ica.cpp

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//=============================================================================================================
 
//=============================================================================================================
// INCLUDES
//=============================================================================================================
 
#include "ica.h"
 
//=============================================================================================================
// EIGEN INCLUDES
//=============================================================================================================
 
#include <Eigen/Dense>
 
//=============================================================================================================
// QT INCLUDES
//=============================================================================================================
 
#include <QDebug>
 
//=============================================================================================================
// C++ INCLUDES
//=============================================================================================================
 
#include <cmath>
#include <random>
 
//=============================================================================================================
// USED NAMESPACES
//=============================================================================================================
 
using namespace UTILSLIB;
using namespace Eigen;
 
//=============================================================================================================
// STATIC MEMBER DEFINITIONS
//=============================================================================================================
 
//=============================================================================================================
// PRIVATE HELPERS
//=============================================================================================================
 
namespace {
 
//=============================================================================================================
void gramSchmidt(VectorXd& w, const MatrixXd& W, int iComp)
{
    for (int j = 0; j < iComp; ++j) {
        w -= w.dot(W.row(j)) * W.row(j).transpose();
    }
}
 
} // anonymous namespace
 
//=============================================================================================================
// MEMBER DEFINITIONS
//=============================================================================================================
 
IcaResult ICA::run(const MatrixXd& matData,
                   int    nComponents,
                   int    maxIter,
                   double tol,
                   int    randomSeed)
{
    const int nCh      = static_cast<int>(matData.rows());
    const int nSamples = static_cast<int>(matData.cols());
 
    if (nComponents <= 0 || nComponents > nCh) {
        nComponents = nCh;
    }
 
    //----------------------------------------------------------------------------------------------------------
    // 1. Center: subtract per-channel mean
    //----------------------------------------------------------------------------------------------------------
    VectorXd vecMean = matData.rowwise().mean();
    MatrixXd matCentered = matData.colwise() - vecMean;
 
    //----------------------------------------------------------------------------------------------------------
    // 2. Whiten
    //----------------------------------------------------------------------------------------------------------
    MatrixXd matWhitening, matDewhitening;
    MatrixXd matWhite = whiten(matCentered, nComponents, matWhitening, matDewhitening);
 
    //----------------------------------------------------------------------------------------------------------
    // 3. FastICA — deflationary approach with logcosh (tanh) nonlinearity
    //
    //    For each component i, iterate:
    //      g   = tanh(W[i]^T * X_white)                    [1 x nSamples]
    //      g'  = 1 - g^2                                    [1 x nSamples]
    //      w_new = (1/n) * X_white * g^T - mean(g') * w_i
    //      Gram-Schmidt orthogonalise against already-found rows
    //      Normalise
    //      Convergence: |w_new · w_old| ≥ 1 - tol
    //----------------------------------------------------------------------------------------------------------
    std::mt19937 rng(static_cast<unsigned>(randomSeed));
    std::normal_distribution<double> dist(0.0, 1.0);
 
    MatrixXd W_ica(nComponents, nComponents);   // unmixing in whitened space
    bool bConverged = true;
 
    for (int i = 0; i < nComponents; ++i) {
        // Random unit-vector initialisation
        VectorXd w(nComponents);
        for (int k = 0; k < nComponents; ++k) {
            w(k) = dist(rng);
        }
        w.normalize();
 
        bool compConverged = false;
        for (int iter = 0; iter < maxIter; ++iter) {
            // g = tanh(w^T * X_white)  →  row vector (1 x nSamples)
            RowVectorXd u = w.transpose() * matWhite;
            RowVectorXd g     = u.array().tanh();
            RowVectorXd gPrime = 1.0 - g.array().square();    // derivative of tanh
 
            // Newton update
            VectorXd wNew = (matWhite * g.transpose()) / nSamples
                            - gPrime.mean() * w;
 
            // Deflation: orthogonalise against already-converged components
            gramSchmidt(wNew, W_ica, i);
 
            // Normalise
            double norm = wNew.norm();
            if (norm < 1e-12) {
                // Degenerate — reinitialise randomly and restart this component
                for (int k = 0; k < nComponents; ++k) {
                    w(k) = dist(rng);
                }
                w.normalize();
                continue;
            }
            wNew /= norm;
 
            // Convergence check: |w_new · w_old| should approach 1
            double delta = std::abs(wNew.dot(w)) - 1.0;
            w = wNew;
 
            if (std::abs(delta) < tol) {
                compConverged = true;
                break;
            }
        }
 
        if (!compConverged) {
            bConverged = false;
            qWarning() << "ICA::run: component" << i << "did not converge within" << maxIter << "iterations.";
        }
 
        W_ica.row(i) = w.transpose();
    }
 
    //----------------------------------------------------------------------------------------------------------
    // 4. Compose full (sensor-space) unmixing and mixing matrices
    //
    //    W_full = W_ica * W_whitening      (n_comp x n_ch)
    //    A_full = W_dewhitening * W_ica^T  (n_ch x n_comp)  — exact inverse when n_comp == n_ch,
    //                                                          pseudo-inverse otherwise
    //----------------------------------------------------------------------------------------------------------
    MatrixXd matUnmixing = W_ica * matWhitening;                     // n_comp x n_ch
    MatrixXd matMixing   = matDewhitening * W_ica.transpose();       // n_ch   x n_comp
 
    //----------------------------------------------------------------------------------------------------------
    // 5. Compute source time series
    //----------------------------------------------------------------------------------------------------------
    MatrixXd matSources = matUnmixing * matCentered;                 // n_comp x n_samples
 
    IcaResult result;
    result.matMixing   = std::move(matMixing);
    result.matUnmixing = std::move(matUnmixing);
    result.matSources  = std::move(matSources);
    result.vecMean     = std::move(vecMean);
    result.bConverged  = bConverged;
 
    return result;
}
 
//=============================================================================================================
 
MatrixXd ICA::applyUnmixing(const MatrixXd& matData, const IcaResult& result)
{
    // Centre using the training mean, then project
    MatrixXd matCentered = matData.colwise() - result.vecMean;
    return result.matUnmixing * matCentered;
}
 
//=============================================================================================================
 
MatrixXd ICA::excludeComponents(const MatrixXd& matData,
                                  const IcaResult& result,
                                  const QVector<int>& excludedComponents)
{
    if (excludedComponents.isEmpty()) {
        return matData;
    }
 
    // Project to source space
    MatrixXd matSources = applyUnmixing(matData, result);
 
    // Zero the excluded components
    for (int idx : excludedComponents) {
        if (idx >= 0 && idx < static_cast<int>(matSources.rows())) {
            matSources.row(idx).setZero();
        }
    }
 
    // Back-project and add mean
    MatrixXd matRecon = result.matMixing * matSources;
    return matRecon.colwise() + result.vecMean;
}
 
//=============================================================================================================
 
MatrixXd ICA::whiten(const MatrixXd& matCentered,
                      int             nComponents,
                      MatrixXd&       matWhitening,
                      MatrixXd&       matDewhitening)
{
    const int nSamples = static_cast<int>(matCentered.cols());
 
    // Sample covariance (unscaled)
    MatrixXd cov = matCentered * matCentered.transpose() / static_cast<double>(nSamples);
 
    // Eigendecomposition — SelfAdjointEigenSolver returns eigenvalues in ascending order
    SelfAdjointEigenSolver<MatrixXd> eig(cov);
 
    const int nCh = static_cast<int>(cov.rows());
    // Take the nComponents largest eigenvalues/vectors (rightmost columns)
    VectorXd eigenvalues  = eig.eigenvalues().tail(nComponents).cwiseMax(1e-12);
    MatrixXd eigenvectors = eig.eigenvectors().rightCols(nComponents);   // n_ch x n_comp
 
    // Whitening  : W_w = D^{-1/2} * V^T   (n_comp x n_ch)
    // Dewhitening: W_d = V * D^{1/2}       (n_ch   x n_comp)
    VectorXd sqrtEig    = eigenvalues.cwiseSqrt();
    VectorXd invSqrtEig = sqrtEig.cwiseInverse();
 
    matWhitening   = invSqrtEig.asDiagonal() * eigenvectors.transpose();
    matDewhitening = eigenvectors * sqrtEig.asDiagonal();
 
    return matWhitening * matCentered;
}