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Entrywise Power Matrix Factorization Complexity Mapped

By PulseAugur Editorial · [2 sources] ·

Researchers have analyzed the computational complexity of entrywise power matrix factorization (EPMF), a problem that includes modulus models and component-wise square factorization as special cases. They established a complete complexity landscape for both exact and approximate EPMF. For the exact case, they proved it is equivalent to the signing problem, which is strongly NP-hard but solvable in polynomial time for a fixed rank. In the approximate case, EPMF was shown to be NP-hard even for a rank of two. AI

IMPACT This research provides theoretical insights into matrix factorization techniques, which could inform future algorithm development in machine learning.

RANK_REASON The cluster contains a research paper detailing computational complexity analysis of a mathematical problem. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Entrywise Power Matrix Factorization Complexity Mapped

COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Nicolas Gillis, Subhayan Saha, Stefano Sicilia, Arnaud Vandaele ·

    On the Complexity of Entrywise Power Matrix Factorization

    arXiv:2607.04875v1 Announce Type: cross Abstract: Given a nonnegative matrix $X$, a factorization rank $r$ and a real parameter $p$, 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|^{\ci…

  2. arXiv stat.ML TIER_1 English(EN) · Arnaud Vandaele ·

    On the Complexity of Entrywise Power Matrix Factorization

    Given a nonnegative matrix $X$, a factorization rank $r$ and a real parameter $p$, 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…

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