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The majorization approach to multidimensional scaling for Minkowski distances. (English) Zbl 0825.92158


MSC:

91C15 One- and multidimensional scaling in the social and behavioral sciences

Software:

KYST
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References:

[1] ARABIE, P. (1991), ?Was Euclid an Unnecessarily Sophisticated Psychologist??Psychometrika, 56, 567-587. · Zbl 0761.92050 · doi:10.1007/BF02294491
[2] CARROLL, J. D., and WISH, M. (1977), ?Multidimensional Perceptual Models and Measurement Methods,? inHandbook of Perception, Vol. II Eds., E. C. Carterette and M.P. Friedman, New York: Academic Press, 391-447.
[3] DE LEEUW, J. (1977), ?Applications of Convex Analysis to Multidimensional Scaling,? inRecent Developments in Statistics, Eds., J. R. Barra, F. Brodeau, G. Romier and B. van Cutsem, Amsterdam: North-Holland, 133-145.
[4] DE LEEUW, J. (1984), ?Differentiability of Kruskal’s Stress at a Local Minimum,?Psychometrika, 49, 111-113. · doi:10.1007/BF02294209
[5] DE LEEUW, J. (1988), ?Convergence of the Majorization Method for Multidimensional Scaling,?Journal of Classification, 5, 163-180. · Zbl 0692.62056 · doi:10.1007/BF01897162
[6] DE LEEUW, J. (1992),Fitting Distances by Least Squares, unpublished manuscript, Los Angeles: UCLA.
[7] DE LEEUW, J., and HEISER, W. J. (1977), ?Convergence of Correction-Matrix Algorithms for Multidimensional Scaling? inGeometric Representations of Relational Data, Ed., J. C. Lingoes, Ann Arbor, Michigan: Mathesis Press, 735-751.
[8] DE LEEUW, J., and HEISER, W. J. (1980), ?Multidimensional Scaling with Restrictions on the Configuration,? inMultivariate Analysis V, Ed., P. R. Krishnaiah, Amsterdam: North-Holland, 501-522. · Zbl 0468.62054
[9] GREEN, P. E., CARMONE, F. J. Jr, and SMITH, S. M. (1989),Multidimensional Scaling, Concepts and Applications, Boston: Allyn and Bacon.
[10] GROENEN, P. J. F., and HEISER, W. J. (1991),An Improved Tunneling Function for Finding a Decreasing Series of Local Minima, internal report RR-91-06, Leiden: Department of Data Theory.
[11] GUTTMAN, L. (1968), ?A General Nonmetric Technique for Finding the Smallest Coordinate Space for a Configuration of Points,?Psychometrika, 33, 469-506. · Zbl 0205.49302 · doi:10.1007/BF02290164
[12] HEISER, W. J. (1988), ?Multidimensional Scaling with Least Absolute Residuals,? inClassification and Related Methods of Data Analysis, Ed., H. H. Bock, Amsterdam: North-Holland, 455-462.
[13] HEISER, W. J. (1989), ?The City-Block Model for Three-Way Multidimensional Scaling,? inMultiway Data Analysis, Eds., R. Coppi and S. Bolasco, Amsterdam: North-Holland, 395-404.
[14] HEISER, W. J. (1991), ?A Generalized Majorization Method for Least Squares Multidimensional Scaling of Pseudodistances That may be Negative,?Psychometrika, 56, 7-27. · Zbl 0726.92032 · doi:10.1007/BF02294582
[15] HUBERT, L. J., and ARABIE, P. (1986), ?Unidimensional Scaling and Combinatorial Optimization,? inMultidimensional Data Analysis, Eds., J. De Leeuw, W. J. Heiser, J. Meulman and F. Critchley, Leiden: DSWO Press, 181-196.
[16] HUBERT, L. J., ARABIE, P., and HESSON-MCINNIS, M. (1992), ?Multidimensional Scaling in the City-Block Metric: A Combinatorial Approach,?Journal of Classification, 9, 211-236. · doi:10.1007/BF02621407
[17] KRUSKAL, J. B. (1964a), ?Multidimensional Scaling by Optimizing Goodness of Fit to a Non-Metric Hypothesis,?Psychometrika, 29, 1-27. · Zbl 0123.36803 · doi:10.1007/BF02289565
[18] KRUSKAL, J. B. (1964b), ?Nonmetric Multidimensional Scaling: A Numerical Method,?Psychometrika, 29, 115-129. · Zbl 0123.36804 · doi:10.1007/BF02289694
[19] KRUSKAL, J. B. (1977), ?Multidimensional Scaling and Other Methods for Discovering Structure,? inStatistical Methods for Digital Computers, Vol III, Eds., K. Enslein, A. Ralston and H. S. Wilf, New York: Wiley, 296-339.
[20] KRUSKAL, J. B., YOUNG, F. W., and SEERY, J. B. (1977),How to Use KYST-2, a Very Flexible Program to do Multidimensional Scaling and Unfolding, Murray Hill, NJ: AT&T Bell Labs.
[21] MATHAR, R., and GROENEN, P. J. F. (1991), ?Algorithms in Convex Analysis Applied to Multidimensional Scaling,? inSymbolic-Numeric Data Analysis and Learning, Eds., E. Diday, and Y. Lechevallier, Commack, New York: Nova Science, 45-56.
[22] MATHAR, R., and MEYER, R. (1992),Algorithms in Convex Analysis to Fit l p-distance matrices, unpublished report, Aachen: RWTH.
[23] MEULMAN, J. J. (1986),A Distance Approach to Nonlinear Multivariate Analysis, Leiden: DSWO Press.
[24] PETERS, G., and WILKINSON, J. H. (1971), ?The Calculation of Specified Eigenvectors by Inverse Iteration,? inHandbook for Automatic Computation, Vol. II, Linear Algebra, Eds., J. H. Wilkinson and C. Reinsch, Berlin: Springer, 418-439.
[25] ZANGWILL, W. I. (1969),Nonlinear Programming, a Unified Approach, Englewood Cliffs, NJ: Prentice-Hall. · Zbl 0195.20804
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