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MvarModel

Namespace: CONNECTIVITYLIB  ·  Library: Connectivity Library

#include <connectivity/mvar_model.h>

class CONNECTIVITYLIB::MvarModel

Multivariate autoregressive (MVAR) model fit and its frequency-domain decomposition into transfer function H(f) and spectral matrix S(f).

The model order p is either supplied by the caller or selected automatically by Bayesian Information Criterion over [1, 20]; the coefficient matrices are estimated by Levinson-Durbin recursion on the Yule-Walker equations. The resulting H and S are consumed by the three directed-connectivity metrics in this library (Granger Causality, DTF, PDC) and are exposed via transferFunction and spectralMatrix at arbitrary normalised frequencies.

MVAR model fit; provides H(f) and S(f) for Granger Causality, DTF and PDC.

src/examples/ex_connectivity_metrics/main.cpp
MatrixXd average = MatrixXd::Zero(3, kSamples);
for (int i = 0; i < settings.size(); ++i) {
    average += settings.at(i).matData / settings.size();
}
MvarModel mvar;
mvar.fit(average, 4);                                       // pass 0 to select the order by BIC
const QVector<MatrixXd> coefficients = mvar.coefficients(); // A_1 .. A_p
const QVector<MatrixXcd> transfer = mvar.transferFunction(VectorXd::LinSpaced(5, 0.0, 0.5));

Public Methods​

MvarModel()​

Constructs a default MvarModel object.

fit(data, p)​

Fits an MVAR model of order p to multi-channel data.

Parameters:

  • data : const Eigen::MatrixXd & The input data matrix (nChannels x nSamples).

  • p : int The model order. If 0, the order is auto-selected via BIC.

coefficients()​

Returns the fitted coefficient matrices A_1 .

. A_p (each nChannels x nChannels).

Returns:

  • QVector< Eigen::MatrixXd > — The MVAR coefficient matrices.

noiseCov()​

Returns the noise covariance matrix (nChannels x nChannels).

Returns:

  • Eigen::MatrixXd — The noise covariance matrix.

order()​

Returns the fitted model order.

Returns:

  • int — The model order p.

transferFunction(freqs)​

Computes the transfer function H(f) at the given normalized frequencies.

H(f) = (I - sum_{k=1}^{p} A_k * exp(-2piifk))^{-1}

Parameters:

  • freqs : const Eigen::VectorXd & Vector of normalized frequencies in [0, 0.5].

Returns:

  • QVector< Eigen::MatrixXcd > — Vector of nChannels x nChannels complex matrices, one per frequency.

spectralMatrix(freqs)​

Computes the spectral matrix S(f) = H(f) * Sigma * H(f)^H.

Parameters:

  • freqs : const Eigen::VectorXd & Vector of normalized frequencies in [0, 0.5].

Returns:

  • QVector< Eigen::MatrixXcd > — Vector of nChannels x nChannels complex matrices, one per frequency.

Example​

Used in examples​

ex_connectivity_metrics​

Connectivity metrics on synthetic data with a known coupling.

src/examples/ex_connectivity_metrics/main.cpp, line 251
MvarModel mvar;
mvar.fit(average, 4);                                       // pass 0 to select the order by BIC
const QVector<MatrixXd> coefficients = mvar.coefficients(); // A_1 .. A_p
const QVector<MatrixXcd> transfer = mvar.transferFunction(VectorXd::LinSpaced(5, 0.0, 0.5));
ok &= expect(mvar.order() == 4 && coefficients.size() == 4 && transfer.size() == 5,
             "MvarModel stores order 4 and evaluates H(f) at 5 frequencies");
ok &= expect(std::fabs(coefficients[kDelay - 1](1, 0)) > 0.5,
             QString("|A_3(1,0)| %1 > 0.5: channel 1 depends on channel 0 three samples back")
                 .arg(std::fabs(coefficients[kDelay - 1](1, 0))));

Authors of this file​