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New framework accelerates weighted low-rank matrix approximation methods

By PulseAugur Editorial · [3 sources] ·

This paper introduces Weighted Low-Rank Matrix Approximation (WLRMA) as a generalization of classical low-rank approximation and matrix completion. It presents a unified framework for developing efficient optimization methods, including accelerated algorithms based on Nesterov momentum and Anderson acceleration, for both rank-constrained and nuclear-norm WLRMA problems. The research also proposes scalable implementations for large sparse data matrices and an effective-rank criterion, demonstrating substantial computational gains and applications in matrix completion and generalized linear low-rank modeling. AI

IMPACT Introduces new computational methods for statistical modeling and matrix completion, potentially improving efficiency in machine learning tasks.

RANK_REASON The item is an academic paper detailing new methods and applications for weighted low-rank matrix approximation. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New framework accelerates weighted low-rank matrix approximation methods

COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · Lavinia Ghita, Dhruv Desai, Jake Goldberg, Roman Yokunda Enzmann ·

    Low-Rank Dependence Decomposition via Accelerated Symmetric Non-negative Matrix Factorization

    arXiv:2607.24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes. We present a large-scale GPU study o…

  2. arXiv stat.ML TIER_1 English(EN) · Elena Tuzhilina, Trevor Hastie ·

    Weighted Low-Rank Matrix Approximation: Acceleration and Applications

    arXiv:2109.11057v2 Announce Type: replace Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights. Such formulations arise naturally in a broad class of statistical model…

  3. arXiv cs.CV TIER_1 English(EN) · Hiroki Hasegawa ·

    Structural Loss Metrics for Tensor Approximation via Matrix Low-Rank Approximation

    arXiv:2607.24009v1 Announce Type: new Abstract: Matricized low-rank approximation via SVD is a standard surrogate for tensor decompositions, but entry-wise reconstruction error fails to capture multiway geometric degradation. Under an orthogonal Tucker model, we characterize this…

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