mlsanityData to 14 Oct 2026

Signal Recovery on Graphs: Variation Minimization

arXiv 1411.7414 ↗First posted 26 Nov 2014cs.SI cs.LG stat.MLcited by 26

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Abstract (arXiv)

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a corresponding optimization problem. We provide a general solution by using the alternating direction methods of multipliers. We next show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery, and provide corresponding specific solutions and theoretical analysis. Finally, we validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system, and expert opinion combination of online blog classification.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Nov 2014.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 4; 2024: 6; 2025: 5; 2026: 1.

26 papers.

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  1. 2021Graph Signal Restoration Using Nested Deep Algorithm Unrollingcited by 13
  2. 2021Signal processing on simplicial complexescited by 12
  3. 2024Gegenbauer Graph Neural Networks for Time-varying Signal Reconstructioncited by 12
  4. 2022Robust Graph Representation Learning for Local Corruption Recoverycited by 6
  5. 2022Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignmentcited by 4
  6. 2023Joint Signal Recovery and Graph Learning from Incomplete Time-Seriescited by 3
  7. 2024Multilinear Kernel Regression and Imputation via Manifold Learningcited by 3
  8. 2024Robust Offline Active Learning on Graphscited by 3
  9. 2024Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learningcited by 3
  10. 2021Graphmax for Text Generationcited by 2
  11. 2023Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizercited by 2
  12. 2025Heterogeneous Graph Structure Learning through the Lens of Data-generating Processescited by 2
14 more
  1. 2025Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approachescited by 2
  2. 2022When Do We Need Graph Neural Networks for Node Classification?cited by 1
  3. 2022Learning Optimal Graph Filters for Clustering of Attributed Graphscited by 1
  4. 2023Distributional Signals for Node Classification in Graph Neural Networkscited by 1
  5. 2023Inhomogeneous graph trend filtering via a l2,0 cardinality penaltycited by 1
  6. 2021DPC: Unsupervised Deep Point Correspondence via Cross and Self Constructioncited by 0
  7. 2022Stratified Graph Spectracited by 0
  8. 2022Unsupervised Graph Spectral Feature Denoising for Crop Yield Predictioncited by 0
  9. 2024Joint Data Inpainting and Graph Learning via Unrolled Neural Networkscited by 0
  10. 2024A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networkscited by 0
  11. 2025Lightweight and Interpretable Transformer via Mixed Graph Algorithm Unrolling for Traffic Forecastcited by 0
  12. 2025Efficient Learning of Balanced Signed Graphs via Sparse Linear Programmingcited by 0
  13. 2025Robust Spatiotemporally Contiguous Anomaly Detection Using Tensor Decompositioncited by 0
  14. 2026Filter Learning for Subgraphs: Algebras and Performance Risk Boundscited by 0