Data Whitening Procedure

Data whitening is a common preprocessing technique primarily used to eliminate correlations between features and give data unit variance. Implementing data whitening in MATLAB can significantly enhance machine learning algorithm performance, particularly for dimensionality reduction or feature extraction methods like PCA and ICA.

The core concept of data whitening involves applying a linear transformation to convert original data into a new coordinate system where the transformed data's covariance matrix becomes an identity matrix. The standard implementation typically includes three key steps: first computing the data covariance matrix using MATLAB's `cov()` function, then performing eigenvalue decomposition through `eig()` or singular value decomposition via `svd()`, and finally constructing the whitening transformation matrix using the decomposition results.

In MATLAB implementation, the whitening transformation matrix can be built using the formula: W = V * D^(-1/2), where V contains eigenvectors and D is the diagonal matrix of eigenvalues from the covariance matrix decomposition. Whitened data not only accelerates algorithm convergence but also reduces feature redundancy by ensuring all dimensions share the same scale. The whitening process can be implemented through matrix operations: X_white = (X - mean(X)) * W.

It's important to note that data whitening is sensitive to outliers, so appropriate data cleaning and standardization should be performed beforehand. Additionally, whitening techniques are widely applied in image processing, signal analysis, and serve as crucial preprocessing steps in advanced data processing pipelines. For robust implementation, consider using z-score normalization before whitening and validate results by checking if cov(X_white) approximates the identity matrix.