pyriemann.classification.class_distinctiveness

pyriemann.classification.class_distinctiveness(X, y, exponent=1, metric='riemann', return_num_denom=False)

Measure class distinctiveness between classes of SPD matrices.

For two class problem, the class distinctiveness between class \(K_1\) and \(K_2\) on the manifold of SPD matrices is quantified as [1]:

\[\mathrm{classDis}(K_1, K_2, p) = \frac{d \left( \mathbf{M}_{K_1}, \mathbf{M}_{K_2} \right)^p} {\frac{1}{2} \left( \sigma_{K_1}^p + \sigma_{K_2}^p \right)}\]

where \(\mathbf{M}_K\) is the center of class \(K\), ie the mean of matrices from class \(K\) (see pyriemann.utils.mean.mean_covariance()); and \(\sigma_K\) is the class dispersion, ie the mean of distances between matrices from class \(K\) and their center of class \(\mathbf{M}_K\):

\[\sigma_K^p = \frac{1}{m} \sum_{i=1}^m d \left(X_i, \mathbf{M}_K \right)^p\]

and \(p\) is the exponentiation of the distance.

For more than two classes, it is quantified as:

\[\mathrm{classDis} \left( \left\{K_{j} \right\}_{j=1}^c, p \right) = \frac{\sum_{j=1}^c d\left(\mathbf{M}_{K_{j}},\bar{\mathbf{M}}\right)^p} {\sum_{j=1}^c \sigma_{K_{j}}^p}\]

where \(\bar{\mathbf{M}}\) is the mean of centers of class of all \(c\) classes.

Parameters:
Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yndarray, shape (n_matrices,)

Labels for each matrix.

exponentint, default=1

Parameter for exponentiation of distances, corresponding to p in the above equations:

  • exponent = 1 gives the formula originally defined in [1];

  • exponent = 2 gives the Fisher criterion generalized on the manifold, ie the ratio of the variance between the classes to the variance within the classes.

metricstring | dict, default=’riemann’

The type of metric used for centroid and distance estimation. See mean_covariance for the list of supported metric. The metric could be a dict with two keys, mean and distance in order to pass different metrics for the centroid estimation and the distance estimation. The original equation of class distinctiveness in [1] uses ‘riemann’ for both the centroid estimation and the distance estimation but you can customize other metrics with your interests.

return_num_denombool, default=False

Whether to return numerator and denominator of class_dis.

Returns:
class_disfloat

Class distinctiveness value.

numfloat

Numerator value of class_dis. Returned only if return_num_denom is True.

denomfloat

Denominator value of class_dis. Returned only if return_num_denom is True.

Notes

New in version 0.4.

References

[1] (1,2,3)

Defining and quantifying users’ mental imagery-based BCI skills: a first step F. Lotte, and C. Jeunet. Journal of neural engineering, 15(4), 046030, 2018.