Exact Guarantees on the Absence of Spurious Local Minima for
Non-negative Rank-1 Robust Principal Component Analysis

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Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis

30 December 2018

Somayeh Sojoudi

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Papers citing "Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis"

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Title
$$\ell_1$-norm rank-one symmetric matrix factorization has no spurious second-order stationary points$ $\ell_1$ -norm rank-one symmetric matrix factorization has no spurious second-order stationary points Jiewen Guan Anthony Man-Cho So 111 2 0 07 Oct 2024
Low solution rank of the matrix LASSO under RIP with consequences for rank-constrained algorithms Andrew D. McRae 88 1 0 19 Apr 2024
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses Ziye Ma Ying Chen Javad Lavaei Somayeh Sojoudi 53 1 0 10 Mar 2024
Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensing Ziye Ma Javad Lavaei Somayeh Sojoudi 76 2 0 24 Oct 2023
Personalized Dictionary Learning for Heterogeneous Datasets Geyu Liang Naichen Shi Raed Al Kontar Salar Fattahi 85 6 0 24 May 2023
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points Ziye Ma Igor Molybog Javad Lavaei Somayeh Sojoudi 82 3 0 15 Feb 2023
Simple Alternating Minimization Provably Solves Complete Dictionary Learning Geyu Liang G. Zhang Salar Fattahi Richard Y. Zhang 83 6 0 23 Oct 2022
Behind the Scenes of Gradient Descent: A Trajectory Analysis via Basis Function Decomposition Jianhao Ma Li-Zhen Guo Salar Fattahi 87 4 0 01 Oct 2022
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing Baturalp Yalcin Ziye Ma Javad Lavaei Somayeh Sojoudi 59 7 0 15 Aug 2022
Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solution Jianhao Ma Salar Fattahi 80 5 0 15 Jul 2022
Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate Ziye Ma Somayeh Sojoudi 76 7 0 08 Mar 2022
Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods Baturalp Yalcin Haixiang Zhang Javad Lavaei Somayeh Sojoudi 136 13 0 19 Oct 2021
Sign-RIP: A Robust Restricted Isometry Property for Low-rank Matrix Recovery Jianhao Ma Salar Fattahi 76 12 0 05 Feb 2021
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization T. Hou Zhenzhen Li Ziyun Zhang 72 18 0 31 Dec 2020
Adversarial Crowdsourcing Through Robust Rank-One Matrix Completion Qianqian Ma Alexander Olshevsky 84 32 0 23 Oct 2020
Asymptotic Convergence Rate of Alternating Minimization for Rank One Matrix Completion Rui Liu Alexander Olshevsky 50 0 0 11 Aug 2020
Global Optimality Guarantees for Nonconvex Unsupervised Video Segmentation Brendon G. Anderson Somayeh Sojoudi VOS 34 3 0 09 Jul 2019