PCA and ZCA Covariance Whitening
Whiten a covariance while comparing rotated and orientation-preserving views.
Free theory articleWhiten a covariance while comparing rotated and orientation-preserving views.
Concept & interpretation
Covariance whitening transformations map a set of variables with a known covariance matrix into a new set of variables whose covariance is the identity matrix. When the data has zero mean, this transformation spheres the data. PCA and ZCA represent two such transformations with different mathematical properties and physical interpretations.
Experiment
We can visualize how PCA and ZCA whitening differ in transforming data distributions and single points.
- Open the PCA and ZCA Covariance Whitening module.
- Set the Correlation to 0.5 and observe the transformed ellipse for PCA vs ZCA.
- Change the point to Opposed and note how ZCA preserves the spatial arrangement relative to the original point better than PCA, minimizing the mean squared displacement.
- Set Correlation to 1. Notice that whitening becomes impossible due to a singular covariance matrix.