public void Test()
{
// Make a random list.
RandomHelper.Random = new Random(77);
List <VectorF> points = new List <VectorF>();
for (int i = 0; i < 10; i++)
{
var vector = new VectorF(4);
RandomHelper.Random.NextVectorF(vector, -1, 10);
points.Add(vector);
}
PrincipalComponentAnalysisF pca = new PrincipalComponentAnalysisF(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.
MatrixF cov = StatisticsHelper.ComputeCovarianceMatrix(points);
MatrixF 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!
VectorF v0 = pca.V.GetColumn(0);
VectorF v0Result = cov * v0;
Assert.IsTrue(VectorF.AreNumericallyEqual(v0.Normalized, v0Result.Normalized));
VectorF v1 = pca.V.GetColumn(1);
VectorF v1Result = cov * v1;
Assert.IsTrue(VectorF.AreNumericallyEqual(v1.Normalized, v1Result.Normalized));
VectorF v2 = pca.V.GetColumn(2);
VectorF v2Result = cov * v2;
Assert.IsTrue(VectorF.AreNumericallyEqual(v2.Normalized, v2Result.Normalized));
VectorF v3 = pca.V.GetColumn(3);
VectorF v3Result = cov * v3;
Assert.IsTrue(VectorF.AreNumericallyEqual(v3.Normalized, v3Result.Normalized));
}
public void ComputeCovarianceMatrix3DWithEmptyList()
{
var result = StatisticsHelper.ComputeCovarianceMatrix(new List <Vector3D>());
foreach (var element in result.ToList(MatrixOrder.RowMajor))
{
Assert.IsNaN(element);
}
}
public void ComputeCovarianceMatrixDWithVectorsOfDifferentLength()
{
List <VectorD> points = new List <VectorD>(new[]
{
new VectorD(new double[] { -1, -2, 1 }),
new VectorD(new double[] { 2, -1, 3, 1 }),
new VectorD(new double[] { 2, -1, 2 }),
});
var result = StatisticsHelper.ComputeCovarianceMatrix(points);
}
public void ComputeCovarianceMatrixFWithVectorsOfDifferentLength()
{
List <VectorF> points = new List <VectorF>(new[]
{
new VectorF(new float[] { -1, -2, 1 }),
new VectorF(new float[] { 2, -1, 3 }),
new VectorF(new float[] { 2, -1, 2, 3 }),
});
var result = StatisticsHelper.ComputeCovarianceMatrix(points);
}
// Computes the covariance matrix for a list of points.
private static MatrixF ComputeCovarianceMatrixFromPoints(IList <Vector3> points)
{
// Convert IList<Vector3> to IList<VectorF> which is required for PCA.
int numberOfPoints = points.Count;
List <VectorF> pointsCopy = new List <VectorF>(numberOfPoints);
for (int i = 0; i < numberOfPoints; i++)
{
var point = points[i];
pointsCopy.Add(point.ToVectorF());
}
return(StatisticsHelper.ComputeCovarianceMatrix(pointsCopy));
}
public void ComputeCovarianceMatrixDWithEmptyList()
{
var result = StatisticsHelper.ComputeCovarianceMatrix(new List <VectorD>());
}
public void ComputeCovarianceMatrixDWithArgumentNull()
{
StatisticsHelper.ComputeCovarianceMatrix((List <VectorD>)null);
}
public void ComputeCovarianceMatrix3F()
{
// Make a random list.
List <Vector3F> points3F = new List <Vector3F>(new[]
{
new Vector3F(-1, -2, 1),
new Vector3F(1, 0, 2),
new Vector3F(2, -1, 3),
new Vector3F(2, -1, 2),
});
Matrix33F cov3F = StatisticsHelper.ComputeCovarianceMatrix(points3F);
Assert.AreEqual(3f / 2, cov3F[0, 0]);
Assert.AreEqual(1f / 2, cov3F[0, 1]);
Assert.AreEqual(3f / 4, cov3F[0, 2]);
Assert.AreEqual(1f / 2, cov3F[1, 0]);
Assert.AreEqual(1f / 2, cov3F[1, 1]);
Assert.AreEqual(1f / 4, cov3F[1, 2]);
Assert.AreEqual(3f / 4, cov3F[2, 0]);
Assert.AreEqual(1f / 4, cov3F[2, 1]);
Assert.AreEqual(1f / 2, cov3F[2, 2]);
// Compare with Vector3D version.
List <Vector3D> points3D = new List <Vector3D>();
foreach (var point in points3F)
{
points3D.Add(point.ToVector3D());
}
Matrix33D cov3D = StatisticsHelper.ComputeCovarianceMatrix(points3D);
for (int i = 0; i < cov3F.ToArray1D(MatrixOrder.RowMajor).Length; i++)
{
var item3F = cov3F.ToArray1D(MatrixOrder.RowMajor)[i];
var item3D = cov3D.ToArray1D(MatrixOrder.RowMajor)[i];
Assert.AreEqual(item3F, item3D);
}
// Compare with VectorF version.
List <VectorF> pointsF = new List <VectorF>();
foreach (var point in points3F)
{
pointsF.Add(point.ToVectorF());
}
MatrixF covF = StatisticsHelper.ComputeCovarianceMatrix(pointsF);
for (int i = 0; i < cov3F.ToArray1D(MatrixOrder.RowMajor).Length; i++)
{
var item3F = cov3F.ToArray1D(MatrixOrder.RowMajor)[i];
var itemF = covF.ToArray1D(MatrixOrder.RowMajor)[i];
Assert.AreEqual(item3F, itemF);
}
// Compare with VectorF version.
List <VectorD> pointsD = new List <VectorD>();
foreach (var point in points3D)
{
pointsD.Add(point.ToVectorD());
}
MatrixD covD = StatisticsHelper.ComputeCovarianceMatrix(pointsD);
for (int i = 0; i < cov3F.ToArray1D(MatrixOrder.RowMajor).Length; i++)
{
var item3F = cov3F.ToArray1D(MatrixOrder.RowMajor)[i];
var itemD = covD.ToArray1D(MatrixOrder.RowMajor)[i];
Assert.AreEqual(item3F, itemD);
}
}