sqfa.statistics

Functions to compute class statistics of labeled data points.

Functions

class_statistics(points, labels[, estimator])	Compute the mean, covariance and second moment matrix of each class.
oas_covariance(points[, assume_centered])	Compute the OAS covariance matrix of the given points.
pca(points[, n_components])	Compute the principal components of the given points.
pca_from_scatter(scatters[, n_components])	Compute the principal components of the given scatter matrices.
sample_covariance(points[, assume_centered])	Compute the sample covariance matrix of the given points.

sqfa.statistics.class_statistics(points, labels, estimator='empirical')

Compute the mean, covariance and second moment matrix of each class.

Parameters:

• points (torch.Tensor) – Data points with shape (n_points, n_dim).

• labels (torch.Tensor) – Class labels of each point with shape (n_points).

• estimator – Covariance estimator to use. Options are “empirical” and “oas”. Default is “empirical”.

Returns:

statistics_dict – Dictionary containing the mean, covariance and second moment matrix of each class.

Return type:

dict

sqfa.statistics.oas_covariance(points, assume_centered=False)

Compute the OAS covariance matrix of the given points.

Parameters:

points (torch.Tensor) – Data points with shape (n_points, n_dim).

Returns:

oas_covariance – OAS covariance matrix of the points.

Return type:

torch.Tensor

References

[1]

:arxiv:`"Shrinkage algorithms for MMSE covariance estimation.", Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O. IEEE Transactions on Signal Processing, 58(10), 5016-5029, 2010. <0907.4698>`

sqfa.statistics.pca(points, n_components=None)

Compute the principal components of the given points.

Parameters:

• points (torch.Tensor) – Data points with shape (n_points, n_dim).

• n_components (int) – Number of principal components to compute. Default is min(n_points, n_dim).

Returns:

components – Principal components of the points. (n_components, n_dim)

Return type:

torch.Tensor

sqfa.statistics.pca_from_scatter(scatters, n_components=None)

Compute the principal components of the given scatter matrices. The scatter matrices are averaged and the principal components are computed from the average scatter matrix.

Parameters:

• scatters (torch.Tensor) – Scatter matrices with shape (n_classes, n_dim, n_dim).

• n_components (int) – Number of principal components to compute. Default is n_dim.

Returns:

components – Principal components of the scatter matrices. (n_components, n_dim)

Return type:

torch.Tensor