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Statistics.MDScaleMetric Function

Classical multidimensional scaling.

Pascal
procedure MDScaleMetric(const D: TMtx; const Y: TMtx; const EigenValues: TVec; const NumDim: Integer);
Parameters 
Description 
Distance matrix. 
Returns the coordinates of object in reduced space.> 
EigenValues 
 
NumDim 
Defines number of dimensions/variables to use in classical MD scaling algorithm. 
Uses MtxExpr,Math387,Statistics;
procedure Example;
var D,Y,X,DHat: Matrix;
  Eigen: Vector;
  stress: double;
begin
  X.SetIt(5,2,false,[1,2,3,4,3,11,7,8,9,4]);
  // Use all dimensions i.e. 2
  PairwiseDistance(X,D,2);
  // Reduce to just one variable (1d subspace)
  MDScaleMetric(D,Y,Eigen,1);
  // Calculate estimated distance matrix
  PairwiseDistance(Y,DHat,1);
  // Calculate stress - measure of GOF
  stress := MDScaleStress(D,DHat);
  // if stress > 0.2, the GOF is poor.
end;
#include "MtxExpr.hpp"
#include "Math387.hpp"
#include "Statistics.hpp"
void __fastcall Example()
{
    sMatrix X,Y,D,DHat;
    sVector eigen;
    X.SetIt(5,2,false,OPENARRAY(double,(1,2,3,4,3,11,7,8,9,4)));
    // Use all dimensions i.e. 2
    PairwiseDistance(X,D,2);
    // Reduce to just one variable (1d subspace)
    MDScaleMetric(D,Y,eigen,1);
    // Calculate estimated distance matrix
    PairwiseDistance(Y,DHat,1);
    // Calculate stress - measure of GOF
    double stress = MDScaleStress(D,DHat);
    // if stress > 0.2, the GOF is poor.
}
Examples on GitHub
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