spd_learn.functional.distance_mahalanobis#

spd_learn.functional.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:

  • X (ndarray, shape (..., n, m)) – Vectors.

  • cov (ndarray, shape (..., n, n)) – Covariance matrix of the multivariate Gaussian distribution.

  • mean (None | ndarray, shape (..., n, 1), default=None) – Mean vector of the multivariate Gaussian distribution. If None, distribution is considered as centered.

  • squared (bool, default=False) –

    Return squared distance.

    Added in version 0.5.

Returns:

d – Mahalanobis distances.

Return type:

ndarray, shape (…, m)

Notes

Added in version 0.4.

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

References