Seriation of asymmetric matrices using integer linear programming

British Journal of Mathematical and Statistical Psychology

Volumn 54, Issue 2, 2001, Pages 367-375

  Brusco, Michael J ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; HUMAN; MATHEMATICAL COMPUTING; PSYCHOMETRY; RESEARCH; SYSTEM ANALYSIS;

HUMAN; MATHEMATICAL COMPUTING; PROGRAMMING, LINEAR; PSYCHOMETRICS; RESEARCH;

EID: 0035512539     PISSN: 00071102     EISSN: None     Source Type: Journal    
DOI: 10.1348/000711001159500     Document Type: Article

References (28)

1. 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.
2. Blin, M. J., & Whinston, A. B. (1974). A note on majority rule under transitivity constraints. Management Science, 20, 1439-1440.
3. Bowman, V. J., & Colantoni, C. S. (1973). Majority rule under transitivity constraints. Management Science, 19, 1029-1041.
4. Bowman, V. J., & Colantoni, C. S. (1974). Further comments on majority rule under transitivity constraints. Management Science, 20, 1441.
5. Brusco, M. J., & Stahl, S. (2001a). An interactive approach to multiobjective combinatorial data analysis. Psychometrika, 66, 5-24.
6. Brusco, M. J., & Stahl, S. (2001b). Compact integer-programming models for extracting subsets of stimuli from confusion matrices. Psychometrika, in press.
7. DeCani, J. S. (1969). Maximum likelihood paired comparison ranking by linear programming. Biometrika, 56, 537-545.
8. DeCani, J. S. (1972). A branch and bound algorithm for maximum likelihood paired comparison ranking by linear programming. Biometrika, 59, 131-135.
9. 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.
10. Flueck, J. A., & Korsh, J. F. (1974). A branch search algorithm for maximum likelihood paired comparison ranking. Biometrika, 61, 621-626.
11. Groenen, P. J. F., & Heiser, W. J. (1996). The tunneling method for global optimization in multi-dimensional scaling. Psychometrika, 61, 529-550.
12. Heiser, W. J. (1988) Selecting a stimulus set with prescribed structure from empirical confusion frequencies. British Journal of Mathematical and Statistical Psychology, 41, 37-51.
13. Hubert, L. (1976). Seriation using asymmetric proximity measures. British Journal of Mathematical and Statistical Psychology, 29, 32-52.
14. Hubert, L. J. (1987) Assignment methods in combinatorial data analysis. New York: Marcel Dekker.
15. 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.
16. Hubert, L., Arabie, P., & Meulman, J. (2001). Combinatorial data analysis: Optimization by dynamic programming. Philadelphia: Society for Industrial and Applied Mathematics.
17. Hubert, L. J., & Golledge, R. G. (1981). Matrix reorganization and dynamic programming: Applications to paired comparisons and unidimensional seriation. Psychometrika, 46, 429-441.
18. ILOG CPLEX 6.5 (1999). User's manual. Mountain View, CA: ILOG, Inc.
19. Phillips, J. P. N. (1967). A procedure for determining Slater's i and all nearest adjoining orders. British Journal of Mathematical and Statistical Psychology, 20, 217-225.
20. Phillips, J. P. N. (1969). A further procedure for determining Slater's i and all nearest adjoining orders. British Journal of Mathematical and Statistical Psychology, 22, 97-101.
21. Phillips, J. P. N. (1976). On an algorithm of Smith and Payne for determining Slater's i and all nearest adjoining orders. British Journal of Mathematical and Statistical Psychology, 29, 126-127.
22. Ranyard, R. H. (1976). An algorithm for maximum likelihood ranking and Slater's i from paired comparisons. British Journal of Mathematical and Statistical Psychology, 29, 242-248.
23. Rodgers, J. L. & Thompson, T. D. (1992). Seriation and multidimensional scaling: A data analysis approach to scaling asymmetric proximity matrices. Applied Psychological Measurement, 16, 105-117.
24. Rothkopf, E. Z. (1957). A measure of stimulus similarity and errors in some paired-associate learning tasks. Journal of Experimental Psychology, 53, 94-101.
25. Smith, A. F. M., & Payne, C. D. (1974). An algorithm for determining Slater's i and all nearest adjoining orders. British Journal of Mathematical and Statistical Psychology, 27, 49-52.
26. Thurstone, L. L. (1927). The method of paired comparison of social values. Journal of Abnormal and Social Psychology, 31, 384-400.
27. Van der Heijden, A. H. C., Malhas, M. S. M., & van den Roovaart, B. P. (1984). An empirical interletter confusion matrix for continuous-line capitals. Perceptions & Psychophysics, 35, 85-88.
28. Williams, H. P. (1990). Model building in mathematical programming, 3rd ed. New York: Wiley.