Bayesian Metric Multidimensional Scaling

A Metric Multidimensional Scaling

| Multidimensional Scaling (MDS) techniques always pose the problem of analysing a large number N of points, without collecting all N(N?1) 2 possible interstimuli dissimilarities, and while keeping satisfactory solutions. In the case of metric MDS, it was found that a theoretical minimum of appropriate 2N ?3 exact Euclidean distances are suf-cient for the unique representation of N points in a ...

Reliability and Metric Multidimensional Scaling

Generalized Non-metric Multidimensional Scaling

We consider the non-metric multidimensional scaling problem: given a set of dissimilarities ∆, find an embedding whose inter-point Euclidean distances have the same ordering as ∆. In this paper, we look at a generalization of this problem in which only a set of order relations of the form dij < dkl are provided. Unlike the original problem, these order relations can be contradictory and need no...

Ghodsi 1 Metric Multidimensional Scaling ( MDS )

An alternative perspective on dimensionality reduction is offered by Multidimensional scaling (MDS). MDS is another classical approach that maps the original high dimensional space to a lower dimensional space, but does so in an attempt to preserve pairwise distances. That is MDS addresses the problem of constructing a configuration of t points in Euclidean space by using information about the ...

Better initial configurations for metric multidimensional scaling

Multidimensional scaling (MDS) is a collection of data analytic techniques for constructing con$gurations of points from dissimilarity information about interpoint distances. Two popular measures of how well the constructed distances $t the observed dissimilarities are the raw stress and sstress criteria, each of which must be minimized by numerical optimization. Because iterative procedures fo...