they do recognition by trying to represent the new face as a linear combination of all known faces in the database What is the difference between doing this an

they do recognition by trying to represent the new face as a linear combination of all known faces in the database What is the difference between doing this and just finding the dot product of the facial feature eigenvectors with the feature eigenvalues and choosing the maximal projection? That's how it's been done since forever, AFAIK.