moabb.datasets.preprocessing.EuclideanAlignment#

class moabb.datasets.preprocessing.EuclideanAlignment(estimator='lwf')[source]#

Bases: TransformerMixin, BaseEstimator

Euclidean Alignment of trials (He & Wu, 2020).

Euclidean Alignment (EA) removes the per-domain (subject / session / recording) covariance shift that makes a model trained on one set of recordings transfer poorly to another. It is the simplest member of a larger family of trial-alignment methods — others recenter on the Riemannian or log-Euclidean mean — and is the one most used with deep networks because it is cheap, label-free, and leaves the data as raw trials a network can ingest [He2020] [Junqueira2024].

Each trial is whitened by the inverse square root of a single reference covariance,

\[\bar{C} = \frac{1}{N} \sum_{i=1}^{N} C_i, \qquad \tilde{X}_i = \bar{C}^{-1/2} X_i ,\]

where \(C_i\) is the spatial covariance of trial \(X_i\) and \(\bar{C}\) is their arithmetic (Euclidean) mean. After alignment the trials share an identity-like average covariance, so the domain shift that lived in the second-order statistics is gone.

The transformer is inductive by default: fit() learns \(\bar{C}^{-1/2}\) from the training trials and transform() re-applies that same whitener to unseen trials, so no test information leaks into the alignment (the leakage that the transductive, fit-on-everything form silently introduces). Calling fit_transform() on a single recording recovers the usual transductive, per-recording EA people hand-roll — same object, no second class.

Unlike pyriemann.transfer.TLCenter (with metric="euclid"), which recenters covariance matrices for a Riemannian classifier, this operates directly on the (n_trials, n_channels, n_times) trials, so it drops in front of any time-series model (CSP, EEGNet, …).

Parameters:: estimator (str, default "lwf") – Covariance estimator passed to pyriemann.utils.covariance.covariances(). The shrinkage default "lwf" (Ledoit-Wolf) keeps the per-trial covariances symmetric positive-definite — and hence the reference mean invertible — even on short or noisy trials, where the plain sample covariance ("scm" / "cov") can be ill-conditioned.

inv_sqrt_ref_#

Inverse square root \(\bar{C}^{-1/2}\) of the reference mean covariance learned in fit(); the whitening matrix applied in transform().

Type:: ndarray, shape (n_channels, n_channels)

Examples using `moabb.datasets.preprocessing.EuclideanAlignment`#

Euclidean Alignment for cross-subject transfer

moabb.datasets.preprocessing.EuclideanAlignment#

Examples using moabb.datasets.preprocessing.EuclideanAlignment#

Examples using `moabb.datasets.preprocessing.EuclideanAlignment`#