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I'm working with Python and I've implemented the PCA using this tutorial.
Everything works great, I got the Covariance I did a successful transform, brought it make to the original dimensions not problem.
But how do I perform whitening? I tried dividing the eigenvectors by the eigenvalues:
S, V = numpy.linalg.eig(cov)
V = V / S[:, numpy.newaxis]
and used V to transform the data but this led to weird data values. Could someone please shred some light on this?
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Whitening a data matrix follows the same transformation as for random variables. An empirical whitening transform is obtained by estimating the covariance (e.g. by maximum likelihood) and subsequently constructing a corresponding estimated whitening matrix (e.g. by Cholesky decomposition).
We have used PCA to reduce the dimension of the data. There is a closely related preprocessing step called whitening (or, in some other literatures, sphering) which is needed for some algorithms. If we are training on images, the raw input is redundant, since adjacent pixel values are highly correlated.
PCA Whitening is a processing step for image based data that makes input less redundant. Adjacent pixel or feature values can be highly correlated, and whitening through the use of PCA reduces this degree of correlation.
Normalization of multi-dimensional variables, which we call statistical whitening, not only scales each variance term to 1 , it removes all of the off-diagonal covariance terms. Whitening linearly decorrelates the input dimensions.
If you use python's scikit-learn library for this, you can just set the inbuilt parameter
from sklearn.decomposition import PCA
pca = PCA(whiten=True)
whitened = pca.fit_transform(X)
check the documentation.
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