New initialization strategy for nonnegative matrix factorization

Nonnegative matrix factorization (NMF) has been proved to be a powerful data representation method, and has shown success in applications such as data representation and document clustering. In this paper, we propose a new initialization strategy for NMF. This new method is entitled square nonnegative matrix factorization, SQR-NMF. In this method, we first transform the non-square nonnegative matrix to a square one. Several strategies are proposed to achieve SQR step. Then we take the positive section of eigenvalues and eigenvectors for initialization. Simulation results show that SQR-NMF has faster convergence rate and provides an approximation with lower error rate as compared to SVD-NMF and random initialization methods. Complementing different elements in data matrix also affect the results. The experiments show that complementary elements should be 0 for small data sets and mean values of each row or column of the original nonnegative matrix for large data sets.