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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.
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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.