On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization

Given a nonnegative matrix $X$, a factorization rank $r$ and {a positive integer $p$}, entrywise power matrix factorization (EPMF) looks for a low-rank matrix $X_r$ such that $X = |X_r|^{\circ p}$ (exact case) or $X \approx |X_r|^{\circ p}$ (approximate case), where $(\cdot)^{\circ p}$ denotes the componentwise exponent. EPMF includes the modulus model ($p=1$) and componentwise square factoriza…