  Symmetric nonnegative matrix factorization (NMF), a special but important
class of the general NMF, is demonstrated to be useful for data analysis and in
particular for various clustering tasks. Unfortunately, designing fast
algorithms for Symmetric NMF is not as easy as for the nonsymmetric
counterpart, the latter admitting the splitting property that allows efficient
alternating-type algorithms. To overcome this issue, we transfer the symmetric
NMF to a nonsymmetric one, then we can adopt the idea from the state-of-the-art
algorithms for nonsymmetric NMF to design fast algorithms solving symmetric
NMF. We rigorously establish that solving nonsymmetric reformulation returns a
solution for symmetric NMF and then apply fast alternating based algorithms for
the corresponding reformulated problem. Furthermore, we show these fast
algorithms admit strong convergence guarantee in the sense that the generated
sequence is convergent at least at a sublinear rate and it converges globally
to a critical point of the symmetric NMF. We conduct experiments on both
synthetic data and image clustering to support our result.
