The representation of symmetric proximity data: Dimensions and classifications

Computer Journal

Volumn 41, Issue 8, 1998, Pages 576-577

  Hubert, Lawrence ^a   Arabie, Phipps ^b   Meulman, Jacqueline ^c  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; OBJECT RECOGNITION;

CIRCULAR ANTI-ROBINSON (CAR) MATRIX; SYMMETRIC PROXIMITY MATRIX;

DATA STRUCTURES;

EID: 0032269821     PISSN: 00104620     EISSN: None     Source Type: Journal    
DOI: 10.1093/comjnl/41.8.566     Document Type: Article

References (17)

1. Shepard, R. N. (1962a) Analysis of proximities: Multidimensional scaling with an unknown distance function I. Psychometrika, 27, 125-140.
2. Shepard, R. N. (1962b) Analysis of proximities: Multidimensional scaling with an unknown distance function II. Psychometrika, 27, 219-246.
3. Kruskal, J. B. (1964a) Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-27.
4. Kruskal, J. B. (1954b) Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
5. Pruzansky, S., Tversky, A. and Carroll, J. D. (1982) Spatial versus tree representations of proximity data. Psychometrika, 47, 3-24.
6. Shepard, R. N. (1974) Representation of structure in similarity data: problems and prospects. Psychometrika, 39, 373-421.
7. Hubert, L. J. and Arabie, P. (1994) The analysis of proximity matrices through sums of matrices having (anti-)Robinson forms. Brit. J. Math. Statist. Psych., 47, 1-40.
8. Hubert, L. J. and Arabie, P. (1995) Iterative projection strategies for the least-squares fitting of tree structures to proximity data. Brit. J. Math. Statist. Psych., 48, 281-317.
9. Hubert, L. J., Arabie, P. and Meulman, J. (1997) Linear and circular unidimensional scaling for symmetric proximity matrices. Brit. J. Math. Statist. Psych., 50, 253-284.
10. Hubert, L. J., Arabie, P. and Meulman, J. (1998) Graph-theoretic representations for proximity matrices through strongly-anti-Robinson or circular strongly-anti-Robinson matrices. Psychometrika, 63, 341-358.
11. Kruskal, J. B., Young, F. W. and Seery, J. B. (1977) How to Use KYST2, a Very Flexible Program to Do Multidimensional Scaling and Unfolding. AT&T Bell Laboratories, Murray Hill, NJ.
12. Wilkinson, L. (1988) SYSTAT: The System for Statistics. SYSTAT, Inc, Evanston, IL.
13. Carroll, J. D. (1992) Metric, nonmetric, and quasi-nonmetric analysis of psychological data. Division 5 Presidential Address, American Psychological Association, Washington, DC, August, 1992, Score, Newsletter of Division 5, October, 1992, pp. 4-5.
14. Corter, J. E. and Tversky, A. (1986) Extended similarity trees. Psychometrika, 51, 429-451.
15. Ekman, G. (1954) Dimensions of color vision. J. Psych., 68, 530-536.
16. Kendall, D. G. (1971) Seriation from abundance matrices. In Hodson, F. R., Kendall, D. G. and Tǎutu P. (eds), Mathematics in the Archaeological and Historical Sciences, pp. 215-252. Edinburgh University Press, Edinburgh.
17. Johnson, E. J. and Tversky, A. (1984) Representations of perceptions of risks. J. Exp. Psych.: Gen., 113, 55-70.