Summary
Least squares multidimensional scaling (NIDS) methods are attractive candidates to approximate proximities between subjects in multivariate data (Meulman, 1992). Distances in the subject space will resemble the proximities as closely as possible, in contrast to traditional multivariate methods. When we wish to represent the variables in the same display — after using NIDS to represent the subjects — various possibilities exist. A major distinction is between linear and nonlinear biplots. Both types will be discussed briefly, including their drawbacks. To circumvent these drawbacks, a third alternative will be proposed. By expanding the optimal p-space (where p denotes the dimensionality of the subject space) into an m-dimensional space of rank p (with m > p), we obtain a coordinate system that is appropriate for the evaluation of the MDS solution directly in terms of the m original variables. The latter are represented graphically as vectors in p-space, and their entries as markers that are located on these vectors. The overall approach, including the analysis of mixed sets of continuous and categorical variables, can be viewed as a distance-based alternative for the graphical display of multivariate data in Gifi (1990).
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Meulman, J.J. (1998). A Distance-Based Biplot for Multidimensional Scaling of Multivariate Data. In: Hayashi, C., Yajima, K., Bock, HH., Ohsumi, N., Tanaka, Y., Baba, Y. (eds) Data Science, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65950-1_56
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DOI: https://doi.org/10.1007/978-4-431-65950-1_56
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