public void Compute(int components)
{
NumberOfOutputs = components;
// First, the data should be centered by subtracting
// the mean of each column in the source data matrix.
double[][] matrix = Adjust(sourceMatrix.ToJagged(), overwriteSourceMatrix);
// Pre-process the centered data matrix to have unit variance
double[][] whiten = Statistics.Tools.Whitening(matrix, out whiteningMatrix);
// Generate a new unitary initial guess for the de-mixing matrix
double[][] initial = Jagged.Random(components, matrix.Columns());
// Compute the demixing matrix using the selected algorithm
if (algorithm == IndependentComponentAlgorithm.Deflation)
{
revertMatrix = deflation(whiten, components, initial);
}
else // if (algorithm == IndependentComponentAlgorithm.Parallel)
{
revertMatrix = parallel(whiten, components, initial);
}
// Combine the rotation and demixing matrices
revertMatrix = whiteningMatrix.DotWithTransposed(revertMatrix);
revertMatrix.Divide(revertMatrix.Sum(), result: revertMatrix);
// Compute the original source mixing matrix
mixingMatrix = Matrix.PseudoInverse(revertMatrix);
mixingMatrix.Divide(mixingMatrix.Sum(), result: mixingMatrix);
// Demix the data into independent components
resultMatrix = Matrix.Dot(matrix, revertMatrix).ToMatrix();
this.demix = createRegression(revertMatrix, columnMeans, columnStdDev, analysisMethod);
this.mix = demix.Inverse();
// Creates the object-oriented structure to hold the principal components
var array = new IndependentComponent[components];
for (int i = 0; i < array.Length; i++)
{
array[i] = new IndependentComponent(this, i);
}
this.componentCollection = new IndependentComponentCollection(array);
}
public void learn_test()
{
Accord.Math.Random.Generator.Seed = 0;
#region doc_learn
// Let's create a random dataset containing
// 5000 samples of two dimensional samples.
//
double[][] source = Jagged.Random(5000, 2);
// Now, we will mix the samples the dimensions of the samples.
// A small amount of the second column will be applied to the
// first, and vice-versa.
//
double[][] mix =
{
new double[] { 0.25, 0.25 },
new double[] { -0.25, 0.75 },
};
// mix the source data
double[][] input = source.Dot(mix);
// Now, we can use ICA to identify any linear mixing between the variables, such
// as the matrix multiplication we did above. After it has identified it, we will
// be able to revert the process, retrieving our original samples again
// Create a new Independent Component Analysis
var ica = new IndependentComponentAnalysis()
{
Algorithm = IndependentComponentAlgorithm.Parallel,
Contrast = new Logcosh()
};
// Learn the demixing transformation from the data
MultivariateLinearRegression demix = ica.Learn(input);
// Now, we can retrieve the mixing and demixing matrices that were
// used to alter the data. Note that the analysis was able to detect
// this information automatically:
double[][] mixingMatrix = ica.MixingMatrix; // same as the 'mix' matrix
double[][] revertMatrix = ica.DemixingMatrix; // inverse of the 'mix' matrix
// We can use the regression to recover the separate sources
double[][] result = demix.Transform(input);
#endregion
// Verify mixing matrix
mixingMatrix = mixingMatrix.Divide(mixingMatrix.Sum());
Assert.IsTrue(mix.IsEqual(mixingMatrix, atol: 0.008));
Assert.IsTrue(revertMatrix.IsEqual(demix.Weights, atol: 0.008));
var dm = demix.Inverse().Weights;
dm = dm.Divide(dm.Sum());
Assert.IsTrue(mixingMatrix.IsEqual(dm, atol: 0.008));
// Verify demixing matrix
double[,] expected =
{
{ 0.75, -0.25 },
{ 0.25, 0.25 },
};
Assert.AreEqual(IndependentComponentAlgorithm.Parallel, ica.Algorithm);
Assert.AreEqual(ica.Contrast.GetType(), typeof(Logcosh));
revertMatrix = revertMatrix.Divide(revertMatrix.Sum());
Assert.IsTrue(expected.IsEqual(revertMatrix, atol: 0.008));
}
