A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for NMF is not easy its nonsymmetric counterpart, since latter admits splitting property that allows state-of-the-art alternating-type algorithms. To overcome this issue, we first split decision variable and transform to penalized one, paving way efficient We then show solving reformulation returns solution original NMF. Moreover, design family they all admit strong convergence guarantee: generated sequence iterates convergent converges at least sublinearly critical point Finally, conduct experiments on both synthetic real image support our theoretical results demonstrate performance