Package smile.mds

Multidimensional scaling.

See: Description

Class Summary

Class	Description
IsotonicMDS	Kruskal's nonmetric MDS.
MDS	Classical multidimensional scaling, also known as principal coordinates analysis.
SammonMapping	The Sammon's mapping is an iterative technique for making interpoint distances in the low-dimensional projection as close as possible to the interpoint distances in the high-dimensional object.

Package smile.mds Description

Multidimensional scaling. MDS is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. An MDS algorithm starts with a matrix of item-item similarities, then assigns a location to each item in N-dimensional space. For sufficiently small N, the resulting locations may be displayed in a graph or 3D visualization.

The major types of MDS algorithms include:

Classical multidimensional scaling

takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain.

Metric multidimensional scaling

A superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. A useful loss function in this context is called stress which is often minimized using a procedure called stress majorization.

Non-metric multidimensional scaling

In contrast to metric MDS, non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. The relationship is typically found using isotonic regression.

Generalized multidimensional scaling

An extension of metric multidimensional scaling, in which the target space is an arbitrary smooth non-Euclidean space. In case when the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another.