pyriemann.utils.distance.distance_mahalanobis¶
- pyriemann.utils.distance.distance_mahalanobis(X, cov, mean=None, squared=False)¶
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, n_vectors)
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 (n_vectors,)
Mahalanobis distances.
Notes
Added in version 0.4.
References