A new arXiv paper delves into the computational complexity of entrywise power matrix factorization (EPMF), a technique used in various applications including the modulus model and componentwise square factorization. The research establishes a complete complexity landscape for both exact and approximate EPMF problems. It demonstrates that the exact EPMF is equivalent to the low-rank matrix signing (LRMS) problem, which is shown to be strongly NP-hard, though solvable in polynomial time for fixed ranks. The paper also proves that approximate EPMF is NP-hard even for the simplest non-trivial case of rank 2. AI
IMPACT This research provides theoretical insights into matrix factorization techniques relevant to machine learning algorithms.
RANK_REASON The cluster contains a single academic paper detailing computational complexity research. [lever_c_demoted from research: ic=1 ai=1.0]
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