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));
}
}