OCLUS: An analytic method for generating clusters with known overlap

Journal of Classification

Volumn 22, Issue 2, 2005, Pages 221-250

  Steinley, Douglas ^a   Henson, Robert ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITY OF NORTH CAROLINA AT GREENSBORO   (United States)

Author keywords

Cluster generation; Overlapping clusters

Indexed keywords

EID: 33744720321     PISSN: 01764268     EISSN: 14321343     Source Type: Journal    
DOI: 10.1007/s00357-005-0015-6     Document Type: Article

References (76)

1. ANDERBERG, M. R. (1973). Cluster Analysis for Applications, New York: Academic Press.
2. ATLAS, R. S., and OVERALL, J. E. (1994). "Comparative Evaluation of Two Superior Stopping Rules for Hierarchical Cluster Analysis," Psychametrika, 59, 581-591.
3. BAKER, F. B., and HUBERT, L. J. (1975). "Measuring the Power of Hierarchical Cluster Analysis," Journal of the American Statistical Association, 70, 31-38.
4. BALAKRISHNAN, P. V., COOPER, M. C., JACOB, V. S., and LEWIS, P. A. (1994). "A Study of Classification Capabilities of Neural Networks Using Unsupervised Learning: A Comparison With K-means Clustering,"Psychometrika, 59, 509-525.
5. BALL, G. H., and HALL, D. J. (1967). "A Clustering Technique for Summarizing Multivariate Data," Behavioral Science, 12, 153-155.
6. BANFIELD, J. D., and RAFTERY, A. E. (1993). "Model-based Gaussian and Non-Gaussian Clustering "Biometrics, 49, 803-821.
7. BAYNE, C. K., BEAUCHAMP, J. J., BEGOVICH, C. L., and KANE, V. E. (1980). "Monte Carlo Comparisons of Selected Clustering Procedures," Pattern Recognition, 12, 51-62.
8. BEAUCHAINE, T. P., and BEAUCHAINE, R. J., III. (2002). "A Comparison of Maximum Covariance and K-means Cluster Analysis in Classifying Cases into Known Taxon Groups," Psychological Methods, 7, 245-261.
9. BEALE, E. M. L. (1969). Cluster Analysis, London: Scientific Control Systems.
10. BICKEL, P. J., and DOKSUM, K. A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics (2nd ed.), Upper Saddle River, NJ: Prentice Hall.
11. BLASHFIELD, R. K. (1976). "Mixture Model Tests of Cluster Analysis: Accuracy of Four Agglomerative Hierarchical Methods" Psychological Bulletin, 83, 377-388.
12. BOZDOGAN, H. (1993). "Choosing the Number of Component Clusters in the Mixture-Model Using a New Informational Complexity Criterion of the Inverse-Fisher Information Matrix," Information and Classification, Eds., O. Opitz, B. Lausen, and R. Klar, Heidelberg: Springer, 40-54.
13. BOZDOGAN, H., and SCLOVE, S. L. (1984). "Multi-Sample Cluster Analysis Using Akaike's Information Criterion," Annals of The Institute of Statistical Mathematics, 36, 163-180.
14. BRUSCO, M. J., and CRADIT, J. D. (2001). "A Variable Selection Heuristic for K-means Clustering," Psychometrika, 66, 249-270.
15. CALINSKI, R. B., and HARABASZ, J. (1974). "A Dendrite Method for Cluster Analysis," Communications in Statistics, 3, 1-21.
16. CARMONE, F. J., KARA, A., and MAXWELL, S. (1999). "HINoV: A New Model to Improve Market Segment Definition by Identifying Noisy Variables, " Journal of Marketing Research, 36, 501-509.
17. CARROLL, J. D., and ARABIE, P. (1983). "INDCLUS: An Individual Differences Generalization of the ADCLUS Model and the MAPCLUS Algorithm," Psychometrika, 48, 157-169.
18. CORMACK, R. M. (1971). "A review of classification," Journal of the Royal Statistical Society, A, 134, 321-361.
19. DAVID, H. A. (1981). Order statistics (2nd ed.), New York: Wiley.
20. DE SOETE, G. (1986). "Optimal Variable Weighting for Ultrametric and Additive Tree Clustering," Quality and Quantity, 20, 169-180.
21. DE SOETE, G., DESARBO, W. S., and CARROLL, J. D. (1985). Optimal Variable Weighting for Hierarchical Clustering: An Alternating Least-Squares Algorithm," Journal of Classification, 2, 173-192.
22. DESARBO, W. S. (1982). "GENNCLUS: New Models for General Nonhierarchical Clustering Analysis,"Psychometrika, 47, 449-475.
23. DESARBO, W. S. (1984). "Constrained Classification: The Use of a Priori Information in Cluster Analysis,"Psychometrika, 49, 187-215.
24. DIDAY, E. (1986). "Orders and Overlapping Clusters by Pyramids," Multidimensional Data Analysis, Eds., J. de Leeuw, W. Heiser, J. Meulman, and F. Critchley, Leiden: DSWO, 201-234.
25. DIDAY, E., and BERTRAND, P. (1986). "An Extension of Hierarchical Clustering: The Pyramidal Presentation," Pattern recognition in practice II, Eds., E. S. Gelsema and L. N. Kanal, Amsterdam: North-Holland, 411-424.
26. DUDA, R. O., and HART, P. E. (1973). Pattern Classification and Scene Analysis, New York: Wiley.
27. EDELBROOK, C. (1979). "Comparing the Accuracy of Hierarchical Clustering Algorithms: The Problem of Classifying Everybody," Multivariate Behavioral Research, 14,367-384.
28. EVANS, M., HASTINGS, N., and PEACOCK, B. (2000). Statistical distributions (3rd ed.), New York: Wiley.
29. FLEISHMAN, A. J. (1978). "A Method for Simulating Non-Normal Distributions,"Psychometrika, 43, 521-532.
30. GOLD, E. M., and HUFFMAN, P. J. (1976). "Flange Detection Cluster Analysis," Multivariate Behavioral Research, 11, 211-235.
31. GORDON, A. D. (1987). "A Review of Hierarchical Classification," Journal of the Royal Statistical Society, A, 150, 119-137.
32. FOWLKES, E. B., GNANADESIKAN, R., and KETTERING, J. R. (1987). "Variable Selection in Clustering and Other Contexts," Design, Data, and Analysis, Ed., C. L. Mallows, New York: Wiley, 13-34
33. FOWLKES, E. B., GNANADESIKAN, R., and KETTERING, J. R. (1988). "A Method for Comparing Two Hierarchical Clusterings (with Comments and Rejoinder)," Journal of the American Statistical Association, 78, 553-584.
34. GORDON, A. D. (1996). "Hierarchical classification," Clustering and Classification, Eds., P. Arabie, L. J. Hubert, and G. De Soete, River Edge, NJ: World Scientific, 65-121.
35. GORDON, A. D. (1999). Classification (2nd ed.), New York: Chapman and Hall/CRC.
36. HAMPBEL, F. R., RONCHETTI, E. M., ROUSSEEUW, P. J., and STAHEL, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, New York: Wiley.
37. HANSEN, P., JAUMARD, B., and SANLAVILLE, E. (1994). "Partitioning Problems in Cluster Analysis: A Review of Mathematical Programming Approaches," New Approaches in Classification and Data Analysis, Eds., E. Diday, Y. Lechevallier, M. Schader, P. Bertrand, and B. Burtchy, Springer: Berlin, 228-240.
38. HARTIGAN, J. A. (1975). Clustering Algorithms, New York: John Wiley and Sons.
39. HARTIGAN, J. A. (1988). "The Span Test of Unimodality, Classification and Related Methods, Ed., H. H. Bock, Amsterdam: North Holland, 229-236.
40. HARTIGAN, J. A. (2000). "Testing for Antimodes," Data Analysis: Scientific Modelling and Practical Application, Eds., W. Gaul, O. Opitz, and M. Schader, Berlin: Springer, 385-392.
41. HARTIGAN, J. A., and HARTIGAN, P. M. (1985). "The Dip Test of Multimodality," Annals of Statistics, 13, 70-84.
42. HARTIGAN, J. A., and MOHANTY, S. (1992). "The Runt Test for Multimodality," Journal of Classification, 9, 63-70.
43. HARTIGAN, J. A., and WONG, M. A. (1979). "Algorithm AS 136. A K-means Clustering Algorithm," Applied Statistics, 28, 100-108.
44. HELSEN, K., and GREEN, P. E. (1991). "A Computational Study of Replicated Clustering with an Application to Market Segmentation," Decision Sciences, 22, 1124-1141.
45. HOGG, R. V., and CRAIG, A. T. (1995). Introduction to Mathematical Statistics (5th ed.), Upper Saddle River, NJ: Prentice Hall.
46. HUBERT, L. J., and LEVIN, J. R. (1976). "A General Statistical Framework for Assessing Categorical Clustering in Free Recall," Psychological Bulletin, 83, 1072-1080.
47. JARDINE, N., and SIBSON, R. (1968). "The Construction of Hierarchic and Non-Hierarchic Classifications," The Computer Journal, 11, 177-184.
48. KRZANOWSKI, W. J., and MARRIOTT, F. H. C. (1994). Multivariate Analysis Part I: Distributions, Ordination, and Inference, New York: Wiley.
49. KUIPER, F. K., and FISHER, L. (1975). "A Monte Carlo Comparison for Six Clustering Procedures," Biometrics, 31, 777-784.
50. LANCE, G. N., and WILLIAMS, W. T. (1966). "A Generalised Sorting Strategy for Computer Classifications," Nature, 212, 218.
51. LANCE, G. N., and WILLIAMS, W. T. (1967). "A General Theory of Classificatory Strategies I. Hierarchical Systems," The Computer Journal, 9, 373-380.
52. LEHMAN, E. L., and CASELLA, G. (1998). Theory of Point Estimation, New York: Springer.
53. MACQUEEN, J. (1967). "Some Methods for Classification and Analysis of Multivariate Observations," Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Eds., L. M. Le Cam and J. Neyman, Berkeley: University of California Press, 281-297.
54. MCINTYRE, R. M., and BLASHFIELD, R. K. (1980). "A Nearest-Centroid Technique for Evaluating the Minimum Variance Clustering Procedure," Multivariate Behavioral Research, 15, 225-238.
55. MCQUITTY, L. L. (1960). "Hierarchical Linkage Analysis for the Isolation of Types." Educational and Psychological Measurement, 20, 55-67.
56. MILLIGAN, G. W. (1980). "The Validation of Four Ultrametric Clustering Algorithms," Pattern Recognition, 12, 41-50.
57. MILLIGAN, G. W. (1985). "An Algorithm for Generating Artificial Test Clusters," Psychometrika, 50, 123-127.
58. MILLIGAN, G. W. (1996). "Clustering Validation: Results and Implications for Applied Analyses," Eds., P. Arabie, L. J. Hubert, and G. De Soete, River Edge, NJ: World Scientific, 341-375.
59. MILLIGAN, G. W., and COOPER, M. C. (1986). "A Study of the Comparability of External Criteria for Hierarchical Cluster Analysis," Multivariate Behavioral Research, 21, 441-458.
60. MILLIGAN, G. W., and COOPER, M. C. (1988). "A Study of Standardization of Variables in Cluster Analysis," Journal of Classification, 5, 181-204.
61. MILLIGAN, G. W., SOON, S. C., and SOKAL, L. M. (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, 5, 40-47.
62. MOJENA, R. (1977). "Hierarchical Grouping Methods and Stopping Rules-An Evaluation," The Computer Journal, 20, 359-363.
63. PRICE, L. J. (1993). "Identifying Cluster Overlap with NORMIX Population Membership Probabilities," Multivariate Behavioral Research, 28, 235-262.
64. ROUSSEEUW, P. J., and LEROY, A. M. (1987). Robust Regression and Outlier Detection, New York: Wiley.
65. SHEPARD, R.N., and ARABIE, P. (1979). "Additive Clustering: Representation of Similarities as Combinations of Discrete Overlapping Properties," Psychological Review, 86, 87-123.
66. SNEATH, P. H. A. (1957). "The Application of Computers in Taxonomy," Journal of General Microbiology, 17, 201-226.
67. SOKAL, R. R., and MICHENER, C. D. (1958). "A Statistical Method for Evaluating Systematic Relationships," University of Kansas Science Bulletin, 38, 1409-1438.
68. STEINLEY, D. (2003). "Local Optima in K-means Clustering: What You Don't Know May Hurt You," Psychological Methods, 8, 294-304.
69. STEINLEY, D. (2004). "Standardizing Variables in K-means Clustering," Classification, Clustering, and Data Mining Applications, Eds., D. Banks, L. House, F. R. McMorris, P. Arabie, and W. Gaul, New York: Springer, 53-60.
70. TADKIKAMALLA, P. R. (1980). "On Simulating Non-Normal Distributions," Psychometrika, 45, 273-279.
71. VALE, C. D., and MAURELLI, V. A. (1983). "Simulating Multivariate Nonnormal Distributions," Psychometrika, 48, 465-471.
72. WALLER, N. G., KAISER, H. A., ILLIAN, J. B., and MANRY, M. (1998). "A Comparison of the Classification Capabilities of the 1-dimensional Kohonen Neural Network with Two Partitioning and Three Hierarchical Cluster Analysis Algorithms," Psychometrika, 63, 5-22.
73. WALLER, N. G., UNDERBILL, J. M., and KAISER, H. A. (1999). "A Method for Generating Simulated Plasmodes and Artificial Test Clusters with User-Defined Shape, Size, and Orientation," Multivariate Behavioral Research, 34, 123-142.
74. WARD, Jr., J. H. (1963). "Hierarchical Grouping to Optimize an Objective Function," Journal of the American Statistical Association, 58, 236-244.
75. WEISSTEIN, E. W. (2003). CRC Concise Encyclopedia of Mathematics (2nd ed.), London: Chapman and Hall/CRC.
76. WINDHAM, M. P., and CUTLER, A. (1992). "Information Ratios for Validating Cluster Analyses," Journal of the American Statistical Association, 87, 1188-1192.