New SVD based initialization strategy for Non-negative Matrix Factorization
This work addresses initialization challenges in NMF for applications like face recognition, but it is incremental as it builds on prior SVD-based methods.
The paper tackles the problems of rank selection and initialization for Non-negative Matrix Factorization (NMF) by using Singular Value Decomposition (SVD) to determine the rank and propose a new initialization method called SVD-NMF, which outperforms the existing NNDSVD method on ORL and YALE face databases.
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.