ON METRIC MULTIDIMENSIONAL UNFOLDING

Multidimensional Scaling and Unfolding

Multidimensional scaling (MDS) techniques are statistical techqnies that convert information about distances between a number of objects into a spatial representation of these objects. These techniques were first discussed systematically in psychometrics [Torgerson, 1958; Coombs, 1964] as multidimensional extensions of univariate psychophysics and sensory scaling. Because they needed considerab...

Metric Multidimensional Information Space

The rationale and methodology for retrieval based on the relative locations of documents within a geometric information space are introduced. Results from category A routing and filtering experiments in TREC-5 are discussed. The techniques used are related to the vector space model, latent semantic indexing, and other methods that rely on statistical qualities of texts to assess document relate...

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 ...

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...

Reliability and Metric Multidimensional Scaling