ArticleAdvances in neural information processing systems2019
Manifold Denoising by Nonlinear Robust Principal Component Analysis.
Article in Advances in neural information processing systems, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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Who cites it
17 citing papers in PubMed.
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- ORCH: many analyses, one merge-a deterministic multi-agent orchestrator for discrete-choice reasoning with EMA-guided routing.Frontiers in artificial intelligence · 2026Article
- Evaluating the real-world robustness of face-swap detection models under compression and noise.Frontiers in artificial intelligence · 2026Article
- Deep neural architectures for Kashmiri-English machine translation.Scientific reports · 2025Article
- Tempo oscillations in rhythmic human networks.Scientific reports · 2025Article
- Accurate prediction of virulence factors using pre-train protein language model and ensemble learning.BMC genomics · 2025Article
- BLOCK DIFFUSION: INTERPOLATING BETWEEN AU-TOREGRESSIVE AND DIFFUSION LANGUAGE MODELS.... International Conference on Learning Representations · 2025Article
- A Review of Embodied Grasping.Sensors (Basel, Switzerland) · 2025Review
- Curvature estimation techniques for advancing neurodegenerative disease analysis: a systematic review of machine learning and deep learning approaches.American journal of neurodegenerative disease · 2025Review
- Hazediff: A training-free diffusion-based image dehazing method with pixel-level feature injection.PloS one · 2025Article
- An improved U-net and attention mechanism-based model for sugar beet and weed segmentation.Frontiers in plant science · 2024Article
- Overcoming the Challenges in the Development and Implementation of Artificial Intelligence in Radiology: A Comprehensive Review of Solutions Beyond Supervised Learning.Korean journal of radiology · 2023Review
- An Innovative Approach for Removing Stripe Noise in Infrared Images.Sensors (Basel, Switzerland) · 2023Article
- High Dimensional Semiparametric Scale-Invariant Principal Component Analysis.IEEE transactions on pattern analysis and machine intelligence · 2014Article
- Sparse Covariance Matrix Estimation With Eigenvalue Constraints.Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America · 2014Article
Corrections and comments
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Authors and funding
6 authors.
Funding
Abstract
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.
Identifiers
34305366PMC8297813What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.