hyperspy.learn.whitening module

hyperspy.learn.whitening.whiten_data(X, centre=True, method='PCA', epsilon=1e-10)

Centre and whiten the data X.

A whitening transformation is used to decorrelate the variables, such that the new covariance matrix of the whitened data is the identity matrix.

If X is a random vector with non-singular covariance matrix C, and W is a whitening matrix satisfying W^T W = C^-1, then the transformation Y = W X will yield a whitened random vector Y with unit diagonal covariance. In ZCA whitening, the matrix W = C^-1/2, while in PCA whitening, the matrix W is the eigensystem of C. More details can be found in [Kessy2015].

Parameters:

  • X (numpy array, shape (m, n)) – The input data.

  • centre (bool, default True) – If True, centre the data along the features axis. If False, do not centre the data.

  • method ({"PCA", "ZCA"}) – How to whiten the data. The default is PCA whitening.

  • epsilon (float) – Small floating-point value to avoid divide-by-zero errors.

Returns:

  • Y (numpy array, shape (m, n)) – The centred and whitened data.

  • W (numpy array, shape (n, n)) – The whitening matrix.

References

[Kessy2015]

A. Kessy, A. Lewin, and K. Strimmer, “Optimal Whitening and Decorrelation”, arXiv:1512.00809, (2015), https://arxiv.org/pdf/1512.00809.pdf