public class SammonMapping
extends java.lang.Object
Ideally when we project from a high dimensional space to a low dimensional space the image would be geometrically congruent to the original figure. This is called an isometric projection. Unfortunately it is rarely possible to isometrically project objects down into lower dimensional spaces. Instead of trying to achieve equality between corresponding interpoint distances we can minimize the difference between corresponding interpoint distances. This is one goal of the Sammon's mapping algorithm. A second goal of the Sammon's mapping algorithm is to preserve the topology as best as possible by giving greater emphasize to smaller interpoint distances. The Sammon's mapping algorithm has the advantage that whenever it is possible to isometrically project an object into a lower dimensional space it will be isometrically projected into the lower dimensional space. But whenever an object cannot be projected down isometrically the Sammon's mapping projects it down to reduce the distortion in interpoint distances and to limit the change in the topology of the object.
The projection cannot be solved in a closed form and may be found by an iterative algorithm such as gradient descent suggested by Sammon. Kohonen also provides a heuristic that is simple and works reasonably well.
Constructor and Description 

SammonMapping(double[][] proximity)
Constructor.

SammonMapping(double[][] proximity,
double[][] coordinates)
Constructor.

SammonMapping(double[][] proximity,
double[][] init,
double lambda,
double tol,
int maxIter)
Constructor.

SammonMapping(double[][] proximity,
int k)
Constructor.

SammonMapping(double[][] proximity,
int k,
double lambda,
double tol,
int maxIter)
Constructor.

Modifier and Type  Method and Description 

double[][] 
getCoordinates()
Returns the coordinates of projected data.

double 
getStress()
Returns the final stress achieved.

public SammonMapping(double[][] proximity)
proximity
 the nonnegative proximity matrix of dissimilarities. The
diagonal should be zero and all other elements should be positive and symmetric.public SammonMapping(double[][] proximity, int k)
proximity
 the nonnegative proximity matrix of dissimilarities. The
diagonal should be zero and all other elements should be positive and symmetric.k
 the dimension of the projection.public SammonMapping(double[][] proximity, double[][] coordinates)
proximity
 the nonnegative proximity matrix of dissimilarities. The
diagonal should be zero and all other elements should be positive and symmetric.coordinates
 the initial projected coordinates, of which the column
size is the projection dimension.public SammonMapping(double[][] proximity, int k, double lambda, double tol, int maxIter)
proximity
 the nonnegative proximity matrix of dissimilarities. The
diagonal should be zero and all other elements should be positive and symmetric.k
 the dimension of the projection.lambda
 initial value of the step size constant in diagonal Newton method.tol
 tolerance for stopping iterations.maxIter
 maximum number of iterations.public SammonMapping(double[][] proximity, double[][] init, double lambda, double tol, int maxIter)
proximity
 the nonnegative proximity matrix of dissimilarities. The
diagonal should be zero and all other elements should be positive and symmetric.init
 the initial projected coordinates, of which the column
size is the projection dimension.lambda
 initial value of the step size constant in diagonal Newton method.tol
 tolerance for stopping iterations.maxIter
 maximum number of iterations.