DIMACS Working Group on Algorithms for Multidimensional Scaling

Algorithms for Multidimensional Scaling I

Working Group Meeting: August 6 - 9, 2001

Public Workshop: Friday, August 10, 2001

Location: DIMACS Center, CoRE Building, Rutgers University

Organizers:

J. Douglas Carroll, Rutgers University, dcarroll@rci.rutgers.edu

Phipps Arabie, Rutgers University, arabie@andromeda.rutgers.edu

Lawrence J. Hubert, University of Illinois, lhubert@s.psych.uiuc.edu

This material is based upon work supported by the National Science Foundation under Grant No. 0100921

References for Algorithms for Multidimensional Scaling Working Group

[B1] Abney, S., Volinsky, C., and Buja, A., Mining large call graphs, AT&T Labs Technical Memorandum, Florham Park, NJ, 1998.
[B2] Brusco, M.J., Morph-based local-search heuristics for large-scale combinatorial data analysis, J. Classification, 16 (1999), 163-180.
[B3] Brusco, M.J., and Stahl, S., Using quadratic assignment methods to generate initial permutations for least-squares unidimensional scaling of symmetric proximity matrices, working paper, Florida State University, 2000.
[B4] Brusco, M.J., and Stahl, S., A simulated annealing heuristic for unidimensional and multidimensional (city-block) scaling of symmetric proximity matrices, working paper, Florida State University, 2000.
[B5] Buja, A., Swayne, D.F., Littman, M.L., and Dean, N., XGvis: Interactive data visualization with multidimensional scaling, J. of Computational and Graphical Statistics, to appear.
[B6] Carroll, J.D., Some multidimensional scaling and related procedures devised at Bell Laboratories, with ecological applications, in P. Legendre and L. Legendre (eds.), Developments in Numerical Ecology, NATO ASI Series, Vol. G14, Springer-Verlag, Berlin-Heidelberg, 1987, pp. 65-138.
[B7] Carroll, J.D., and Arabie, P., Multidimensional scaling, in M.H. Birnbaum (ed.), Handbook of Perception and Cognition, Volume 3: Measurement, Judgment and Decision Making, Academic Press, San Diego, CA, 1998, pp. 179-250.
[B8] Carroll, J.D. and Chang, J.J., Analysis of individual differences in multidimensional scaling via an N-way generalization of ``Eckart-Young'' decomposition, Psychometrika, 35 (1970), 283-319. [Reprinted in P. Davies and A. P. M. Coxon (eds.), Key Texts in Multidimensional Scaling, Heinemann, Portsmouth, NH, 1984, pp. 229-252.]
[B9] Carroll, J.D., and Chaturvedi, A., A general approach to clustering and multidimensional scaling of two-way, three-way, or higher-way data, in R. D. Luce, M. D'Zmura, D. D. Hoffman, G. Iverson and A. K. Romney (eds.), Geometric Representations of Perceptual Phenomena, Erlbaum, Mahwah, NJ, 1995, pp. 295-318.
[B10] Carroll, J.D., and Corter, J., A graph-theoretic method for organizing overlapping clusters into trees, multiple trees, or extended trees, J. Classification, 12 (1995), 283-313.
[B11] Carroll, J.D., De Soete, G., and Pruzansky, S., A comparison of three rational initialization methods for INDSCAL, in E. Diday (ed.), Data Analysis and Informatics V, North-Holland, Amsterdam, 1988, pp. 131-142.
[B12] Carroll, J.G., De Soete, G., and Pruzansky, S., An evaluation of five algorithms for generating an initial configuration for SINDSCAL, J. Classification, 6 (1989), 105--119.
[B13] Carroll, J.D., and Pruzansky, S., The CANDECOMP-CANDELINC family of models and methods for multidimensional data analysis, in H. G. Law, W. Snyder, J. Hattie, and R. P. McDonald (eds.), Research Methods for Multimode Data Analysis, Praeger, New York, 1984, pp. 372-402.
[B14] Carroll, J.D. and Pruzansky, S., Discrete and hybrid models for proximity data, in W. Gaul and M. Schader (eds.) Classification as a Tool of Research, North-Holland, Amsterdam, 1986, pp. 47-59.
[B15] Carroll, J.D., Pruzansky, S., and Kruskal, J.B., CANDELINC: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters, Psychometrika, 45 (1980), 3-24.
[B16] Chandon, J.L., and De Soete, G., Fitting a least squares ultrametric to dissimilarity data: Approximation versus optimization, in E. Diday, M. Jambu, L. Lebart, J. Pages, and R. Tomassone (eds.), Data Analysis and Informatics III, North-Holland, Amsterdam, 1984, pp. 213-221.
[B17] Chen, G., Metric two-way multidimensional scaling and circular unidimensional scaling: Global optimization by mixed integer programming approaches, Doctoral Dissertation, Rutgers University, 2000.
[B18] Crippen, G.M., and Havel, T.F., Stable calculation of coordinates from distance information, Acta Crystallographica, A34 (1978), 282-284.
[B19] de Leeuw, J., and Heiser, W., Convergence of correction-matrix algorithms for multidimensional scaling, in J. C. Lingoes (ed.), Geometric Representations of Relational Daata: Readings in multidimensional scaling, Mathesis, Ann Arbor, MI, 1977, pp. 735-752.
[B20] Glunt, W., Hayden, T.L, and Raydan, M., Molecular conformation from distance matrices, J. Computational Chemistry, 14 (1993), 114-120.
[B21] Hagerty, C.G., Muchnik, I., Kulikowski, C., and Kim, S-H., Two indices can approximate four hundred and two amino acid properties, Proceedings of the 1999 IEEE International Symposium on Intelligent Control/Intelligent Systems and Semiotics, Cambridge, MA, September 1999, pp. 365-369.
[B22] Havel, T.F., An evaluation of computational strategies for use in the determination of protein structure from distance constraints obtained by nuclear magnetic resonance, Progress in Biophysics and Molecular Biology, 56 (1991), 43-78.
[B23] Heiser, W.J., Order invariant unfolding analysis under smoothness restrictions, in G. De Soete, H. Feger, and C. Klauer (eds.), New Developments in Psychological Choice Modeling, North-Holland, Amsterdam, 1989, pp. 3-31.
[B24] Hubert, L.J., and Arabie, P., Unidimensional scaling and combinatorial optimization, in J. de Leeuw, W. Heiser, J. Meulman, and F. Critchley (eds.), Multidimensional Data Analysis, DSWO Press, Leiden 1986, pp. 181-196.
[B25] Hubert, L.J., and Arabie, P. Iterative projection strategies for the least-squares fitting of tree structures to proximity data, British J. Math. Statist. Psych., 48 (1995), 281-317.
[B26] Hubert, L.J. and Arabie, P., The approximation of two-mode proximity matrices by sums of order-constrained matrices, Psychometrika, 60 (1995), 573--605.
[B27] Hubert, L.J., Arabie P.,, and Hesson-Mcinnis, M., Multidimensional scaling in the city-block metric: A combinatorial approach, J. Classification, 9 (1992), 211--236.
[B28] Hubert, L.J., Arabie, P., and Meulman, J., Linear and circular unidimensional scaling for symmetric proximity matrices, British J. Math. Statist. Psych., 50, 253-284.
[B29] Kruskal, J.B., Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis, Psychometrika, 29 (1964), 1-27.
[B30] Kruskal, J.B., Nonmetric multidimensional scaling: A numerical method, Psychometrika, 29 (1964), 115-129.
[B31] Kruskal, J.B., and Hart, R.E., A geometric interpretation of diagnostic data from a digital machine: Based on a study of the Morris, Illinois Electronic Central Office, Bell Sys. Tech. J., 45 (1966), 1299-1338.
[B32] Legendre, P., and Legendre, L., Numerical Ecology, Elsevier, Amsterdam, 1998.
[B33] Littman, M., Swayne, D.F., Dean, N., and Buja, A., Visualizing the embedding of objects in Euclidean space, Computing Science and Statistics: Proc. of the 24th Symp. on the Interface, Interface Foundation of North America, Fairfax Station, VA, 1992, 208-217.
[B34] Luczkovich, J.J., Borgatti, S.P., Johnson, J.C., and Everett, M.G., Defining and measuring trophic role similarity in food webs using regular coloration, in preparation.
[B35] Shepard, R.N., The analysis of proximities: Multidimensional scaling with an unknown distance function. I, Psychometrika, 27 (1962), 125-140.
[B36] Shepard, R.N., The analysis of proximities: Multidimensional scaling with an unknown distance function. II, Psychometrika, 27 (1962), 219-246.
[B37] Simantiraki, E., Unidimensional Scaling: A linear programming approach minimizing absolute deviations, J. Classification, 13 (1996), 19-25.
[B38] Watts, D., Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, Princeton, NJ, 1999.

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Document last modified on April 11, 2001.