/// <summary>
/// Learns a model that can map the given inputs to the desired outputs.
/// </summary>
/// <param name="x">The model inputs.</param>
/// <param name="weights">The weight of importance for each input sample.</param>
/// <returns>
/// A model that has learned how to produce suitable outputs
/// given the input data <paramref name="x" />.
/// </returns>
public MultivariateLinearRegression Learn(double[][] x, double[] weights = null)
{
if (weights != null)
{
throw new ArgumentException(Accord.Properties.Resources.NotSupportedWeights, "weights");
}
// Calculate common measures to speedup other calculations
this.columnMeans = Measures.Mean(x, dimension: 0);
this.columnStdDev = Measures.StandardDeviation(x, columnMeans);
NumberOfInputs = x.Columns();
if (NumberOfOutputs == 0)
{
NumberOfOutputs = NumberOfInputs;
}
// First, the data should be centered by subtracting
// the mean of each column in the source data matrix.
var matrix = Adjust(x, overwriteSourceMatrix);
// Pre-process the centered data matrix to have unit variance
var whiten = Statistics.Tools.Whitening(matrix, out whiteningMatrix);
// Generate a new unitary initial guess for the de-mixing matrix
var initial = Jagged.Random(NumberOfOutputs, matrix.Columns());
// Compute the demixing matrix using the selected algorithm
if (algorithm == IndependentComponentAlgorithm.Deflation)
{
revertMatrix = deflation(whiten, NumberOfOutputs, initial);
}
else // if (algorithm == IndependentComponentAlgorithm.Parallel)
{
revertMatrix = parallel(whiten, NumberOfOutputs, 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);
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[NumberOfOutputs];
for (int i = 0; i < array.Length; i++)
{
array[i] = new IndependentComponent(this, i);
}
this.componentCollection = new IndependentComponentCollection(array);
return(demix);
}
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);
}
/// <summary>
/// Computes the Independent Component Analysis algorithm.
/// </summary>
///
public void Compute(int components)
{
// First, the data should be centered by subtracting
// the mean of each column in the source data matrix.
double[,] matrix = Adjust(sourceMatrix, 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 = Matrix.Random(components, matrix.GetLength(1), 0, 1);
// 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.MultiplyByTranspose(revertMatrix);
normalize(revertMatrix);
// Compute the original source mixing matrix
mixingMatrix = Matrix.PseudoInverse(revertMatrix);
normalize(mixingMatrix);
// Demix the data into independent components
resultMatrix = matrix.Multiply(revertMatrix);
// 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);
}