Mahalanobis distance

Intermediate Netflix, Spotify+5

Measure distance in units of the data's own spread

The Mahalanobis distance between x and y under a covariance matrix S is sqrt((x - y)^T S^-1 (x - y)). It is Euclidean distance after whitening the data, so it accounts for feature scales and for correlations between features.

Implement mahalanobis(x, y, cov).

x and y are 1-D arrays of length d. cov is a d by d matrix.
cov must be symmetric and positive definite. Check this with a Cholesky factorization, and return the distance as a float.

Constraints

x and y must have length d, and cov must be d by d. Otherwise raise ValueError.
A cov that is not symmetric raises ValueError.
A cov that is not positive definite raises ValueError.
Do not modify the inputs.

Hints

Hint 1

If cov = L L^T is the Cholesky factorization, then z = L^-1 (x - y) is the whitened difference, and the distance is ||z||.

Keywords

classical-mldistancemahalanobiscovarianceanomaly-detection

Python

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