mlsanityData to 7 Oct 2026

Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent

arXiv 2406.07409 ↗First posted 11 Jun 2024stat.ML cs.IT cs.LGcited by 3

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Abstract (arXiv)

This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel Structured Newton-Like Descent (HSNLD), to tackle the robust Hankel recovery problem. HSNLD is highly efficient with linear convergence, and its convergence rate is independent of the condition number of the underlying Hankel matrix. The recovery guarantee has been established under some mild conditions. Numerical experiments on both synthetic and real datasets show the superior performance of HSNLD against state-of-the-art algorithms.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 20 of its 52 references that are in the map. First posted on arXiv 11 Jun 2024.

Builds on

20 of 52 references.

References · 20

  1. 2020Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descentcited by 70
  2. 2014Non-convex Robust PCAcited by 41
  3. 2016Fast Algorithms for Robust PCA via Gradient Descentcited by 39
  4. 2021Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detectioncited by 34
  5. 2017Accelerated Alternating Projections for Robust Principal Component Analysiscited by 25
  6. 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
  7. 2016Guarantees of Riemannian Optimization for Low Rank Matrix Completioncited by 19
  8. 2022Laplacian Convolutional Representation for Traffic Time Series Imputationcited by 18
  9. 2020Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimationcited by 16
  10. 2013Robust Spectral Compressed Sensing via Structured Matrix Completioncited by 13
  11. 2016Nearly-optimal Robust Matrix Completioncited by 13
  12. 2017Robust PCA by Manifold Optimizationcited by 13
8 more
  1. 2022Matrix Completion with Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Samplingcited by 12
  2. 2019Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learningcited by 11
  3. 2022Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completioncited by 11
  4. 2023Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptioncited by 11
  5. 2022Riemannian CUR Decompositions for Robust Principal Component Analysiscited by 7
  6. 2018Structured low-rank matrix completion for forecasting in time series analysiscited by 6
  7. 2017Spectral Compressed Sensing via Projected Gradient Descentcited by 5
  8. 2024On the Robustness of Cross-Concentrated Sampling for Matrix Completioncited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 1.

3 papers.

  1. 2024Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recoverycited by 4
  2. 2024Structured Sampling for Robust Euclidean Distance Geometrycited by 2
  3. 2026Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Samplingcited by 0