Tensor factorization for low-rank tensor completion
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 …
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
Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …
optimization procedures for solving statistical estimation problems. For various problems like …
Low-rank matrix completion: A contemporary survey
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 …
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
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 …
processing, machine learning and imaging science. A popular approach in practice is to …
Guarantees of Riemannian optimization for low rank matrix recovery
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 …
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
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 …
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
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 …
objective function to be minimized is non-convex and even non-smooth, which makes the …
Accelerated alternating projections for robust principal component analysis
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 …
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
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 …
perturbed by complex noises. Traditional matrix completion algorithms are always based on …
A Riemannian rank-adaptive method for low-rank matrix completion
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 …
fixed-rank manifold. However, a drawback of the known approaches is that the rank …