Optimal least-squares unidimensional scaling: Improved branch-and-bound procedures and comparison to dynamic programming

Psychometrika

Volumn 70, Issue 2, 2005, Pages 253-270

  Brusco, Michael J ^a   Stahl, Stephanie ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b Florida State University ^*

Author keywords

Branch and bound; Combinatorial data analysis; Dynamic programming; Least squares unidimensional scaling

Indexed keywords

EID: 24344457780     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-002-1032-6     Document Type: Review

References (31)

1. Arabie, P., & Hubert, L.J. (1992). Combinatorial data analysis. Annual Review of Psychology, 43, 169-203.
2. Baker, F.B., & Hubert, L.J. (1977). Applications of combinatorial programming to data analysis: Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 30, 154-164.
3. Brusco, M.J. (2002a). A branch-and-bound algorithm for fitting anti-Robinson structures to symmetric dissimilarity matrices. Psychometrika, 67, 459-471.
4. Brusco, M.J. (2002b). Identifying a reordering of the rows and columns of multiple proximity matrices using multiobjective programming. Journal of Mathematical Psychology, 46, 731-745.
5. Brusco, M.J., & Stahl, S. (2000). Using quadratic assignment methods to generate initial permutations for least-squares unidimensional scaling of symmetric proximity matrices. Journal of Classification, 17, 197-223.
6. Brusco, M.J., & Stahl, S. (2001). An interactive approach to multiobjective combinatorial data analysis. Psychometrika, 66, 5-24.
7. DeCani, J.S. (1972). A branch and bound algorithm for maximum likelihood paired comparison ranking by linear programming. Biometrika, 59, 131-135.
8. Defays, D. (1978). A short note on a method of seriation. British Journal of Mathematical and Statistical Psychology, 31, 49-53.
9. de Leeuw, J., & Heiser, W.J. (1977). Convergence of correction-matrix algorithms for multidimensional scaling. In J. C. Lingoes (Ed.), Geometric Representations of Relational Data: Readings in Multidimensional Scaling (pp. 735-752). Ann Arbor Michigan: Mathesis Press.
10. De Soete, G., Hubert, L., & Arabie, P. (1988). The comparative performance of simulated annealing on two problems of combinatorial data analysis. In E. Diday (Ed.), Data Analysis and Informatics, vol. 5 (pp. 489-496). Amsterdam: North Holland.
11. Flueck, J.A., & Korsh, J.F. (1974). A branch search algorithm for maximum likelihood paired comparison ranking. Biometrika, 61, 621-626.
12. Groenen, P.J.F. (1993). The Majorization Approach to Multidimensional Scaling: Some Problems and Extensions. Leiden, Netherlands: DSWO Press.
13. Groenen, P.J.F., & Heiser, W.J. (1996). The tunneling method for global optimization in multidimensional scaling. Psychometrika, 61, 529-550.
14. Groenen, P.J.F., Heiser, W.J., & Meulman, J. J. (1999). Global optimization of least-squares multidimensional scaling by distance smoothing. Journal of Classification, 16, 225-254.
15. Hubert, L.J. (1976). Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 29, 32-52.
16. Hubert, L.J., & Arabie, P. (1986). Unidimensional scaling and combinatorial optimization. In J. de Leeuw, W. Heiser, J. Meulman, and F. Critchley (Eds.), Multidimensional Data Analysis (pp. 181-196). Leiden, Netherlands: DSWO Press.
17. Hubert, L., & Arabie, P. (1994). The analysis of proximity matrices through sums of matrices having (anti-) Robinson forms. British Journal of Mathematical and Statistical Psychology, 47, 1-40.
18. Hubert, L., Arabie, P., & Meulman, J. (1997). Linear and circular unidimensional scaling for symmetric proximity matrices. British Journal of Mathematical and Statistical Psychology, 50, 253-284.
19. Hubert, L., Arabie, P., & Meulman, J. (1998). Graph-theoretic representations for proximity matrices through strongly anti-Robinson or circular strongly anti-Robinson matrices. Psychometrika, 63, 341-358.
20. Hubert, L., Arabie, P., & Meulman, J. (2001). Combinatorial Data Analysis: Optimization by Dynamic Programming. Philadelphia: Society for Industrial and Applied Mathematics.
21. 2-Norm: Basic optimization methods using MATLAB. Journal of Classification, 19, 303-328.
22. Hubert, L.J., & Baker, F.B. (1977). The comparison and fitting of given classification schemes. Journal of Mathematical Psychology, 16, 233-253.
23. Hubert, L.J., & Golledge, R.G. (1981). Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation. Psychometrika, 46, 429-441.
24. Lawler, E.L. (1964). A comment on minimum feedback arc sets. IEEE Transactions on Circuit Theory, 11, 296-297.
25. Manning, S.K., & Shofner, E. (1991). Similarity ratings and confusability of lipread consonants compared with similarity ratings of auditory and orthographic stimuli. American Journal of Psychology, 104, 587-604.
26. Morgan, B.J.T., Chambers, S.M., & Morton, J. (1973). Acoustic confusion of digits in memory and recognition. Perception & Psychophysics, 14, 375-383.
27. Pliner, V. (1996). Metric unidimensional scaling and global optimization. Journal of Classification, 13, 3-18.
28. Robinson, W.S. (1951). A method for chronologically ordering archaeological deposits. American Antiquity, 16, 293-301.
29. Ross, B.H., & Murphy, G.L. (1999). Food for thought: Cross-classification and category organization in a complex real-world domain. Cognitive Psychology, 38, 495-553.
30. Rothkopf, E.Z. (1957). A measure of stimulus similarity and errors in some paired-associate learning tasks. Journal of Experimental Psychology, 53, 94-101.
31. Younger, D.H. (1963). Minimum feedback arc sets for a directed graph. IEEE Transactions on Circuit Theory, 10, 238-245.