Positive Semidefinite Matrix Factorization: A Connection With Phase Retrieval and Affine Rank Minimization

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative as the inner product two positive (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is equivalent factorization. Applications include combinatorial optimization, quantum-based statistical models, and recommender systems, among others. However, despite increasing interest in PSDMF, only few PSDMF algorithms were proposed literature. In work, we provide collection tools for by showing that can designed based on phase retrieval (PR) affine rank minimization (ARM) algorithms. This procedure allows shortcut designing new algorithms, it leverage some useful numerical properties existing PR ARM methods framework. Motivated idea, introduce family iterative hard thresholding (IHT). subsumes previously-proposed projected gradient methods. We show there high variability optimization problems makes beneficial try number different principles tackle difficult problems. certain cases, our able find solution. other they converge faster. Our results support claim framework inherit desired from leading more efficient motivate further study links between models.