Tensor factorization for low-rank tensor completion

P Zhou, C Lu, Z Lin, C Zhang - IEEE Transactions on Image …, 2017 - ieeexplore.ieee.org
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor
completion problem, which has achieved state-of-the-art performance on image and video …

Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion

C Ma, K Wang, Y Chi, Y Chen - International Conference on …, 2018 - proceedings.mlr.press
Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

Low-rank matrix completion: A contemporary survey

LT Nguyen, J Kim, B Shim - IEEE Access, 2019 - ieeexplore.ieee.org
As a paradigm to recover unknown entries of a matrix from partial observations, low-rank
matrix completion (LRMC) has generated a great deal of interest. Over the years, there have …

Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent

T Tong, C Ma, Y Chi - Journal of Machine Learning Research, 2021 - jmlr.org
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal
processing, machine learning and imaging science. A popular approach in practice is to …

Guarantees of Riemannian optimization for low rank matrix recovery

K Wei, JF Cai, TF Chan, S Leung - SIAM Journal on Matrix Analysis and …, 2016 - SIAM
We establish theoretical recovery guarantees of a family of Riemannian optimization
algorithms for low rank matrix recovery, which is about recovering an m*n rank r matrix from …

Low-rank matrix recovery with scaled subgradient methods: Fast and robust convergence without the condition number

T Tong, C Ma, Y Chi - IEEE Transactions on Signal Processing, 2021 - ieeexplore.ieee.org
Many problems in data science can be treated as estimating a low-rank matrix from highly
incomplete, sometimes even corrupted, observations. One popular approach is to resort to …

Preconditioning matters: Fast global convergence of non-convex matrix factorization via scaled gradient descent

X Jia, H Wang, J Peng, X Feng… - Advances in Neural …, 2024 - proceedings.neurips.cc
Low-rank matrix factorization (LRMF) is a canonical problem in non-convex optimization, the
objective function to be minimized is non-convex and even non-smooth, which makes the …

Accelerated alternating projections for robust principal component analysis

HQ Cai, JF Cai, K Wei - Journal of Machine Learning Research, 2019 - jmlr.org
We study robust PCA for the fully observed setting, which is about separating a low rank
matrix L and a sparse matrix S from their sum D= L+ S. In this paper, a new algorithm …

Robust matrix completion via maximum correntropy criterion and half-quadratic optimization

Y He, F Wang, Y Li, J Qin… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries
perturbed by complex noises. Traditional matrix completion algorithms are always based on …

A Riemannian rank-adaptive method for low-rank matrix completion

B Gao, PA Absil - Computational Optimization and Applications, 2022 - Springer
The low-rank matrix completion problem can be solved by Riemannian optimization on a
fixed-rank manifold. However, a drawback of the known approaches is that the rank …