Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
- J. B. Kruskal
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.
- Abelson, R. P. and Tukey, J. W. Efficient conversion of nonmetric information into metric information.Proc. Amer. statist. Ass. Meetings, Social statist. Section, 1959, 226–230.
- Aumann, R. J., Kruskal, J. B. (1958) The coefficients in an allocation problem. Naval Res. Logistics Quart. 5: pp. 111-123
- Aumann, R. J., Kruskal, J. B. (1959) Assigning quantitative values to qualitative factors in the Naval electronics problem. Naval Res. Logistics Quart. 6: pp. 1-16
- Bartholomew, D. J. (1959) A test of homogeneity for ordered alternatives. Biometrika 46: pp. 36-48
- Coombs, C. H. (1958) An application of a nonmetric model for multidimensional analysis of similarities. Psychol. Rep. 4: pp. 511-518
- Coombs, C. H., Kao, R. C. (1960) On a connection between factor analysis and multidimensional unfolding. Psychometrika 25: pp. 219-231
- Ekman, G. (1954) Dimensions of color vision. J. Psychol. 38: pp. 467-474
- Hardy, G. H., Littlewood, J. E., Polya, G. (1952) Inequalities. Cambridge Univ. Press, Cambridge, Eng.
- Indow, T., Uchizono, T. (1960) Multidimensional mapping of Munsell colors varying in hue and chroma. J. exp. Psychol. 59: pp. 321-329
- Indow, T., Kanazawa, K. (1960) Multidimensional mapping of colors varying in hue, chroma and value. J. exp. Psychol. 59: pp. 330-336
- Kolmogorov, A. N., Fomin, S. V. (1957) Elements of the theory of functions and functional analysis. Vol. 1.Metric and normed spaces. Graylock Press, Rochester, N. Y.
- Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, (accepted for publication, June, 1964).
- Rothkopf, E. Z. (1957) A measure of stimulus similarity and errors in some paired-associate learning tasks. J. exp. Psychol. 53: pp. 94-101
- Shepard, R. N. (1957) Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika 32: pp. 325-345
- Shepard, R. N. (1962) The analysis of proximities: Multidimensional scaling with an unknown distance function. Psychometrika 27: pp. 125-139
- Shepard, R. N. (1963) Analysis of proximities as a technique for the study of information processing in man. Human Factors 5: pp. 19-34
- Torgerson, W. S. (1958) Theory and methods of scaling. Wiley, New York
- Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
Volume 29, Issue 1 , pp 1-27
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors
- J. B. Kruskal (1)
- Author Affiliations
- 1. Bell Telephone Laboratories, Murray Hill, N. J.