In the slides over here by NVidia, they describe methods for BRDF compression. They first create a BRDF matrix where each column(or row) corresponds to a single light direction (or outgoing view direction). This matrix is then compressed by decomposing it either by using SVD or Normalized decomposition. My question is that they claim SVD gives better results than Normalized decomposition for similar compression sizes. Does anyone know what could be the possible reason for this?
The singular value decomposition produces the Eigenvalues with largest magnitude, and their corresponding Eigenvectors. If one were to decompose every Eigenvector of a matrix, they have performed a Principle Component Analysis.
The principal components represent the 'n'-dimensional axes on which the most variance is encoded. Therefore they can be used as lossy compression; they optimize which normal vector in the 'n'-space to direct a scalar value, such that the line defined by this normal best represents the information in the original matrix.