ZCA whitening

Decorrelate without rotating the data

Whitening makes features uncorrelated with unit variance. PCA whitening does this by rotating into the principal axes, which can make images look unlike the original. ZCA whitening applies the same decorrelation but rotates back, so the output stays as close to the input as a whitening transform can be.

Implement zca_whiten(X, eps=1e-8). Return an array of the same shape as X.

1. Center the columns of X.
2. Compute the sample covariance C = Xᵀ X / (n − 1).
3. Take the eigendecomposition C = V Λ Vᵀ.
4. Build the whitening matrix W = V diag(1 / sqrt(λ + eps)) Vᵀ.
5. Return X_centered · W.

Constraints

• X must have at least 2 rows, otherwise raise ValueError.
• eps must be nonnegative, otherwise raise ValueError.
• Do not modify X.

Hints