Nonmetric multidimensional scaling: A numerical method
Tóm tắt
We describe the numerical methods required in our approach to multi-dimensional scaling. The rationale of this approach has appeared previously.
Tài liệu tham khảo
Barton, D. E. and Mallows, C. L. The randomization bases of the amalgamation of weighted means.J. roy. statist. Soc., Series B, 1961,23, 423–433.
Bartholomew, D. J. A test of homogeneity for ordered alternatives.Biometrika, 1959,46, 36–48.
Bartholomew, D. J. A test of homogeneity of means under restricted alternatives (with discussion).J. roy. statist. Soc., Series B, 1961,23, 239–281.
Hardy, G. H., Littlewood, J. E., and Polya, G.Inequalities. (2nd ed.) Cambridge, Eng.: Cambridge Univ. Press, 1952.
Hildebrandt, P. and Isbitz H. Radix-exchange—An internal sorting method for digital computers.J. Assoc. computing Machinery, 1959,6, 156–163.
Kolmogorov, A. N. and Fomin, S. V.Elements of the theory of functions and functional analysis. Vol. 1.Metric and normed spaces. Translated from the first (1954) Russian Edition by Leo F. Boron, Rochester, N. Y., Graylock Press, 1957.
Kruskal, J. Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–28.
Miles, R. E. The complete amalgamation into blocks, by weighted means, of a finite set of real numbers.Biometrika, 1959,46, 317–327.
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function.Psychometrika (I and II), 1962,27, 125–139, 219–246.
Spang, H. A. III. A review of minimization techniques for nonlinear functions.SIAM Rev., 1962,4, 343–365.
van Eeden, C. Maximum likelihood estimation of partially or completely ordered parameters, I.Proc. Akademie van Wetenschappen, Series A, 1957,60, 128–136.
van Eeden, C. Note on two methods for estimating ordered parameters of probability distributions.Proc. Akademie van Wetenschappen, Series A, 1957,60, 506–512.