  This paper describes a new algorithm for computing Nonnegative Low Rank
Matrix (NLRM) approximation for nonnegative matrices. Our approach is
completely different from classical nonnegative matrix factorization (NMF)
which has been studied for more than twenty five years. For a given nonnegative
matrix, the usual NMF approach is to determine two nonnegative low rank
matrices such that the distance between their product and the given nonnegative
matrix is as small as possible. However, the proposed NLRM approach is to
determine a nonnegative low rank matrix such that the distance between such
matrix and the given nonnegative matrix is as small as possible. There are two
advantages. (i) The minimized distance by the proposed NLRM method can be
smaller than that by the NMF method, and it implies that the proposed NLRM
method can obtain a better low rank matrix approximation. (ii) Our low rank
matrix admits a matrix singular value decomposition automatically which
provides a significant index based on singular values that can be used to
identify important singular basis vectors, while this information cannot be
obtained in the classical NMF. The proposed NLRM approximation algorithm was
derived using the alternating projection on the low rank matrix manifold and
the non-negativity property. Experimental results are presented to demonstrate
the above mentioned advantages of the proposed NLRM method compared the NMF
method.
