moabb.pipelines.classification.SSVEP_TRCA#

class moabb.pipelines.classification.SSVEP_TRCA(n_fbands=5, is_ensemble=True, method='original', estimator='scm')[source]#

Task-Related Component Analysis (TRCA) method for SSVEP detection [1].

TRCA is a data-driven spatial filtering approach that enhances SSVEP detection by maximizing the reproducibility of task-related EEG components across multiple trials. Unlike CCA which uses predefined sinusoidal references, TRCA learns optimal spatial filters directly from the training data.

Mathematical Formulation

Given N_t training trials \mathbf{X}^{(h)} \in \mathbb{R}^{N_c \times N_s} for a stimulus frequency, TRCA finds the optimal spatial filter \mathbf{w} that maximizes the inter-trial covariance while constraining the variance:

\hat{\mathbf{w}} = \arg\max_{\mathbf{w}} \frac{\mathbf{w}^T \mathbf{S} \mathbf{w}}{\mathbf{w}^T \mathbf{Q} \mathbf{w}}

Inter-trial Covariance Matrix S

The matrix \mathbf{S} captures the covariance between different trials:

S_{j_1, j_2} = \sum_{h_1=1}^{N_t} \sum_{h_2=1, h_2 \neq h_1}^{N_t} \text{Cov}(x_{j_1}^{(h_1)}(t), x_{j_2}^{(h_2)}(t))

where x_j^{(h)}(t) is the signal from channel j in trial h.

Variance Constraint Matrix Q

The matrix \mathbf{Q} represents the pooled variance across all trials:

\mathbf{Q} = \sum_{h=1}^{N_t} \mathbf{X}^{(h)} (\mathbf{X}^{(h)})^T

Generalized Eigenvalue Problem

The optimization is solved as a generalized eigenvalue problem:

\mathbf{S} \mathbf{w} = \lambda \mathbf{Q} \mathbf{w}

The eigenvector corresponding to the largest eigenvalue gives the optimal spatial filter \hat{\mathbf{w}}.

Template Construction

For each stimulus frequency f_n, the template is the average of spatially filtered training trials:

\bar{\mathbf{X}}_n = \frac{1}{N_t} \sum_{h=1}^{N_t} \mathbf{X}_n^{(h)}

Ensemble TRCA

The ensemble method combines spatial filters from all stimulus frequencies into a filter bank \mathbf{W} = [\mathbf{w}_1, \mathbf{w}_2, ..., \mathbf{w}_{N_f}] for improved robustness.

Filter Bank Approach

To capture harmonic components, EEG signals are decomposed into N_m sub-bands using a filter bank. The correlation coefficient for sub-band m is:

r_n^{(m)} = \rho\left((\mathbf{X}^{(m)})^T \mathbf{W}^{(m)}, (\bar{\mathbf{X}}_n^{(m)})^T \mathbf{W}^{(m)}\right)

Classification Rule

The final feature combines sub-band correlations with weights a^{(m)} = m^{-1.25} + 0.25:

\rho_n = \sum_{m=1}^{N_m} a^{(m)} \cdot (r_n^{(m)})^2

The predicted class is: \hat{\tau} = \arg\max_n \rho_n

Parameters:

n_fbands (int, default=5) – Number of sub-bands N_m for the filter bank decomposition. Each sub-band captures different harmonic components of the SSVEP.
is_ensemble (bool, default=True) – If True, use ensemble TRCA which combines spatial filters from all stimulus frequencies for improved robustness. If False, use only the class-specific spatial filter.
method (str, default='original') –
Method for computing the inter-trial covariance matrix \mathbf{S}:
- 'original': Euclidean mean as in the original paper [1].
- 'riemann': Geodesic (Riemannian) mean, more robust to outliers but sensitive to ill-conditioned matrices.
- 'logeuclid': Log-Euclidean mean, a computationally stable alternative to the Riemannian mean.
estimator (str, default='scm') –
Covariance estimator for regularization. Options include:
- 'scm': Sample covariance matrix (no regularization, as in [1]).
- 'lwf': Ledoit-Wolf shrinkage estimator.
- 'oas': Oracle Approximating Shrinkage estimator.
- 'schaefer': Schäfer-Strimmer shrinkage estimator.

fb_coefs#

Sub-band weights a^{(m)} = m^{-1.25} + 0.25 for filter bank fusion.

Type:: list of float, length n_fbands

classes_#

Encoded class labels extracted at fit time.

Type:: ndarray of shape (n_classes,)

n_classes#

Number of unique stimulus frequencies/classes.

Type:: int

templates_#

Average templates \bar{\mathbf{X}}_n^{(m)} for each class and sub-band.

Type:: ndarray of shape (n_classes, n_fbands, n_channels, n_samples)

weights_#

Spatial filter weights \mathbf{w}_n^{(m)} for each sub-band and class.

Type:: ndarray of shape (n_fbands, n_classes, n_channels)

freqs_#

List of stimulus frequencies from training data.

Type:: list of str

peaks_#

Numeric frequency values for filter bank design.

Type:: ndarray of shape (n_classes,)

sfreq_#

Sampling frequency of the training data.

Type:: float

References

[1] (1,2,3,4)

M. Nakanishi, Y. Wang, X. Chen, Y.-T. Wang, X. Gao, and T.-P. Jung, “Enhancing detection of SSVEPs for a high-speed brain speller using task-related component analysis”, IEEE Trans. Biomed. Eng, 65(1):104-112, 2018. https://doi.org/10.1109/TBME.2017.2694818