scipy.stats.Covariance.whiten#

Covariance.whiten(x)[source]#

Perform a whitening transformation on data.

“Whitening” (“white” as in “white noise”, in which each frequency has equal magnitude) transforms a set of random variables into a new set of random variables with unit-diagonal covariance. When a whitening transform is applied to a sample of points distributed according to a multivariate normal distribution with zero mean, the covariance of the transformed sample is approximately the identity matrix.

Parameters:

xarray_like: An array of points. The last dimension must correspond with the dimensionality of the space, i.e., the number of columns in the covariance matrix.

Returns:

x_array_like: The transformed array of points.

References

[1]

“Whitening Transformation”. Wikipedia. https://en.wikipedia.org/wiki/Whitening_transformation

[2]

Novak, Lukas, and Miroslav Vorechovsky. “Generalization of coloring linear transformation”. Transactions of VSB 18.2 (2018): 31-35. DOI:10.31490/tces-2018-0013

Examples

>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()
>>> n = 3
>>> A = rng.random(size=(n, n))
>>> cov_array = A @ A.T  # make matrix symmetric positive definite
>>> precision = np.linalg.inv(cov_array)
>>> cov_object = stats.Covariance.from_precision(precision)
>>> x = rng.multivariate_normal(np.zeros(n), cov_array, size=(10000))
>>> x_ = cov_object.whiten(x)
>>> np.cov(x_, rowvar=False)  # near-identity covariance
array([[0.97862122, 0.00893147, 0.02430451],
       [0.00893147, 0.96719062, 0.02201312],
       [0.02430451, 0.02201312, 0.99206881]])