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Matrix optimization landscape analyzed using Riemannian geometry

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This paper analyzes the global landscape of a fixed-rank matrix optimization problem using the Burer-Monteiro factorization and Riemannian geometry. The research characterizes the search space into three regions based on geodesic convexity and smoothness properties. It provides a geometric explanation for the effectiveness of gradient descent in this factorization and offers a quantitative bound for convexity radius in Bures-Wasserstein space. AI

RANK_REASON The cluster contains an academic paper detailing a novel mathematical analysis of an optimization problem. [lever_c_demoted from research: ic=1 ai=0.4]

Read on arXiv cs.LG →

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

Matrix optimization landscape analyzed using Riemannian geometry

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The cluster contains an academic paper detailing a novel mathematical analysis of an optimization problem. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Yuetian Luo, Nicolas Garcia Trillos ·

    Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective

    arXiv:2209.15130v3 Announce Type: replace-cross Abstract: We study a general matrix optimization problem with a fixed-rank positive semidefinite (PSD) constraint. We perform the Burer-Monteiro factorization and consider a particular Riemannian quotient geometry in a search space …

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