mahalanobis

mvpy.math.mahalanobis(x: ndarray | Tensor, y: ndarray | Tensor, Σ: ndarray | Tensor, *args: Any) → ndarray | Tensor

Computes mahalanobis distance between x and y using inverse covariance matrix Σ.

Parameters:

xUnion[np.ndarray, torch.Tensor]

Matrix ([samples …] x features)

yUnion[np.ndarray, torch.Tensor]

Matrix ([samples …] x features)

ΣUnion[np.ndarray, torch.Tensor]

Precision matrix (features x features)

Returns:

Union[np.ndarray, torch.Tensor]

Vector or matrix of distances.

Notes

Mahalanobis distance is defined as:

\[d(x, y) = \sqrt{(x - y)^T Σ^{-1} (x - y)}\]

where \(x\) and \(y\) are the matrices to compute the distance between, and \(Σ\) is the covariance matrix.

Examples

>>> import torch
>>> from mvpy.math import mahalanobis
>>> from mvpy.estimators import Covariance
>>> x, y = torch.normal(0, 1, (10, 50)), torch.normal(0, 1, (10, 50))
>>> Σ = Covariance().fit(torch.cat((x, y), 0)).covariance_
>>> Σ = torch.linalg.inv(Σ)
>>> d = mahalanobis(x, y, Σ)
>>> d.shape
torch.Size([10])