Block Iteratively Reweighted Algorithms for Robust Symmetric Nonnegative Matrix Factorization

This letter is concerned with the symmetric nonnegative matrix factorization in the presence of heavy-tailed outliers. We address this problem under a formulation involving some robust loss functions, instead of the standard squared-error loss. To handle the original computationally intractable problem, we present an efficient block iteratively reweighted algorithmic framework with provable convergence guarantee. Each iteration of the proposed method is obtained by minimizing a fourth-order nonnegative polynomial optimization with a closed-form solution. Simulation results illustrate that the proposed algorithm attains a significant performance improvement over existing benchmark methods in heavy-tailed noise environment.