  There are two problems need to be dealt with for Non-negative Matrix
Factorization (NMF): choose a suitable rank of the factorization and provide a
good initialization method for NMF algorithms. This paper aims to solve these
two problems using Singular Value Decomposition (SVD). At first we extract the
number of main components as the rank, actually this method is inspired from
[1, 2]. Second, we use the singular value and its vectors to initialize NMF
algorithm. In 2008, Boutsidis and Gollopoulos [3] provided the method titled
NNDSVD to enhance initialization of NMF algorithms. They extracted the positive
section and respective singular triplet information of the unit matrices
{C(j)}k j=1 which were obtained from singular vector pairs. This strategy aims
to use positive section to cope with negative elements of the singular vectors,
but in experiments we found that even replacing negative elements by their
absolute values could get better results than NNDSVD. Hence, we give another
method based SVD to fulfil initialization for NMF algorithms (SVD-NMF).
Numerical experiments on two face databases ORL and YALE [16, 17] show that our
method is better than NNDSVD.
