smile.mds

Class MDS

java.lang.Object

smile.mds.MDS

public class MDS
extends java.lang.Object

Classical multidimensional scaling, also known as principal coordinates analysis. Given a matrix of dissimilarities (e.g. pairwise distances), MDS finds a set of points in low dimensional space that well-approximates the dissimilarities. We are not restricted to using an Euclidean distance metric. However, when Euclidean distances are used MDS is equivalent to PCA.

See Also:

PCA, SammonMapping

Field Summary

Fields

Modifier and Type	Field and Description
double[][]	coordinates The principal coordinates.
double[]	proportion The proportion of variance contained in each principal component.
double[]	scores The component scores.

Constructor Summary

Constructors

Constructor and Description
MDS(double[] scores, double[] proportion, double[][] coordinates) Constructor.

Method Summary

Modifier and Type	Method and Description
static MDS	of(double[][] proximity) Fits the classical multidimensional scaling.
static MDS	of(double[][] proximity, int k) Fits the classical multidimensional scaling.
static MDS	of(double[][] proximity, int k, boolean positive) Fits the classical multidimensional scaling.
static MDS	of(double[][] proximity, java.util.Properties prop) Fits the classical multidimensional scaling.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

scores

public final double[] scores

The component scores.

coordinates

public final double[][] coordinates

The principal coordinates.

proportion

public final double[] proportion

The proportion of variance contained in each principal component.

Constructor Detail

MDS

public MDS(double[] scores,
           double[] proportion,
           double[][] coordinates)

Constructor.

Parameters:

scores - the component scores.

proportion - the proportion of variance contained in each principal component.

coordinates - the principal coordinates

Method Detail

of

public static MDS of(double[][] proximity)

Fits the classical multidimensional scaling. Map original data into 2-dimensional Euclidean space.

Parameters:

proximity - the nonnegative proximity matrix of dissimilarities. The diagonal should be zero and all other elements should be positive and symmetric. For pairwise distances matrix, it should be just the plain distance, not squared.

of

public static MDS of(double[][] proximity,
                     int k)

Fits the classical multidimensional scaling.

Parameters:

proximity - the nonnegative proximity matrix of dissimilarities. The diagonal should be zero and all other elements should be positive and symmetric. For pairwise distances matrix, it should be just the plain distance, not squared.

k - the dimension of the projection.

of

public static MDS of(double[][] proximity,
                     java.util.Properties prop)

Fits the classical multidimensional scaling.

Parameters:

proximity - the nonnegative proximity matrix of dissimilarities. The diagonal should be zero and all other elements should be positive and symmetric. For pairwise distances matrix, it should be just the plain distance, not squared.

of

public static MDS of(double[][] proximity,
                     int k,
                     boolean positive)

Fits the classical multidimensional scaling.

Parameters:

proximity - the nonnegative proximity matrix of dissimilarities. The diagonal should be zero and all other elements should be positive and symmetric. For pairwise distances matrix, it should be just the plain distance, not squared.

k - the dimension of the projection.

positive - if true, estimate an appropriate constant to be added to all the dissimilarities, apart from the self-dissimilarities, that makes the learning matrix positive semi-definite. The other formulation of the additive constant problem is as follows. If the proximity is measured in an interval scale, where there is no natural origin, then there is not a sympathy of the dissimilarities to the distances in the Euclidean space used to represent the objects. In this case, we can estimate a constant c such that proximity + c may be taken as ratio data, and also possibly to minimize the dimensionality of the Euclidean space required for representing the objects.