Minimum sum of squares clustering in a low dimensional space

Journal of Classification

Volumn 15, Issue 1, 1998, Pages 37-55

  Hansen, Pierre ^a   Jaumard, Brigitte ^b   Mladenovic, Nenad ^b  

^a HEC MONTRÉAL   (Canada)

^b GERAD   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032395795     PISSN: 01764268     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003579900019     Document Type: Article

References (30)

1. BUFFON, G. L. LECLERC, Comte de (1749), Histoire Naturelle, Premier Discours: De la manière d'étudier et de traiter l'histoire naturelle, Paris.
2. BENZÉCRI, J. P. (1982), "Construction d'une classification ascendante hiérarchique par la recherche en chaîne des voisins réciproques," Les Cahiers de l'Analyse des Données, VII(2), 209-218.
3. DAY, H. E., and EDELSBRUNNER, H. (1984), "Efficient Algorithms for Agglomerative Hierarchical Clustering Methods," Journal of Classification, 1, 7-24.
4. DE SOETE, G., and CARROLL, J. D. (1994), "K-means Clustering in a Low-dimensional Euclidean Space," in New Approaches in Classification and Data Analysis, Eds., D. Diday et al., Berlin: Springer, 212-219.
5. EDELSBRUNNER, H., O'ROURKE, J. O., and SEIDEL, R. (1986), "Constructing Arrangements of Lines and Hyperplanes with Applications," SIAM Journal on Computing, 15, 341-343.
6. EDWARDS, A. W. F., and CAVALLI-SFORZA, L. L. (1965), "A Method for Cluster Analysis," Biometrics, 21, 362-375.
7. EVERITT, B. (1980), Cluster Analysis, New York: Halsted.
8. FISHER, W. D. (1958), "On Grouping for Maximum Homogeneity," Journal of the American Statistical Association, 53, 789-798.
9. FISHER, L., and VAN NESS, J. W. (1971), "Admissible Clustering Procedures," Biometrika, 58, 91-104.
10. GARFIELD, E., (editor) (1965-1996), Science Citation Index, Philadelphia: Institute for Scientific Information Press.
11. GOODMAN, J. E., and POLLACK, R. (1983), "Multidimensional Sorting," SIAM Journal on Computing, 12(3), 484-507.
12. GOODMAN, J. E., and POLLACK, R. (1991), "The Complexity of Point Configurations," Discrete Applied Mathematics, 31, 167-180.
13. GORDON, A. D. (1981), Classification, London: Chapman and Hall.
14. GORDON, A. D., and HENDERSON, J. T. (1977), "An Algorithm for Euclidean Sum of Squares Classification," Biometrics, 33, 355-362.
15. GOWER, J. C. (1967), "A Comparison of some Methods of Cluster Analysis," Biometrics, 23, 623-637.
16. HARDING, E. F. (1967), "The Number of Partitions of a Set of N Partitions in k Dimensions Induced by Hyperplanes," Proceedings of the Edinburgh Mathematical Society (Series II), 15, 285-289.
17. HARTIGAN, J. A. (1975), Clustering Algorithms, New York: Wiley.
18. JANCEY, R. C. (1966), "Multidimensional Group Analysis," Australian Journal of Botany, 14, 127-130.
19. JUAN, J. (1982), "Programme de classification hiérarchique par l'algorithme de la recherche en chaîne des voisins réciproques," Les Cahiers de l'Analyse des Données, VII(2), 219-225.
20. KAUFMAN, L., and ROUSSEEUW, P. J. (1990), Finding Groups in Data: An Introduction to Cluster Analysis, New York: Wiley.
21. LANCE, G. N., and WILLIAMS, W. T. (1967), "A General Theory of Classificatory Sorting Strategies: I. Hierarchical Systems," Computer Journal, 9, 373-380.
22. MACQUEEN, J. B. (1967), "Some Methods for Classification and Analysis of Multivariate Observations," Proceedings of the 5-th Berkeley Symposium on Mathematical Statistics and Probability, 1, 281-297.
23. MURTAGH, F. (1983), "Expected-Time Complexity Results for Hierarchical Clustering Algorithms which use Cluster Centers," Information Processing Letters, 16, 237-241.
24. RAO, M. R. (1971), "Cluster Analysis and Mathematical Programming," Journal of the American Statistical Association, 66, 622-626.
25. ROMESBURG, H. C. (1990), Cluster Analysis for Researchers, Malubar, Florida: Krieger.
26. RUSPINI, E. H. (1970), "Numerical Methods for Fuzzy Clustering," Information Sciences, 2, 319-350.
27. SCOTT, A. J., and SYMONS, M. J. (1971), "On the Edwards and Cavalli-Sforza Method of Cluster Analysis," Biometrics, 27 217-219.
28. SPÄTH, H. (1980), Cluster Analysis Algorithms for Data Reduction and Classification of Objects, Chichester: Ellis Horwood.
29. SPÄTH, H. (1985), Cluster Dissection and Analysis (Theory, Fortran Programs, Examples), Chichester: Ellis Horwood.
30. WARD, J. H. (1963), ̈Hierarchical Grouping to Optimize an Objective Function,̈ Journal of the American Statistical Association, 58, 236-244.