Advanced SearchSearch Tips
Multidimensional Scaling of Asymmetric Distance Matrices
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Multidimensional Scaling of Asymmetric Distance Matrices
Huh, Myung-Hoe; Lee, Yong-Goo;
  PDF(new window)
In most cases of multidimensional scaling(MDS), the distances or dissimilarities among units are assumed to be symmetric. Thus, it is not an easy task to deal with asymmetric distances. Asymmetric MDS developed so far face difficulties in the interpretation of results. This study proposes a much simpler asymmetric MDS, that utilizes the notion of "altitude". The analogy arises in mountaineering: It is easier (more difficult) to move from the higher (lower) point to the lower (higher). The idea is formulated as a quantification problem, in which the disparity of distances is maximally related to the altitude difference. The proposed method is demonstrated in three examples, in which the altitudes are visualized by rainbow colors to ease the interpretability of users.
Multidimensional scaling(MDS);similarity;asymmetric distance matrix;altitude model;social network analysis;
 Cited by
비대칭 다차원척도법의 시각화,이수기;최용석;이보희;

응용통계연구, 2014. vol.27. 4, pp.619-627 crossref(new window)
Visualizations for Matched Pairs Models Using Modified Correspondence Analysis,;;

Communications for Statistical Applications and Methods, 2014. vol.21. 4, pp.275-284 crossref(new window)
Visualizations for Matched Pairs Models Using Modified Correspondence Analysis, Communications for Statistical Applications and Methods, 2014, 21, 4, 275  crossref(new windwow)
Visualizations of Asymmetric Multidimensional Scaling, Korean Journal of Applied Statistics, 2014, 27, 4, 619  crossref(new windwow)
Carroll, D. J. and Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an N-Way generalization of "Eckart-Young" decomposition, Psychometrika, 35, 283-319. crossref(new window)

Cox, T. F. and Cox, M. A. A. (2001). Multidimensional Scaling, Second Edition, Chapman & Hall/CRC, Boca Raton, Section 4.8.

Chino, N. (2006). Asymmetric multidimensional scaling and related topics, Manuscript for the invited talk at the Weierstrass Institute for Applied Analysis and Stochastics, Berlin.

Chino, N. (2011). Asymmetric multidimensional scaling: 1. Introduction, Journal of the Institute for Psychological and Physical Sciences, 3, 101-107.

Constantine, A. G. and Gower, J. C. (1978). Graphical representation of asymmetry, Applied Statistics, 27, 297-304. crossref(new window)

Freeman, L. C. and Freeman, S. C. (1980). A semi-visible college: Structural effects on a social networks group. 77-85 in Henderson, M. M. and McNaughton, M. J. (eds.) Electronic Communication: Technology and Impacts, Boulder, CO: Westview Press.

Hanneman, R. A. and Riddle, M. (2005). Introduction to Social Network Methods, Available at

Lattin, J., Carroll, J. D. and Green, P. E. (2003). Analyzing Multivariate Data, Pacific Grove, CA: Brooks/Cole. 231.

Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S, Fourth edition. Springer. 303.

Wasserman, S. and Faust, K. (1994). Social Network Analysis: Methods and Applications, New York and Cambridge: Cambridge University Press. 62-65.

Young, F. W. (1975). An asymmetric Euclidian model for multiprocess asymmetric data. Paper presented at U.S.-Japan Seminar on MDS. San Diego, U.S.A. 79-88.