K Adithya Apuroop. A riemannian geometry for low-rank matrix completion. arXiv preprint arXiv:1211.1550, 2012.
HanQin Cai, Jialin Liu, and Wotao Yin. Learned robust pca: A scalable deep unfolding approach for high-dimensional outlier detection. Advances in Neural Information Processing Systems, 34: 16977-16989, 2021.
Emmanuel J Candès, Xiaodong Li, Yi Ma, and John Wright. Robust principal component analysis? Journal of the ACM (JACM), 58(3):1-37, 2011.
Kabir Aladin Chandrasekher, Mengqi Lou, and Ashwin Pananjady. Alternating minimization for generalized rank one matrix sensing: Sharp predictions from a random initialization. arXiv preprint arXiv:2207.09660, 2022.
Vasileios Charisopoulos, Yudong Chen, Damek Davis, Mateo Diaz, Lijun Ding, and Dmitriy Drusvyatskiy. Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence. Foundations of Computational Mathematics, 21(6):1505-1593, 2021.
Yuxin Chen, Yuejie Chi, Jianqing Fan, and Cong Ma. Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval. Mathematical Programming, 176:5-37, 2019.
Yuejie Chi, Yue M Lu, and Yuxin Chen. Nonconvex optimization meets low-rank matrix factorization: An overview. IEEE Transactions on Signal Processing, 67(20):5239-5269, 2019.
Simon S Du, Wei Hu, and Jason D Lee. Algorithmic regularization in learning deep homogeneous models: layers are automatically balanced. Advances in Neural Information Processing Systems, 31:382-393, 2018.
Rong Ge, Jason D Lee, and Tengyu Ma. Matrix completion has no spurious local minimum. Advances in Neural Information Processing Systems, pages 2981-2989, 2016.
Rong Ge, Chi Jin, and Yi Zheng. No spurious local minima in nonconvex low rank problems: A unified geometric analysis. In International Conference on Machine Learning, pages 1233-1242. PMLR, 2017.
Thomas Y Hou, Zhenzhen Li, and Ziyun Zhang. Fast global convergence for low-rank matrix recovery via riemannian gradient descent with random initialization. arXiv preprint arXiv:2012.15467, 2020.
Prateek Jain, Praneeth Netrapalli, and Sujay Sanghavi. Low-rank matrix completion using alternating minimization. In Proceedings of the forty-fifth annual ACM symposium on Theory of computing, pages 665-674, 2013.
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan. How to escape saddle points efficiently. In International conference on machine learning, pages 1724-1732. PMLR, 2017.
Qiuwei Li, Zhihui Zhu, and Gongguo Tang. The non-convex geometry of low-rank matrix optimization. Information and Inference: A Journal of the IMA, 8(1):51-96, 2019a.
Zhenzhen Li, Jian-Feng Cai, and Ke Wei. Toward the optimal construction of a loss function without spurious local minima for solving quadratic equations. IEEE Transactions on Information Theory, 66(5):3242-3260, 2019b.
Cong Ma, Yuanxin Li, and Yuejie Chi. Beyond procrustes: Balancing-free gradient descent for asymmetric low-rank matrix sensing. IEEE Transactions on Signal Processing, 69:867-877, 2021.
Jianhao Ma and Salar Fattahi. Global convergence of sub-gradient method for robust matrix recovery: Small initialization, noisy measurements, and over-parameterization. arXiv preprint arXiv:2202.08788, 2022.