Probabilistic Metric Based Multidimensional Scaling

Probabilistic Multidimensional Scaling Using a City-Block Metric.

Using a probabilistic model, exact and approximate probability density functions (PDFs) for city-block distances and distance ratios are developed. The model assumes that stimuli can be represented by random vectors having multivariate normal distributions. Comparisons with the more common Euclidean PDFs are presented. The potential ability of the proposed model to correctly detect Euclidean an...

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 ...