. Boca Raton, FL: Chapman and Hall/CRC; 2005.
27. Steinley D. K-means clustering: a half-century synthesis. Br J Math Stat Psychol 2006, 59:1-34.
28. Chiang M-T, Mirkin B. Intelligent choice of the number of clusters in K-means clustering: an experimental study with different cluster spreads. Jf Classification 2010, 28. doi: 10.1007/s00357-010. In press.
29. Saha S, Bandyopadhyaya S. A symmetry based multiobjective clustering technique for automatic evolution of clusters. Pattern Recognit 2010, 43:738-751.
30. Milligan GW, Cooper MC. An examination of procedures for determining the number of clusters in a data set. Psychometrika 1985, 50:159-179.
31. Calinski T, Harabasz J. A dendrite method for cluster analysis. Commun Stat 1974, 3(1): 1-27.
32. Casillas A, Gonzales De Lena MT, Martinez H. Document clustering into an unknown number of clusters using a genetic algorithm. Text, Speech, and Dialogue: 6th Int Conf. Springer: Berlin; 2003, 43-49.
33. Tibshirani R, Walther G, Hastie T. Estimating the number of clusters in a dataset via the gap statistics. J Royal Stat Soc B 2001, 63:411-423.
34. YanM, Ye K. Determining the number of clusters using the weighted gap statistic. Biometrics 2007, 63:1031-1037.
35. Krzhanowski W, Lai Y. A criterion for determining the number of groups in a dataset using sum of squares clustering. Biometrics 1985, 44:23-34.
36. Sugar CA, James GM. Finding the number of clusters in a data set: an information-theoretic approach. J Am Stat Assoc 2003, 98:750-778.
37. Kim D, Park Y, Park D. A novel validity index for determination of the optimal number of clusters. IEICE Tans Inf Syst 2001, E84: 281-285.
38. Shen J, Chang SI, Lee ES, Deng Y, Brown SJ. Determination of cluster number in clustering microarray data. Appl Math Comput 2005, 169:1172-1185.
39. Bel Mufti G, Bertrand P, El Moubarki L. Determining the number of groups from measures of cluster stability, In: Proceedings of International Symposium on Applied Stochastic Models and Data Analysis. Brest: France; 2005, 404-412.
40. Kaufman L, Rousseeuw P. Finding Groups in Data: An Introduction to Cluster Analysis. New York: John Wiley & Sons; 1990.
41. Pollard KS, van der Laan MJ. A method to identify significant clusters in gene expression data. UnivCalif Berkeley Div Biostat Working Pap Ser 2002, 107.
42. Chae SS, Dubien JL, Warde WD. A method of predicting the number of clusters using Rand's statistic. Comput Stat Data Anal 2006, 50:3531-3546.
43. Kuncheva LI, Vetrov DP. Evaluation of stability of kmeans cluster ensembles with respect to random initialization. IEEE Trans Pattern Anal Machine Intell 2005, 28:1798-1808.
44. Monti S, Tamayo P, Mesirov J, Golub T. Consensus clustering: a resampling-based method for class discovery and visualization of gene expression microarray data. Machine Learn 2003, 52:91-118.
45. Minaei-Bidgoli B, Topchy A, PunchWF. A comparison of resampling methods for clustering ensembles. International conference on Machine Learning; Models, Technologies and Application (MLMTA04). CSREA Press: Las Vegas, Nevada; 2004, 939-945.
46. Dudoit S, Fridlyand J. A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biol 2002, 3: research0036.1-0036.21.
47. McLachlan GJ, Khan N. On a resampling approach for tests on the number of clusters with mixture modelbased clustering of tissue samples. J Multivariate Anal 2004, 90:90-1005.
48. Roth V, Lange V, Braun M, Buhmann J. Stabilitybased validation of clustering solutions. Neural Comput 2004, 16:1299-1323.
49. Tibshirani R, Walther G. Cluster validation by prediction strength. J Comput Graphical Stat 2005, 14:511-528.
50. Hand D, Krzhanowski WJ. Optimising k-means clustering results with standard software packages. Comput Stat Data Anal 2005, 49:969-973.
51. Hardy A. On the number of clusters. Comput Stat Data Anal 1996, 23:83-96.
52. Steinley D, Brusco M. Initializing K-means batch clustering: a critical evaluation of several techniques. J Classification 2007, 24:99-121.
53. Pena JM, Lozano JA, Larranga P. An empirical comparison of four initialization methods for K-means algorithm. Pattern Recognit Lett 1999, 20:1027-1040.
54. Castellano C, Fortunato S, Loreto V. Statistical physics of social dynamics. ReviMod Phys 2009, 81:591-646.
55. Springel V, White SDM, Jenkins A, Frenk CS, Yoshida N, Gao L, Navarro J, Thacker R, Croton D, Helly J, et al. Simulations of the formation, evolution and clustering of galaxies and quasars. Nature, 2005, 435: 629-636.
56. Newman MEJ, Barabasi AL, Watts DJ. Structure and Dynamics of Networks. Princeton, NJ: Princeton University Press; 2006.
57. Jonnalagadda S, Srinivanasan R. NIFTI: an evolutionary approach for finding number of clusters inmicroarray data. BMC Bioinformatics 2009, 10:40. Available at: http://www.biomedcentral.com/1471-2105-10-40.
58. Shubert J, Sedenbladh H. Sequential clustering with particle filters-estimating the number of clusters from data. Proceedings of 8th International Conference on Information Fusion. Piscataway NJ: IEEE; 2005, A4-A3, 1-8.
59. Evanno G, Regnaut S, Goudet J. Detecting the number of clusters of individuals using the software STRUCTURE: a simulation study. Mol Ecol 2005, 14:2611-2620.
60. von Luxburg U. A tutorial on spectral clustering. Stat Comput 2007, 17:395-416.
61. Dotan-Cohen D, Kasif S, Melkman AA. Seeing the forest for the trees: using the gene ontology to restructure hierarchical clustering. Bioinformatics 2009, 25:1789-1795.
62. Freudenberg JM, Joshi VK, Hu Z, Medvedovic M. CLEAN: clustering enrichment analysis. BMC Bioinformatics 2009, 10:234.
63. Lottaz C, Toedling J, Spang R. Annotation-based distance measures for patient subgroup discovery in clinicalmicroarray studies. Bioinformatics 2007, 23: 2256-2264.
64. Mirkin B, Camargo R, Fenner T, Loizou G, Kellam P. Similarity clustering of proteins using substantive knowledge and reconstruction of evolutionary gene histories in herpesvirus. Theor Chem Acc 2010, 125:569-581.