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A property of Principal Components Analysis (PCA) is that the first dimension is the most informative, next the second and so on. Is this property true also for multidimensional scaling (MDS)?

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    $\begingroup$ I would say "highest variance" rather than "most informative". "Informative" can mean different things; sometimes the second (or later) PC is the most informative in a particular context. E.g. sometimes the first PC is a sort of general property of the observations that is already known while later ones are new discoveries. $\endgroup$ – Peter Flom - Reinstate Monica Nov 10 '12 at 12:29
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Most MDS implementations sort the obtained dimensions in the order of decreasing variance along them. Thus, the answer to your question is "typically, yes". In this respect MDS is similar to PCA. Both are techniques to map-in-low-dimensions. However, PCA is dimensions-reduction technique which cuts-off informatively "weak" dimensions, leaving just m dimensions, whereas iterative MDS algorithms (such as ALSCAL or PROXSCAL) are dimensions-fitting technique which lays the cloud of points in m dimensional space. Due to that, the MDS methods reconstruct euclidean distances between points a bit more precisely than PCA does. See also related themes here and here.

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