Selecting the rank of truncated SVD by Maximum Approximation Capacity
Truncated Singular Value Decomposition (SVD) calculates the closest
rank-$k$ approximation of a given input matrix. Selecting the
appropriate rank $k$ defines a critical model order choice in most
applications of SVD. To obtain a principled cut-off criterion for the
spectrum, we convert the underlying optimization problem into a
noisy channel coding problem. The optimal approximation capacity of
this channel controls the appropriate strength of regularization to
suppress noise. In simulation experiments, this information theoretic
method to determine the optimal rank competes with state-of-the art
model selection techniques.