Non-metric multidimensional

Fig. 38.6. Three-dimensional configuration according to a non-metric multidimensional scaling applied to 24 types of bread differing in appearance as assessed by 12 panellists.

Kruskal, J. B. (1964) Non-metric multidimensional scaling A numerical method. Psychometrika 29, 115-129. 

Taguchi Y, Oono Y. Relational patterns of gene expression via non-metric multidimensional scaling analysis. Bioinformatics 2005 21 730-40. 

Alternate projection methods aim to reduce the data dimensionality by optimizing the representation in the lower-dimension space so that the distances between points in the projected space are as similar as possible to the distances between the corresponding points in the original space. We will describe here a class of methods known as multidimensional scaling (MDS). The aim of these methods is to project data from a pseudo-metric space (i.e., one characterized by a dissimilarity measure) onto a metric space. Such methods are especially useful for preprocessing non-metric data in order to use algorithms valid only for metric input. 

Clearly, the closeness of two points, referred to as their proximity [45], affords a measure of how similar the species are in the multidimensional space. Of the many methods developed to estimate proximities, most have adopted measures that satisfy the three criteria pertaining to metrics, namely they are non-negative distance functions that satisfy the conditions (i) d(x, y) 0 ... 

---