API reference

SPD Matrices Estimation

Covariances([estimator])	Estimation of covariance matrices.
ERPCovariances([classes, estimator, svd])	Estimate special form covariance matrices for ERP.
XdawnCovariances([nfilter, applyfilters, ...])	Estimate special form covariance matrices for ERP combined with Xdawn.
BlockCovariances(block_size[, estimator])	Estimation of block covariance matrices.
CrossSpectra([window, overlap, fmin, fmax, fs])	Estimation of cross-spectral matrices.
CoSpectra([window, overlap, fmin, fmax, fs])	Estimation of co-spectral matrices.
Coherences([window, overlap, fmin, fmax, ...])	Estimation of squared coherence matrices.
TimeDelayCovariances([delays, estimator])	Estimation of covariance matrices with time delay matrices.
Kernels([metric, n_jobs])	Estimation of kernel matrices between channels of time series.
Shrinkage([shrinkage])	Regularization of SPD/HPD matrices by shrinkage.

Embedding

locally_linear_embedding(X, *[, ...])	Perform a Locally Linear Embedding (LLE) of SPD matrices.
barycenter_weights(X, Y, indices[, metric, ...])	Compute barycenter weights of X from Y along the first axis.
SpectralEmbedding([n_components, metric, eps])	Spectral Embedding of SPD/HPD matrices.
LocallyLinearEmbedding([n_components, ...])	Locally Linear Embedding of SPD matrices.
TSNE([n_components, perplexity, metric, ...])	T-distributed Stochastic Neighbor Embedding (t-SNE) of SPD/HPD matrices.

Classification

MDM([metric, n_jobs])	Classification by Minimum Distance to Mean.
FgMDM([metric, tsupdate, n_jobs])	Classification by Minimum Distance to Mean with geodesic filtering.
TSClassifier([metric, tsupdate, clf])	Classification in the tangent space.
KNearestNeighbor([n_neighbors, metric, n_jobs])	Classification by k-nearest neighbors.
SVC(*[, metric, kernel_fct, Cref, C, ...])	Classification by support-vector machine.
MeanField([power_list, method_label, ...])	Classification by Mean Field.
NearestConvexHull([metric, n_jobs, method])	Classification by Nearest Convex Hull.

class_distinctiveness(X, y[, exponent, ...])

Measure class distinctiveness between classes of SPD/HPD matrices.

Regression

KNearestNeighborRegressor([n_neighbors, metric])	Regression by k-nearest-neighbors.
SVR(*[, metric, kernel_fct, Cref, tol, C, ...])	Regression by support-vector machine.

Clustering

Kmeans([n_clusters, max_iter, metric, ...])	Clustering by k-means with SPD/HPD matrices as inputs.
KmeansPerClassTransform([n_clusters])	Clustering by k-means for each class with SPD/HPD matrices as inputs.
MeanShift([kernel, bandwidth, metric, tol, ...])	Clustering by mean shift with SPD/HPD matrices as inputs.
Potato([metric, threshold, n_iter_max, ...])	Artifact detection with the Riemannian Potato.
PotatoField([n_potatoes, p_threshold, ...])	Artifact detection with the Riemannian Potato Field.

Tangent Space

TangentSpace([metric, tsupdate])	Tangent space projection.
FGDA([metric, tsupdate])	Fisher geodesic discriminant analysis.

Spatial Filtering

Xdawn([nfilter, classes, estimator, ...])	Xdawn algorithm.
CSP([nfilter, metric, log, ajd_method])	CSP spatial filtering with covariance matrices as inputs.
SPoC([nfilter, metric, log, ajd_method])	SPoC spatial filtering with covariance matrices as inputs.
BilinearFilter(filters[, log])	Bilinear spatial filter.
AJDC([window, overlap, fmin, fmax, fs, ...])	AJDC algorithm.

Preprocessing

Whitening([metric, dim_red, verbose])

Whitening, and optional unsupervised dimension reduction.

Channel selection

ElectrodeSelection([nelec, metric, n_jobs])	Channel selection based on a Riemannian geometry criterion.
FlatChannelRemover()	Flat channel removal.

Transfer Learning

encode_domains(X, y, domain)	Encode the domains of the data in the labels.
decode_domains(X_enc, y_enc)	Decode the domains of the data in the labels.
TLSplitter(target_domain, cv)	Class for handling the cross-validation splits of multi-domain data.
TLEstimator(target_domain, estimator[, ...])	Transfer learning wrapper for estimators.
TLClassifier(target_domain, estimator[, ...])	Transfer learning wrapper for classifiers.
TLRegressor(target_domain, estimator[, ...])	Transfer learning wrapper for regressors.
TLDummy()	No transformation for transfer learning.
TLCenter(target_domain[, metric])	Centering for transfer learning.
TLScale(target_domain[, final_dispersion, ...])	Scaling for transfer learning.
TLRotate(target_domain[, weights, metric, ...])	Rotation for transfer learning.
MDWM(domain_tradeoff, target_domain[, ...])	Classification by Minimum Distance to Weighted Mean.

Stats

PermutationDistance([n_perms, metric, mode, ...])	Permutation test based on distance.
PermutationModel([n_perms, model, cv, ...])	Permutation test using any scikit-learn model for scoring.

Datasets

make_gaussian_blobs([n_matrices, n_dim, ...])	Generate SPD matrices for two classes.
make_outliers(n_matrices, mean, sigma[, ...])	Generate outlier matrices.
make_matrices(n_matrices, n_dim, kind[, rs, ...])	Generate matrices with specific properties.
make_masks(n_masks, n_dim0, n_dim1_min[, rs])	Generate masks defined as semi-orthogonal matrices.
sample_gaussian_spd(n_matrices, mean, sigma)	Sample a Riemannian Gaussian distribution.
make_classification_transfer(n_matrices[, ...])	Generate 2x2 SPD matrices for two classes in source and target domains.
RandomOverSampler([metric, ...])	Random over-sampling for SPD/HPD matrices.

Utils function

Utils functions are low level functions that implement most base components of Riemannian geometry.

Covariance processing

covariances(X[, estimator])	Estimation of covariance matrices.
covariance_mest(X, m_estimator, *[, init, ...])	Robust M-estimators.
covariance_sch(X)	Schaefer-Strimmer shrunk covariance estimator.
covariance_scm(X, *[, assume_centered])	Sample covariance estimator.
covariances_EP(X, P[, estimator])	Special form covariance matrix, concatenating a prototype P.
covariances_X(X[, estimator, alpha])	Special form covariance matrix, embedding input X.
block_covariances(X, blocks[, estimator])	Compute block diagonal covariance.
cross_spectrum(X[, window, overlap, fmin, ...])	Compute the complex cross-spectral matrices of a real signal X.
cospectrum(X[, window, overlap, fmin, fmax, fs])	Compute co-spectral matrices, the real part of cross-spectra.
coherence(X[, window, overlap, fmin, fmax, ...])	Compute squared coherence.
normalize(X, norm)	Normalize a set of square matrices, using corr, trace or determinant.
get_nondiag_weight(X)	Compute non-diagonality weights of a set of square matrices.

Distances

distance(A, B[, metric, squared])	Distance between matrices according to a metric.
distance_chol(A, B[, squared])	Cholesky distance between SPD/HPD matrices.
distance_euclid(A, B[, squared])	Euclidean distance between matrices.
distance_harmonic(A, B[, squared])	Harmonic distance between invertible matrices.
distance_kullback(A, B[, squared])	Kullback-Leibler divergence between SPD/HPD matrices.
distance_kullback_sym(A, B[, squared])	Symmetrized Kullback-Leibler divergence between SPD/HPD matrices.
distance_logchol(A, B[, squared])	Log-Cholesky distance between SPD/HPD matrices.
distance_logdet(A, B[, squared])	Log-det distance between SPD/HPD matrices.
distance_logeuclid(A, B[, squared])	Log-Euclidean distance between SPD/HPD matrices.
distance_poweuclid(A, B, p[, squared])	Power Euclidean distance between SPD/HPD matrices.
distance_riemann(A, B[, squared])	Affine-invariant Riemannian distance between SPD/HPD matrices.
distance_thompson(A, B[, squared])	Thompson distance between SPD/HPD matrices.
distance_wasserstein(A, B[, squared])	Wasserstein distance between SPSD/HPSD matrices.
pairwise_distance(X[, Y, metric, squared])	Pairwise distance matrix.
distance_mahalanobis(X, cov[, mean, squared])	Mahalanobis distance between vectors and a Gaussian distribution.

Means

mean_covariance(X, *args[, metric, ...])	Mean of matrices according to a metric.
mean_ale(X, *[, tol, maxiter, ...])	AJD-based log-Euclidean (ALE) mean of SPD/HPD matrices.
mean_alm(X, *[, tol, maxiter, sample_weight])	Ando-Li-Mathias (ALM) mean of SPD/HPD matrices.
mean_chol(X[, sample_weight])	Mean of SPD/HPD matrices according to the Cholesky metric.
mean_euclid(X[, sample_weight])	Mean of matrices according to the Euclidean metric.
mean_harmonic(X[, sample_weight])	Harmonic mean of invertible matrices.
mean_kullback_sym(X[, sample_weight])	Mean of SPD/HPD matrices according to Kullback-Leibler divergence.
mean_logchol(X[, sample_weight])	Mean of SPD/HPD matrices according to the log-Cholesky metric.
mean_logdet(X, *[, tol, maxiter, init, ...])	Mean of SPD/HPD matrices according to the log-det metric.
mean_logeuclid(X[, sample_weight])	Mean of SPD/HPD matrices according to the log-Euclidean metric.
mean_power(X, p, *[, sample_weight, zeta, ...])	Power mean of SPD/HPD matrices.
mean_poweuclid(X, p, *[, sample_weight])	Mean of SPD/HPD matrices according to the power Euclidean metric.
mean_riemann(X, *[, tol, maxiter, init, ...])	Mean of SPD/HPD matrices according to the Riemannian metric.
mean_thompson(X, *[, tol, maxiter, init, ...])	Mean of SPD/HPD matrices according to the Thompson metric.
mean_wasserstein(X[, tol, maxiter, init, ...])	Mean of SPD/HPD matrices according to the Wasserstein metric.
maskedmean_riemann(X, masks, *[, tol, ...])	Masked Riemannian mean of SPD/HPD matrices.
nanmean_riemann(X[, tol, maxiter, init, ...])	Riemannian NaN-mean of SPD/HPD matrices.

Medians

median_euclid(X, *[, tol, maxiter, init, ...])	Euclidean geometric median of matrices.
median_riemann(X, *[, tol, maxiter, init, ...])	Affine-invariant Riemannian geometric median of SPD/HPD matrices.

Geodesics

geodesic(A, B, alpha[, metric])	Geodesic between matrices according to a metric.
geodesic_chol(A, B[, alpha])	Cholesky geodesic between SPD/HPD matrices.
geodesic_euclid(A, B[, alpha])	Euclidean geodesic between matrices.
geodesic_logchol(A, B[, alpha])	Log-Cholesky geodesic between SPD/HPD matrices.
geodesic_logeuclid(A, B[, alpha])	Log-Euclidean geodesic between SPD/HPD matrices.
geodesic_riemann(A, B[, alpha])	Affine-invariant Riemannian geodesic between SPD/HPD matrices.
geodesic_thompson(A, B[, alpha])	Thompson geodesic between SPD/HPD matrices.
geodesic_wasserstein(A, B[, alpha])	Wasserstein geodesic between SPD/HPD matrices.

Kernels

kernel(X[, Y, Cref, metric, reg])	Kernel matrix between matrices according to a specified metric.
kernel_euclid(X[, Y, Cref, reg])	Euclidean kernel between two sets of matrices.
kernel_logeuclid(X[, Y, Cref, reg])	Log-Euclidean kernel between two sets of SPD matrices.
kernel_riemann(X[, Y, Cref, reg])	Affine-invariant Riemannian kernel between two sets of SPD matrices.

Tangent Space

exp_map(X, Cref, *[, metric])	Project matrices back to manifold by exponential map.
exp_map_euclid(X, Cref)	Project matrices back to manifold by Euclidean exponential map.
exp_map_logchol(X, Cref)	Project matrices back to manifold by log-Cholesky exponential map.
exp_map_logeuclid(X, Cref)	Project matrices back to manifold by log-Euclidean exponential map.
exp_map_riemann(X, Cref[, Cm12])	Project matrices back to manifold by Riemannian exponential map.
exp_map_wasserstein(X, Cref)	Project matrices back to manifold by Wasserstein exponential map.
log_map(X, Cref, *[, metric])	Project matrices in tangent space by logarithmic map.
log_map_euclid(X, Cref)	Project matrices in tangent space by Euclidean logarithmic map.
log_map_logchol(X, Cref)	Project matrices in tangent space by log-Cholesky logarithmic map.
log_map_logeuclid(X, Cref)	Project matrices in tangent space by log-Euclidean logarithmic map.
log_map_riemann(X, Cref[, C12])	Project matrices in tangent space by Riemannian logarithmic map.
log_map_wasserstein(X, Cref)	Project matrices in tangent space by Wasserstein logarithmic map.
upper(X)	Return the weighted upper triangular part of matrices.
unupper(T)	Inverse upper function.
tangent_space(X, Cref, *[, metric])	Transform matrices into tangent vectors.
untangent_space(T, Cref, *[, metric])	Transform tangent vectors back to matrices.
transport(X, A, B[, metric])	Parallel transport.
transport_euclid(X[, A, B])	Parallel transport for Euclidean metric.
transport_logchol(X, A, B)	Parallel transport for log-Cholesky metric.
transport_logeuclid(X, A, B)	Parallel transport for log-Euclidean metric.
transport_riemann(X, A, B)	Parallel transport for affine-invariant Riemannian metric.

Base

ctranspose(X)	Conjugate transpose operator.
expm(C)	Exponential of SPD/HPD matrices.
invsqrtm(C)	Inverse square root of SPD/HPD matrices.
logm(C)	Logarithm of SPD/HPD matrices.
powm(C, alpha)	Power of SPD/HPD matrices.
sqrtm(C)	Square root of SPD/HPD matrices.
nearest_sym_pos_def(X[, reg])	Find the nearest SPD matrices.
ddexpm(X, Cref)	Directional derivative of the matrix exponential.
ddlogm(X, Cref)	Directional derivative of the matrix logarithm.

Aproximate Joint Diagonalization

ajd(X[, method, init, eps, n_iter_max])	Aproximate joint diagonalization (AJD) according to a method.
ajd_pham(X, *[, init, eps, n_iter_max, ...])	Approximate joint diagonalization based on Pham's algorithm.
rjd(X, *[, init, eps, n_iter_max])	Approximate joint diagonalization based on JADE.
uwedge(X, *[, init, eps, n_iter_max])	Approximate joint diagonalization based on UWEDGE.

Matrix Tests

is_square(X)	Check if matrices are square.
is_sym(X)	Check if all matrices are symmetric.
is_skew_sym(X)	Check if all matrices are skew-symmetric.
is_real(X)	Check if all matrices are strictly real.
is_real_type(X)	Check if matrices are real type.
is_hermitian(X)	Check if all matrices are Hermitian.
is_pos_def(X[, tol, fast_mode])	Check if all matrices are positive definite (PD).
is_pos_semi_def(X)	Check if all matrices are positive semi-definite (PSD).
is_sym_pos_def(X[, tol])	Check if all matrices are symmetric positive-definite (SPD).
is_sym_pos_semi_def(X)	Check if all matrices are symmetric positive semi-definite (SPSD).
is_herm_pos_def(X[, tol])	Check if all matrices are Hermitian positive-definite (HPD).
is_herm_pos_semi_def(X)	Check if all matrices are Hermitian positive semi-definite (HPSD).

Visualization

plot_bihist(X, y[, n_bins, title])	Plot histogram of bi-class predictions.
plot_biscatter(X, y)	Plot scatter of bi-class predictions.
plot_cospectra(X, freqs, *[, ylabels, title])	Plot cospectral matrices.
plot_cov_ellipse(ax, X[, n_std])	Plot 2x2 covariance matrix as an ellipse.
plot_embedding(X[, y, embd_type, metric, ...])	Plot embedding of SPD matrices.
plot_waveforms(X, display, *[, times, ...])	Plot repetitions of a multichannel waveform.