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New research details complexity of entrywise power matrix factorization

By PulseAugur Editorial · [1 sources] ·

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]

Read on arXiv cs.IR (Information Retrieval) →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research details complexity of entrywise power matrix factorization

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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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COVERAGE [1]

  1. arXiv cs.IR (Information Retrieval) TIER_1 English(EN) · Arnaud Vandaele ·

    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)^{\ci…

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