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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 method used to find low-rank matrices. They established a complete complexity landscape for both exact and approximate cases. In the exact scenario, EPMF is shown to be equivalent to a "signing problem" involving matrix sign flips, which is proven to be strongly NP-hard but solvable in polynomial time for fixed ranks. For approximate EPMF using the Frobenius norm, the problem is NP-hard even for the simplest non-trivial rank of two. AI

IMPACT Establishes theoretical limits for matrix factorization techniques relevant to machine learning algorithms.

RANK_REASON The cluster contains two identical arXiv preprints detailing a new research paper on computational complexity.

Read on arXiv stat.ML →

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

Entrywise Power Matrix Factorization Complexity Mapped

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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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