Bayesian model order selection for the Karhunen-Loeve transform and the singular value decomposition

Discusses model order selection in relation to the discrete Karhunen-Loeve transform (DKLT) and the singular value decomposition (SVD). There are many applications of the DKLT and SVD where it is necessary to discard some of the small singular values that may represent corrupted signal information. Bayesian methods allow to determine the DKLT model order evidence which indicates the optimal number of basis vectors to choose for reconstruction such that the signal is not over-parameterised. Evidence methods can also be used for the SVD to determine the number of singular values (and hence the effective rank) of a singular or ill-conditioned matrix,