MCS: A Method for Finding the Number of Clusters

Journal of Classification

Volumn 28, Issue 2, 2011, Pages 184-209

  Albatineh, Ahmed N ^a   Niewiadomska Bugaj, Magdalena ^b  

^a FLORIDA INTERNATIONAL UNIVERSITY   (United States)

^b WESTERN MICHIGAN UNIVERSITY   (United States)

Author keywords

Bivariate normal mixture; Circular data; Clustering algorithm; Comparing partitions; Correction for chance agreement; Gap statistic; Number of clusters; Similarity index

Indexed keywords

EID: 79960555635     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-010-9069-1     Document Type: Article

References (50)

1. ALBATINEH, A. N., NIEWIADOMSKA-BUGAJ, M., and MIHALKO, D. P. (2006), "On Similarity Indices and Correction for Chance Agreement", Journal of Classification, 23, 301-313.
2. ALBATINEH, A. N (2010), "Means and Variances for a Family of Similarity Indices Used in Cluster Analysis", Journal of Statistical Planning and Inference, 140, 2828-2838.
3. ANDREWS, D. F. (1972), "Plots of High Dimensional Data", Biometrics, 28, 125-136.
4. BANFIELD, J. D., and RAFTERY, A. E. (1993), "Model-based Gaussian and Non-Gaussian Clustering", Biometrics, 49, 803-821.
5. BARAGONA, R. (2003), "Further Results on Lund's Statistic for Identifying Cluster in a Circular Data Set with Application to Time Series", Communications in Statistics: Simulation and Computation, 32, 943-952.
6. BATSCHELET, E. (1981), Circular Statistics in Biology, London: Academic Press.
7. BOCK, H. H. (1985), "On Some Significance Tests in Cluster Analysis", Journal of Classification, 2, 77-108.
8. BRECKENRIDGE, J. N. (1989), "Replicating Cluster Analysis: Method, Consistency, and Validity", Multivariate Behavioral Research, 24, 147-161.
9. BRUSCO, M. J., and STEINLEY, D. (2007), "A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning", Psychometrika, 72, 583-600.
10. CALINSKI, R. B., and HARABASZ, J. (1974), "A Dendrite Method for Cluster Analysis", Communications in Statistics, 3, 1-27.
11. COHEN, A. J. (1960), "A Coefficient of Agreement for Nominal Scales", Educational and Psychological Measurement, 3, 37-46.
12. DUDOIT, S., and FRIDLYAND, J. (2002), "A Prediction-based Resampling Method for Estimating the Number of Custers in a Dataset", Genome Biology, 3, 1-21.
13. EVERITT, B. S., LANDAU, S., and LEESE, M. (2001), Cluster Analysis, New York: Oxford University Press.
14. FISHER, N. I. (1993), Statistical Analysis of Circular Data, Cambridge: Cambridge University Press.
15. FOWLKES, E. B., and MALLOWS, C. L. (1983), "A Method for Comparing Two Hierarchical Clusterings", Journal of the American Statistical Association, 78, 553-569.
16. FRALEY, C., and RAFTERY, A. E. (1998), "How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis", The Computer Journal, 41, 578-588.
17. GOODMAN, L., and KRUSKAL, W. (1954), "Measures of Association for Cross Classifications", Journal of the American Statistical Association, 49, 732-764.
18. GORDON, A. D. (1999), Classification (2nd ed.), St. Andrews: Chapman & Hall/CRC.
19. GUTTMAN, L. (1941), "An Outline of the Statistical Theory of Prediction", in In Prediction of Personal Adjustment, ed. P. Horst, New York: Social Science Research Council.
20. HARDY, A. (1994), "An Examination of Procedures for Determining the Number of Clusters in a Data Set", in New Approaches in Classification and Data Analysis, ed. E. Diday et al., Paris: Springer-Verlag, pp. 178-185.
21. HARDY, A. (1996), "On the Number of Clusters", Computational Statistics and Data Analysis, 23, 83-96.
22. HUBERT, L., and ARABIE, P. (1985), "Comparing Partitions", Journal of Classification, 2, 193-218.
23. HARTIGAN, J. A. (1975), Clustering Algorithms, New York: Wiley.
24. JAIN, A. K., and DUBES, R. C. (1988), Algorithms for Clustering Data, New Jersey: Prentice Hall.
25. KAUFMAN, L., and ROUSSEEUW, P. J. (1990), Finding Groups in Data: An Introduction to Cluster Analysis, New York: John Wiley & Sons.
26. KOZIOL, J. A. (1990), "Cluster Analysis of Antigenic Profiles of Tumors: Selection of Number of Clusters Using Akaike's Information Criterion", Methods of Information in Medicine, 29, 200-204.
27. KROLAK-SCHWERDT, S., and ECKES, T. (1992), "A Graph Theoretic Criterion for Determining the Number of Clusters in a Data Set", Multivariate Behavior Research, 27, 541-565.
28. KRZANOWSKI, W. J., and LAI, Y. T. (1985), "A Criterion for Determining the Number of Groups in a Data Set Using Sum of Squares Clustering", Biometrics, 44, 23-34.
29. KULCZYNSKI, S. (1927), "Die Pflanzenassociationen der Pienenen", Bulletin of the International Academy of Political Science Letters, Science Mathematics Nature, Series B, Supplement, 2, 57-203.
30. LANGE, T., ROTH, V., BRAUN, M. L., and BUHMANN, J. M. (2004), "Stability-Based Validation of Clustering Solutions", Neural Computations, 16, 1299-1323.
31. LUND, U. (1999), "Cluster Analysis for Directional Data", Communications in Statistics: Simulations and Computations, 4, 1001-1009.
32. MARDIA, K. V., and JUPP, P. E. (2000), Directional Statistics, England: JohnWiley & Sons Ltd.
33. MARRIOTT, F. H. C. (1971), "Practical Problems in a Method of Cluster Analysis", Biometrics, 27, 501-514.
34. MILLIGAN, G., and COOPER, M. (1985), "An Examination of Procedures for Determining the Number of Clusters in a Data Set", Psychometrika, 50, 159-179.
35. MILLIGAN, G., and COOPER, M. (1986), "A Study of the Comparability of External Criteria for Hierarchical Cluster Analysis", Multivariate Behavioral Research, 21, 441-458.
36. MILLIGAN, G., SOON, S., and SOKOL, L. (1983), "The Effect of Cluster Size, Dimensionality, and the Number of Clusters on Recovery of True Cluster Structure", IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-5, 40-47.
37. MOREY, L., and AGRESTI, A. (1984), "The Measurement of Classification Agreement: An Adjustment to the Rand Statistic for Chance Agreement", Educational and Psychological Measurement, 44, 33-37.
38. PECK, R., FISHER, L., and NESS, V. J. (1989), "Approximate Confidence Intervals for the Number of Clusters", Journal of the American Statistical Association, 84, 184-191.
39. R Development Core Team (2007), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, URL http://www. R-project. org.
40. RAND, W. (1971), "Objective Criteria for the Evaluation of Clustering Methods", Journal of the American Statistical Association, 66, 846-850.
41. SAXENA, P. C., and NAVANEERHAM, K. (1991), "The Effect of Cluster Size, Dimensionality, and Number of Clusters on Recovery of True Cluster Structure Through Chernoff-Type Faces", The Statistician, 40, 415-425.
42. SAXENA, P. C., and NAVANEERHAM, K. (1993), "Comparison of Chernoff-Type Face and Non-Graphical Methods for Clustering Multivariate Observations", Computational Statistics and Data Analysis, 15, 63-79.
43. STEINLEY, D., and BRUSCO, M. J. (2007), "Initializing K-means Batch Clustering: A Critical Evaluation of Several Techniques", Journal of Classification, 24, 99-121.
44. STRUYF, A., HUBERT, M., and ROUSSEEUW, P. J. (1997), "Integrating Robust Clustering Techniques in S-PLUS", Computational Statistics and Data Analysis, 26, 17-37.
45. SUGAR, C. A., and JAMES, G. M. (2003), "Finding the Number of Clusters in a Dataset: An Information-Theoretic Approach", Journal of the American Statistical Association, 98, 750-763.
46. TIBSHIRANI, R., WALTHER, G., and HASTIE, T. (2001), "Estimating the Number of Clusters in a Data Set via the Gap Statistic", Journal of the Royal Statistical Society B, 63, 411-423.
47. VASSILLIOU, A., TAMBOURATZIS, D. G., KOUTRAS, M. V., and BERSIMIS, S. (2004), "A New Similarity Measure and Its Use in Determining the Number of Clusters in a Multivariate Data Set", Communications in Statistics, Theory and Methods, 33, 1643-1666.
48. WISHART, D. (1978), CLUSTAN User Manual (3rd ed.), Program Library Unit, University of Edinburgh.
49. WOLFE, J. H. (1970), "Pattern Clustering by Multivariate Mixture Analysis", Multivariate Behavioral Research, 5, 329-350.
50. YANG, M-S., and PAN, J-A. (1997), "On Fuzzy Clustering of Directional Data", Fuzzy Sets and Systems, 91, 319-326.