Efficient method for symmetric nonnegative matrix factorization with an approximate augmented Lagrangian scheme

In this paper, we propose an efficient method for solving symmetric nonnegative matrix factorization following an approximate augmented Lagrangian scheme. The augmented Lagrangian subproblem was solved column by column under the block coordinate descent (BCD) framework. In particular, we extend the recursive formula for rank-k nonnegative least squares problems by Chu et al. (2021) to subproblems generated by BCD framework in our method. Thereafter we derive the closed-form solution for k = 4. Experiments for clustering show that the proposed method is noticeably efficient and achieves competitive performance compared with state-of-the-art methods.