public static DTOs.Responses.PrincipalComponentResponse ToDto(this PrincipalComponent pc)
{
return(new DTOs.Responses.PrincipalComponentResponse
{
Cumulative = pc.Cumulative.GetNumber(),
EigenValue = pc.EigenValue.GetNumber(),
Eigenvector = pc.Eigenvector.GetNumbers(),
Proportion = pc.Proportion.GetNumber(),
SingularValue = pc.SingularValue.GetNumber()
});
}
/// <summary>
/// Creates additional information about principal components.
/// </summary>
///
protected void CreateComponents()
{
int numComponents = singularValues.Length;
componentProportions = new double[numComponents];
componentCumulative = new double[numComponents];
// Calculate proportions
double sum = 0.0;
for (int i = 0; i < eigenvalues.Length; i++)
{
sum += System.Math.Abs(eigenvalues[i]);
}
sum = (sum == 0) ? 0.0 : (1.0 / sum);
for (int i = 0; i < componentProportions.Length; i++)
{
componentProportions[i] = System.Math.Abs(eigenvalues[i]) * sum;
}
// Calculate cumulative proportions
this.componentCumulative[0] = this.componentProportions[0];
for (int i = 1; i < this.componentCumulative.Length; i++)
{
this.componentCumulative[i] = this.componentCumulative[i - 1] + this.componentProportions[i];
}
// Creates the object-oriented structure to hold the principal components
var components = new PrincipalComponent[singularValues.Length];
for (int i = 0; i < components.Length; i++)
{
components[i] = new PrincipalComponent(this, i);
}
this.componentCollection = new PrincipalComponentCollection(components);
if (NumberOfOutputs == 0 || NumberOfOutputs > MaximumNumberOfOutputs)
{
NumberOfOutputs = MaximumNumberOfOutputs;
}
}
public void PrincipalComponentAnalysis()
{
int D = 3;
int N = 10;
// construct a sample
Random rng = new Random(1);
MultivariateSample sample = new MultivariateSample(D);
for (int i = 0; i < N; i++)
{
double x = 1.0 * rng.NextDouble() - 1.0;
double y = 4.0 * rng.NextDouble() - 2.0;
double z = 9.0 * rng.NextDouble() - 3.0;
sample.Add(x, y, z);
}
// get its column means
RowVector mu = new RowVector(D);
for (int i = 0; i < D; i++)
{
mu[i] = sample.Column(i).Mean;
}
// get total variance
double tVariance = GetTotalVariance(sample);
Console.WriteLine(tVariance);
// do a principal component analysis
PrincipalComponentAnalysis pca = sample.PrincipalComponentAnalysis();
Assert.IsTrue(pca.Dimension == sample.Dimension);
Assert.IsTrue(pca.Count == sample.Count);
// check that the PCs behave as expected
for (int i = 0; i < pca.Dimension; i++)
{
PrincipalComponent pc = pca.Component(i);
Assert.IsTrue(pc.Index == i);
Assert.IsTrue(pc.Analysis == pca);
Assert.IsTrue(TestUtilities.IsNearlyEqual(pc.Weight * pc.NormalizedVector(), pc.ScaledVector()));
Assert.IsTrue((0.0 <= pc.VarianceFraction) && (pc.VarianceFraction <= 1.0));
if (i == 0)
{
Assert.IsTrue(pc.VarianceFraction == pc.CumulativeVarianceFraction);
}
else
{
PrincipalComponent ppc = pca.Component(i - 1);
Assert.IsTrue(pc.VarianceFraction <= ppc.VarianceFraction);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ppc.CumulativeVarianceFraction + pc.VarianceFraction, pc.CumulativeVarianceFraction));
}
}
// express the sample in terms of principal components
MultivariateSample csample = pca.TransformedSample();
// check that the explained variances are as claimed
for (int rD = 1; rD <= D; rD++)
{
MultivariateSample rSample = new MultivariateSample(D);
foreach (double[] cEntry in csample)
{
RowVector x = mu.Copy();
for (int i = 0; i < rD; i++)
{
PrincipalComponent pc = pca.Component(i);
x += (cEntry[i] * pc.Weight) * pc.NormalizedVector();
}
rSample.Add(x);
}
double rVariance = GetTotalVariance(rSample);
Console.WriteLine("{0} {1}", rD, rVariance);
Assert.IsTrue(TestUtilities.IsNearlyEqual(rVariance / tVariance, pca.Component(rD - 1).CumulativeVarianceFraction));
}
}
public void PrincipalComponentAnalysis()
{
int D = 3;
int N = 10;
// construct a sample
Random rng = new Random(1);
MultivariateSample sample = new MultivariateSample(D);
for (int i = 0; i < N; i++)
{
double x = 1.0 * rng.NextDouble() - 1.0;
double y = 4.0 * rng.NextDouble() - 2.0;
double z = 9.0 * rng.NextDouble() - 3.0;
sample.Add(x, y, z);
}
// get its column means
RowVector mu = new RowVector(D);
for (int i = 0; i < D; i++)
{
mu[i] = sample.Column(i).Mean;
}
// get total variance
double tVariance = GetTotalVariance(sample);
Console.WriteLine(tVariance);
// do a principal component analysis
PrincipalComponentAnalysis pca = sample.PrincipalComponentAnalysis();
Assert.IsTrue(pca.Dimension == sample.Dimension);
Assert.IsTrue(pca.Count == sample.Count);
// check that the PCs behave as expected
Assert.IsTrue(pca.Components.Count == pca.Dimension);
for (int i = 0; i < pca.Dimension; i++)
{
PrincipalComponent pc = pca.Components[i];
Assert.IsTrue(pc.Index == i);
Assert.IsTrue(pc.Analysis == pca);
Assert.IsTrue(TestUtilities.IsNearlyEqual(pc.Weight * pc.NormalizedVector, pc.ScaledVector()));
Assert.IsTrue(pca.MinimumDimension(pc.CumulativeVarianceFraction) == i + 1);
}
// Check enumerator, and verify that variance fractions behave as expected.
int count = 0;
double cumulative = 0.0;
double previous = Double.PositiveInfinity;
foreach (PrincipalComponent pc in pca.Components)
{
Assert.IsTrue(pc.Index == count);
count++;
Assert.IsTrue((0.0 <= pc.VarianceFraction) && (pc.VarianceFraction <= 1.0));
Assert.IsTrue(pc.VarianceFraction <= previous);
previous = pc.VarianceFraction;
cumulative += pc.VarianceFraction;
Assert.IsTrue(TestUtilities.IsNearlyEqual(cumulative, pc.CumulativeVarianceFraction));
}
Assert.IsTrue(count == pca.Components.Count);
// express the sample in terms of principal components
MultivariateSample csample = pca.TransformedSample();
// check that the explained variances are as claimed
for (int rD = 1; rD <= D; rD++)
{
MultivariateSample rSample = new MultivariateSample(D);
foreach (double[] cEntry in csample)
{
RowVector x = mu.Copy();
for (int i = 0; i < rD; i++)
{
PrincipalComponent pc = pca.Components[i];
x += (cEntry[i] * pc.Weight) * pc.NormalizedVector;
}
rSample.Add(x);
}
double rVariance = GetTotalVariance(rSample);
Console.WriteLine("{0} {1}", rD, rVariance);
Assert.IsTrue(TestUtilities.IsNearlyEqual(rVariance / tVariance, pca.Components[rD - 1].CumulativeVarianceFraction));
}
}
public void PC()
{
Random rng = new Random(1);
double s = 1.0 / Math.Sqrt(2.0);
MultivariateSample MS = new MultivariateSample(2);
RectangularMatrix R = new RectangularMatrix(1000, 2);
for (int i = 0; i < 1000; i++)
{
double r1 = 2.0 * rng.NextDouble() - 1.0;
double r2 = 2.0 * rng.NextDouble() - 1.0;
double x = r1 * 4.0 * s - r2 * 9.0 * s;
double y = r1 * 4.0 * s + r2 * 9.0 * s;
R[i, 0] = x; R[i, 1] = y;
MS.Add(x, y);
}
Console.WriteLine("x {0} {1}", MS.Column(0).Mean, MS.Column(0).Variance);
Console.WriteLine("y {0} {1}", MS.Column(1).Mean, MS.Column(1).Variance);
Console.WriteLine("SVD");
SingularValueDecomposition SVD = R.SingularValueDecomposition();
for (int i = 0; i < SVD.Dimension; i++)
{
Console.WriteLine("{0} {1}", i, SVD.SingularValue(i));
ColumnVector v = SVD.RightSingularVector(i);
Console.WriteLine(" {0} {1}", v[0], v[1]);
}
Console.WriteLine("PCA");
PrincipalComponentAnalysis PCA = MS.PrincipalComponentAnalysis();
Console.WriteLine("Dimension = {0} Count = {1}", PCA.Dimension, PCA.Count);
for (int i = 0; i < PCA.Dimension; i++)
{
PrincipalComponent PC = PCA.Component(i);
Console.WriteLine(" {0} {1} {2} {3}", PC.Index, PC.Weight, PC.VarianceFraction, PC.CumulativeVarianceFraction);
RowVector v = PC.NormalizedVector();
Console.WriteLine(" {0} {1}", v[0], v[1]);
}
// reconstruct
SquareMatrix U = SVD.LeftTransformMatrix();
SquareMatrix V = SVD.RightTransformMatrix();
double x1 = U[0, 0] * SVD.SingularValue(0) * V[0, 0] + U[0, 1] * SVD.SingularValue(1) * V[0, 1];
Console.WriteLine("x1 = {0} {1}", x1, R[0, 0]);
double y1 = U[0, 0] * SVD.SingularValue(0) * V[1, 0] + U[0, 1] * SVD.SingularValue(1) * V[1, 1];
Console.WriteLine("y1 = {0} {1}", y1, R[0, 1]);
double x100 = U[100, 0] * SVD.SingularValue(0) * V[0, 0] + U[100, 1] * SVD.SingularValue(1) * V[0, 1];
Console.WriteLine("x100 = {0} {1}", x100, R[100, 0]);
double y100 = U[100, 0] * SVD.SingularValue(0) * V[1, 0] + U[100, 1] * SVD.SingularValue(1) * V[1, 1];
Console.WriteLine("y100 = {0} {1}", y100, R[100, 1]);
ColumnVector d1 = U[0, 0] * SVD.SingularValue(0) * SVD.RightSingularVector(0) +
U[0, 1] * SVD.SingularValue(1) * SVD.RightSingularVector(1);
Console.WriteLine("d1 = ({0} {1})", d1[0], d1[1]);
ColumnVector d100 = U[100, 0] * SVD.SingularValue(0) * SVD.RightSingularVector(0) +
U[100, 1] * SVD.SingularValue(1) * SVD.RightSingularVector(1);
Console.WriteLine("d100 = ({0} {1})", d100[0], d100[1]);
Console.WriteLine("compare");
MultivariateSample RS = PCA.TransformedSample();
IEnumerator <double[]> RSE = RS.GetEnumerator();
RSE.MoveNext();
double[] dv1 = RSE.Current;
Console.WriteLine("{0} {1}", dv1[0], dv1[1]);
Console.WriteLine("{0} {1}", U[0, 0], U[0, 1]);
RSE.Dispose();
}
