A repetitive branch-and-bound procedure for minimum within-cluster sums of squares partitioning

Psychometrika

Volumn 71, Issue 2, 2006, Pages 347-363

  Brusco, Michael J ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Branch and bound; Cluster analysis; Combinatorial data analysis; K means

Indexed keywords

EID: 33746451728     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-004-1218-1     Document Type: Article

References (41)

1. Anderberg, M.R. (1973). Cluster analysis for applications. New York: Academic Press.
2. Anderson, E. (1935). The irises of the Gaspé peninsula. Bulletin of the American Iris Society, 59, 2-5.
3. Arabie, P., & Hubert, L.J. (1992). Combinatorial data analysis. Annual Review of Psychology, 43, 169-203.
4. Arabie, P., & Hubert, L.J. (1996). An overview of combinatorial data analysis. In P. Arabie, L.J. Hubert, & G. De Soete (Eds.), Clustering and classification (pp. 5-63). River Edge, NJ: World Scientific.
5. Blashfield, R.K., & Aldenferer, M.S. (1988). The methods and problems of cluster analysis. In J.R. Nesselroade & R.B. Cattell (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 447-473). New York: Plenum.
6. Brusco, M.J. (2002). A branch-and-bound algorithm for fitting anti-Robinson structures to symmetric dissimilarity matrices. Psychometrika, 67, 459-471.
7. Brusco, M.J. (2003). An enhanced branch-and-bound algorithm for a partitioning problem. British Journal of Mathematical and Statistical Psychology, 56, 83-92.
8. Brusco, M.J., & Stahl, S. (2005). Branch-and-bound applications in combinatorial data analysis. New York: Springer-Verlag.
9. Clapham, C. (1996). The concise Oxford dictionary of mathematics. (2nd ed.). Oxford, UK: Oxford University Press.
10. Day, W.H.E. (1996). Complexity theory: An introduction for practitioners of classification. In P. Arabie, L.J. Hubert, & G. De Soete (Eds.), Clustering and classification (pp. 199-233). River Edge, NJ: World Scientific.
11. DeCani, J.S. (1972). A branch and bound algorithm for maximum likelihood paired comparison ranking by linear programming. Biometrika, 59, 131-135.
12. Defays, D. (1978). A short note on a method of seriation. British Journal of Mathematical and Statistical Psychology, 37, 49-53.
13. Diehr, G. (1985). Evaluation of a branch and bound algorithm for clustering. SIAM Journal for Scientific and Statistical Computing, 6, 268-284.
14. Du Merle, O., Hansen, P., Jaumard, B., & Mladenovic, N. (2000). An interior point algorithm for minimum sum-of-squares clustering. SIAM Journal on Scientific Computing, 21, 1485-1505.
15. Edwards, A.W.F., & Cavalli-Sforza, L.L. (1965). A method for cluster analysis. Biometrics, 21, 362-375.
16. Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179-188.
17. Fisher, W.D. (1958). On grouping for maximum heterogeneity. Journal of the American Statistical Association, 53, 789-798.
18. Flueck, J.A., & Korsh, J.F. (1974). A branch search algorithm for maximum likelihood paired comparison ranking. Biometrika, 61, 621-626.
19. Forgy, E.W. (1965). Cluster analyses of multivariate data: Efficiency versus interpretability of classifications. Biometrics, 27, 768.
20. Furnival, G.M., & Wilson, R.W. (1974). Regression by leaps and bounds. Technometrics, 16, 499-512.
21. Hair, J.F., Anderson, R.E., Tatham, R. L., & Black,W. C. (1998). Multivariate data analysis (5th ed.). Upper Saddle River, NJ: Prentice Hall.
22. Hand, D.J. (1981a). Discrimination and classification. New York: Wiley.
23. Hand, D.J. (1981b). Branch and bound in statistical data analysis, The Statistician, 30, 1-13.
24. Hartigan, J.A. (1975). Clustering algorithms. New York: Wiley.
25. Hartigan, J.A., & Wong, M.A. (1979). Algorithm AS 136: A k-means clustering program. Applied Statistics, 28, 100-128.
26. Hubert, L., Arabie, P., & Meulman, J. (2001). Combinatorial data analysis: Optimization by dynamic programming. Philadelphia: Society for Industrial and Applied Mathematics.
27. Jensen, R.E. (1969). A dynamic programming algorithm for cluster analysis. Operations Research, 17, 1034-1057.
28. Klein, G., & Aronson, J.E. (1991). Optimal clustering: A model and method. Naval Research Logistics, 38, 447-461.
29. Koontz, W.L.G., Narendra, P.M., & Fukunaga, K. (1975). A branch and bound clustering algorithm. IEEE Transaction on Computers, C-24, 908-915.
30. Luce, R.D., & Krumhansl, C. (1988). Measurement, scaling, and psychophysics. In R.C. Atkinson, R.J. Hemnstein, G. Lindzey, & R.D. Luce (Eds.), Stevens' handbook of experimental psychology (pp. 3-74). New York: Wiley.
31. MacQueen, J.B. (1967). Some methods for classification and analysis of multivariate observations. In L.M. Le Cam & J. Neyman (Eds.), Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (Vol. 1, pp. 281-297), Berkeley, CA: University of California Press.
32. Miller, K.F. (1987). Geometric methods in developmental research. In J. Bisanz, C.J. Brainerd, & R. Kail (Eds.), Formal methods in developmental psychology (pp. 216-262). New York: Springer-Verlag.
33. Milligan, G.W. (1980). An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika, 45, 325-342.
34. Murtaugh, F. (Ed.) (2003). Classification literature automated search service (Vol. 23-31 1994-2002). Chicago: Classification Society of North America.
35. Narendra, P.M., & Fukunaga, K. (1977). A branch and bound algorithm for feature subset selection. IEEE Transactions on Computers C-,. 26, 917-922.
36. Palubeckis, G. (1997). A branch-and-bound approach using polyhedral results for a clustering problem. INFORMS Journal on Computing, 9, 30-42.
37. Rao, M.R. (1971). Cluster analysis and mathematical programming. Journal of the American Statistical Association, 66, 622-626.
38. Späth, H. (1980). Cluster analysis algorithms for data reduction and classification of objects. New York: Wiley.
39. Steinley, D. (2003). Local optima in K-means clustering: What you don't know may hurt you. Psychological Methods, 8, 294-304.
40. Van Os, B.J., & Meulman, J.J. (2004). Improving dynamic programming strategies for partitioning. Journal of Classification, 21, 207-230.
41. Ward, J.H. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 236-244.