A Comparison of the multidimensional scaling of triadic and dyadic distances

Gower, John C. and de Rooij, Mark (2003). A Comparison of the multidimensional scaling of triadic and dyadic distances. Journal of Classification, 20(1) pp. 115–136.

DOI: https://doi.org/10.1007/s00357-003-0008-2

Abstract

We examine the use of triadic distances as a basis for multidimensional scaling (MDS). The MDS of triadic distances (MDS3) and a conventional MDS of dyadic distances (MDS2) both give Euclidean representations. Our analysis suggests that MDS2 and MDS3 can be expected to give very similar results, and this is strongly supported by numerical examples. We have concentrated on the perimeter and generalized Euclidean models of triadic distances, both of which are linear transformations of dyadic distances and so might be suspected of explaining our findings; however an MDS3 of the nonlinear variance definition of triadic distance also closely approximated the MDS2 representation. An appendix gives some matrix results that we have found useful and also gives matrix respresentations and alternative derivations of some known properties of triadic distances.

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