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# Low-Rank Matrix Completion Edit

7 papers with code · Methodology

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# Bounded Manifold Completion

19 Dec 2019

Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research.

# Efficiently escaping saddle points on manifolds

Specifically, for an arbitrary Riemannian manifold $\mathcal{M}$ of dimension $d$, a sufficiently smooth (possibly non-convex) objective function $f$, and under weak conditions on the retraction chosen to move on the manifold, with high probability, our version of PRGD produces a point with gradient smaller than $\epsilon$ and Hessian within $\sqrt{\epsilon}$ of being positive semidefinite in $O((\log{d})^4 / \epsilon^{2})$ gradient queries.

# Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery

Compared to the max norm and the factored formulation of the nuclear norm, factor group-sparse regularizers are more efficient, accurate, and robust to the initial guess of rank.

# Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning

27 Oct 2019

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.

# The Sparse Reverse of Principal Component Analysis for Fast Low-Rank Matrix Completion

4 Oct 2019

The proposed approach maintains smoothness across the matrix, produces accurate estimates of the missing data, converges iteratively, and it is computationally tractable with a controllable upper bound on the number of iterations until convergence.

# Low-rank matrix completion and denoising under Poisson noise

11 Jul 2019

This paper considers the problem of estimating a low-rank matrix from the observation of all, or a subset, of its entries in the presence of Poisson noise.

# A divide-and-conquer algorithm for binary matrix completion

9 Jul 2019

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors.

# Depth Restoration: A fast low-rank matrix completion via dual-graph regularization

5 Jul 2019

As a real scenes sensing approach, depth information obtains the widespread applications.

# Efficiently escaping saddle points on manifolds

Specifically, for an arbitrary Riemannian manifold $\mathcal{M}$ of dimension $d$, a sufficiently smooth (possibly non-convex) objective function $f$, and under weak conditions on the retraction chosen to move on the manifold, with high probability, our version of PRGD produces a point with gradient smaller than $\epsilon$ and Hessian within $\sqrt{\epsilon}$ of being positive semidefinite in $O((\log{d})^4 / \epsilon^{2})$ gradient queries.

# Guaranteed Matrix Completion Under Multiple Linear Transformations

Low-rank matrix completion (LRMC) is a classical model in both computer vision (CV) and machine learning, and has been successfully applied to various real applications.