# pyriemann.tangentspace.TangentSpace¶

class pyriemann.tangentspace.TangentSpace(metric='riemann', tsupdate=False)

Tangent space project TransformerMixin.

Tangent space projection map a set of SPD matrices to their tangent space according to [1]. The Tangent space projection can be seen as a kernel operation, cf [2]. After projection, each matrix is represented as a vector of size $$n (n+1)/2$$, where $$n$$ is the dimension of the SPD matrices.

Tangent space projection is useful to convert SPD matrices in Euclidean vectors while conserving the inner structure of the manifold. After projection, standard processing and vector-based classification can be applied.

Tangent space projection is a local approximation of the manifold. it takes one parameter, the reference point, that is usually estimated using the geometric mean of the SPD matrices set you project. If the function fit is not called, the identity matrix will be used as reference point. This can lead to serious degradation of performances. The approximation will be bigger if the matrices in the set are scattered in the manifold, and lower if they are grouped in a small region of the manifold.

After projection, it is possible to go back in the manifold using the inverse transform.

Parameters
metricstring | dict, default=’riemann’

The type of metric used for reference matrix estimation (see mean_covariance for the list of supported metric) and for tangent space map (see tangent_space for the list of supported metric). The metric could be a dict with two keys, mean and map in order to pass different metrics for the reference matrix estimation and the tangent space mapping.

tsupdatebool, default=False

Activate tangent space update for covariante shift correction between training and test, as described in [2]. This is not compatible with online implementation. Performance are better when the number of matrices for prediction is higher.

FgMDM
FGDA

References

1

Multiclass Brain-Computer Interface Classification by Riemannian Geometry A. Barachant, S. Bonnet, M. Congedo, and C. Jutten. IEEE Transactions on Biomedical Engineering, vol. 59, no. 4, p. 920-928, 2012.

2(1,2)

Classification of covariance matrices using a Riemannian-based kernel for BCI applications A. Barachant, S. Bonnet, M. Congedo and C. Jutten. Neurocomputing, Elsevier, 2013, 112, pp.172-178.

Attributes
reference_ndarray

If fit, the reference point for tangent space mapping.

__init__(metric='riemann', tsupdate=False)

Init.

fit(X, y=None, sample_weight=None)

Fit (estimates) the reference point.

Parameters
Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yNone

Not used, here for compatibility with sklearn API.

sample_weightNone | ndarray, shape (n_matrices,), default=None

Weights for each matrix. If None, it uses equal weights.

Returns
selfTangentSpace instance

The TangentSpace instance.

fit_transform(X, y=None, sample_weight=None)

Fit and transform in a single function.

Parameters
Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

yNone

Not used, here for compatibility with sklearn API.

sample_weightNone | ndarray, shape (n_matrices,), default=None

Weights for each matrix. If None, it uses equal weights.

Returns
tsndarray, shape (n_matrices, n_ts)

Tangent space projections of SPD matrices.

get_params(deep=True)

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

inverse_transform(X, y=None)

Inverse transform.

Project back a set of tangent space vector in the manifold.

Parameters
Xndarray, shape (n_matrices, n_ts)

Set of tangent space projections of the matrices.

yNone

Not used, here for compatibility with sklearn API.

Returns
covndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices corresponding to each of tangent vector.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

Estimator parameters.

Returns
selfestimator instance

Estimator instance.

transform(X)

Tangent space projection.

Parameters
Xndarray, shape (n_matrices, n_channels, n_channels)

Set of SPD matrices.

Returns
tsndarray, shape (n_matrices, n_ts)

Tangent space projections of SPD matrices.