public void Test()
{
// Make a random list.
RandomHelper.Random = new Random(77);
List <VectorD> points = new List <VectorD>();
for (int i = 0; i < 10; i++)
{
var vector = new VectorD(4);
RandomHelper.Random.NextVectorD(vector, -1, 10);
points.Add(vector);
}
PrincipalComponentAnalysisD pca = new PrincipalComponentAnalysisD(points);
Assert.Greater(pca.Variances[0], pca.Variances[1]);
Assert.Greater(pca.Variances[1], pca.Variances[2]);
Assert.Greater(pca.Variances[2], pca.Variances[3]);
Assert.Greater(pca.Variances[3], 0);
Assert.IsTrue(pca.V.GetColumn(0).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(1).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(2).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(3).IsNumericallyNormalized);
// Compute covariance matrix and check if it is diagonal in the transformed space.
MatrixD cov = StatisticsHelper.ComputeCovarianceMatrix(points);
MatrixD transformedCov = pca.V.Transposed * cov * pca.V;
for (int row = 0; row < transformedCov.NumberOfRows; row++)
{
for (int column = 0; column < transformedCov.NumberOfColumns; column++)
{
if (row != column)
{
Assert.IsTrue(Numeric.IsZero(transformedCov[row, column]));
}
}
}
// The principal components must be Eigenvectors which means that multiplying with the covariance
// matrix does only change the length!
VectorD v0 = pca.V.GetColumn(0);
VectorD v0Result = cov * v0;
Assert.IsTrue(VectorD.AreNumericallyEqual(v0.Normalized, v0Result.Normalized));
VectorD v1 = pca.V.GetColumn(1);
VectorD v1Result = cov * v1;
Assert.IsTrue(VectorD.AreNumericallyEqual(v1.Normalized, v1Result.Normalized));
VectorD v2 = pca.V.GetColumn(2);
VectorD v2Result = cov * v2;
Assert.IsTrue(VectorD.AreNumericallyEqual(v2.Normalized, v2Result.Normalized));
VectorD v3 = pca.V.GetColumn(3);
VectorD v3Result = cov * v3;
Assert.IsTrue(VectorD.AreNumericallyEqual(v3.Normalized, v3Result.Normalized));
}
public void Test()
{
// Make a random list.
RandomHelper.Random = new Random(77);
List<VectorD> points = new List<VectorD>();
for (int i = 0; i < 10; i++)
{
var vector = new VectorD(4);
RandomHelper.Random.NextVectorD(vector, -1, 10);
points.Add(vector);
}
PrincipalComponentAnalysisD pca = new PrincipalComponentAnalysisD(points);
Assert.Greater(pca.Variances[0], pca.Variances[1]);
Assert.Greater(pca.Variances[1], pca.Variances[2]);
Assert.Greater(pca.Variances[2], pca.Variances[3]);
Assert.Greater(pca.Variances[3], 0);
Assert.IsTrue(pca.V.GetColumn(0).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(1).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(2).IsNumericallyNormalized);
Assert.IsTrue(pca.V.GetColumn(3).IsNumericallyNormalized);
// Compute covariance matrix and check if it is diagonal in the transformed space.
MatrixD cov = StatisticsHelper.ComputeCovarianceMatrix(points);
MatrixD transformedCov = pca.V.Transposed * cov * pca.V;
for (int row = 0; row < transformedCov.NumberOfRows; row++)
for (int column = 0; column < transformedCov.NumberOfColumns; column++)
if (row != column)
Assert.IsTrue(Numeric.IsZero(transformedCov[row, column]));
// The principal components must be Eigenvectors which means that multiplying with the covariance
// matrix does only change the length!
VectorD v0 = pca.V.GetColumn(0);
VectorD v0Result = cov * v0;
Assert.IsTrue(VectorD.AreNumericallyEqual(v0.Normalized, v0Result.Normalized));
VectorD v1 = pca.V.GetColumn(1);
VectorD v1Result = cov * v1;
Assert.IsTrue(VectorD.AreNumericallyEqual(v1.Normalized, v1Result.Normalized));
VectorD v2 = pca.V.GetColumn(2);
VectorD v2Result = cov * v2;
Assert.IsTrue(VectorD.AreNumericallyEqual(v2.Normalized, v2Result.Normalized));
VectorD v3 = pca.V.GetColumn(3);
VectorD v3Result = cov * v3;
Assert.IsTrue(VectorD.AreNumericallyEqual(v3.Normalized, v3Result.Normalized));
}
