Statistics.MDScaleStress Method

Double MDScaleStress(TMtx D, TMtx DHat)

The stress factor for multidimensional scaling.

#	Name	Description
1	D	Data distance matrix.
2	DHat	Estimated distance matrix.

Returns: Double - The stress factor.

Remarks:

Calculates the GOF statistics for multidimensional scaling. The stress factor is defined as:

\text{stress} = \sqrt{\cfrac{\sum (d_{i,j}-\hat{d}_{i,j})^2}{\sum d_{i,j} ^2} }

where hat(d(i,j)) is the predicted distance based on the MDS model. In his original paper on multi dimensional scaling, Kruskal (1964) gave following advise about stress values based on his experience:

Stress | Goodness-of-fit
0.2 — poor
0.1 — fair
0.05 — good
0.025 — excellent
0.000 — perfect

More recent articles caution against using a table like this since acceptable values of stress depends on the quality of the distance matrix and the number of objects in that matrix.

Examples

using Dew.Math;
using Dew.Stats;
using Dew.Stats.Units;
namespace Dew.Examples
{
    private void Example()
    {
        Matrix D = new Matrix(2, 2);
        Matrix DHat = new Matrix(2, 2);

        D.SetIt(2, 2, false, new double[4] { 0.3, 3, 2, 0.1 });
        DHat.SetIt(2, 2, false, new double[4] { 0.1, 3.1, 2.2, 0.3 });

        // Calculate stress value - measure for GOF
        // Smaller stress value means better GOF.
        double stress = Statistics.MDScaleStress(D, DHat);
    }
}

See Also: Statistics.MDScaleMetric