/// <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)
{
this.NumberOfInputs = x.Columns();
if (Method == PrincipalComponentMethod.Center || Method == PrincipalComponentMethod.Standardize)
{
this.Means = x.Mean(dimension: 0);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: 0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.StandardDeviation(Means);
matrix.Divide(StandardDeviations, dimension: 0, result: matrix);
}
// The principal components of 'Source' are the eigenvectors of Cov(Source). Thus if we
// calculate the SVD of 'matrix' (which is Source standardized), the columns of matrix V
// (right side of SVD) will be the principal components of Source.
// Perform the Singular Value Decomposition (SVD) of the matrix
var svd = new JaggedSingularValueDecomposition(matrix,
computeLeftSingularVectors: false,
computeRightSingularVectors: true,
autoTranspose: true, inPlace: true);
SingularValues = svd.Diagonal;
Eigenvalues = SingularValues.Pow(2);
Eigenvalues.Divide(x.Rows() - 1, result: Eigenvalues);
ComponentVectors = svd.RightSingularVectors.Transpose();
}
else if (Method == PrincipalComponentMethod.CovarianceMatrix ||
Method == PrincipalComponentMethod.CorrelationMatrix)
{
// We only have the covariance matrix. Compute the Eigenvalue decomposition
var evd = new JaggedEigenvalueDecomposition(x,
assumeSymmetric: true, sort: true);
// Gets the Eigenvalues and corresponding Eigenvectors
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = evd.Eigenvectors.Transpose();
}
else
{
// The method type should have been validated before we even entered this section
throw new InvalidOperationException("Invalid method, this should never happen: {0}".Format(Method));
}
if (Whiten)
{
ComponentVectors.Divide(SingularValues, dimension: 1, result: ComponentVectors);
}
// Computes additional information about the analysis and creates the
// object-oriented structure to hold the principal components found.
CreateComponents();
return(CreateRegression());
}
public MultivariateLinearRegression Learn(double[][] x, double[] weights = null)
{
this.NumberOfInputs = x.Columns();
if (Method == PrincipalComponentMethod.Center || Method == PrincipalComponentMethod.Standardize)
{
if (weights == null)
{
this.Means = x.Mean(dimension: 0);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: (VectorType)0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.StandardDeviation(Means);
matrix.Divide(StandardDeviations, dimension: (VectorType)0, result: matrix);
}
var svd = new JaggedSingularValueDecomposition(matrix,
computeLeftSingularVectors: false,
computeRightSingularVectors: true,
autoTranspose: true, inPlace: true);
SingularValues = svd.Diagonal;
Eigenvalues = SingularValues.Pow(2);
Eigenvalues.Divide(x.Rows() - 1, result: Eigenvalues);
ComponentVectors = svd.RightSingularVectors.Transpose();
}
else
{
this.Means = x.WeightedMean(weights: weights);
double[][] matrix = Overwrite ? x : Jagged.CreateAs(x);
x.Subtract(Means, dimension: (VectorType)0, result: matrix);
if (Method == PrincipalComponentMethod.Standardize)
{
this.StandardDeviations = x.WeightedStandardDeviation(weights, Means);
matrix.Divide(StandardDeviations, dimension: (VectorType)0, result: matrix);
}
double[,] cov = x.WeightedCovariance(weights, Means);
var evd = new EigenvalueDecomposition(cov,
assumeSymmetric: true, sort: true);
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = Jagged.Transpose(evd.Eigenvectors);
}
}
else if (Method == PrincipalComponentMethod.CovarianceMatrix ||
Method == PrincipalComponentMethod.CorrelationMatrix)
{
if (weights != null)
{
throw new Exception();
}
var evd = new JaggedEigenvalueDecomposition(x,
assumeSymmetric: true, sort: true);
Eigenvalues = evd.RealEigenvalues;
SingularValues = Eigenvalues.Sqrt();
ComponentVectors = evd.Eigenvectors.Transpose();
}
else
{
throw new InvalidOperationException("Invalid method, this should never happen: {0}".Format(Method));
}
if (Whiten)
{
ComponentVectors.Divide(SingularValues, dimension: (VectorType)1, result: ComponentVectors);
}
CreateComponents();
return(CreateRegression());
}