pyriemann.geometry.distance.distance_mahalanobis

pyriemann.geometry.distance.distance_mahalanobis(X, cov, mean=None, squared=False)[source]

Mahalanobis distance between vectors and a Gaussian distribution.

The Mahalanobis distance between a vector \(x \in \mathbb{C}^n\) and a multivariate Gaussian distribution \(\mathcal{N}(\mu, C)\), with mean vector \(\mu \in \mathbb{C}^n\) and covariance matrix \(C \in \mathbb{C}^{n \times n}\) , is:

\[d(x, \mathcal{N}(\mu, C)) = \sqrt{ (x - \mu)^H C^{-1} (x - \mu) }\]
Parameters:
Xndarray, shape (…, n, m)

Vectors.

covndarray, shape (…, n, n)

Covariance matrix of the multivariate Gaussian distribution.

meanNone | ndarray, shape (…, n, 1), default=None

Mean vector of the multivariate Gaussian distribution. If None, distribution is considered as centered.

squaredbool, default=False

Return squared distance.

Added in version 0.5.

Returns:
dndarray, shape (…, m)

Mahalanobis distances.

Notes

Added in version 0.4.

Changed in version 0.12: Add support for NumPy and PyTorch.

References