Abstract
The majorization method for multidimensional scaling with Kruskal's STRESS has been limited to Euclidean distances only. Here we extend the majorization algorithm to deal with Minkowski distances with 1≤p≤2 and suggest an algorithm that is partially based on majorization forp outside this range. We give some convergence proofs and extend the zero distance theorem of De Leeuw (1984) to Minkowski distances withp>1.
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Acknowledgment: We would like to thank three anonymous referees for carefully reading the manuscript and for several valuable remarks that have improved this paper. A previous version of this paper has appeared as chapter 7 in Groenen, P.J.F.,The Majorization Approach to Multidimensional Scaling: Some Problems and Extensions, DSWO Press, Leiden, 1993.
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Groenen, P.J.F., Mathar, R. & Heiser, W.J. The majorization approach to multidimensional scaling for Minkowski distances. Journal of Classification 12, 3–19 (1995). https://doi.org/10.1007/BF01202265
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DOI: https://doi.org/10.1007/BF01202265