# Robust Graph Learning from Noisy Data

arXiv: https://arxiv.org/abs/1812.06673 · HTML: https://mlsanity.com/paper/1812.06673/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2018.

## Built on by (most cited first, 30 of 34)

- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Pseudo-supervised Deep Subspace Clustering](https://mlsanity.com/paper/2104.03531/) (2021)
- [Self-Supervised Temporal Graph learning with Temporal and Structural Intensity Alignment](https://mlsanity.com/paper/2302.07491/) (2023)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [Semantic Enhanced Text-to-SQL Parsing via Iteratively Learning Schema Linking Graph](https://mlsanity.com/paper/2208.03903/) (2022)
- [A Survey of Graph-based Deep Learning for Anomaly Detection in Distributed Systems](https://mlsanity.com/paper/2206.04149/) (2022)
- [Self-Supervised Graph Structure Refinement for Graph Neural Networks](https://mlsanity.com/paper/2211.06545/) (2022)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [Self-supervised Consensus Representation Learning for Attributed Graph](https://mlsanity.com/paper/2108.04822/) (2021)
- [CDC: A Simple Framework for Complex Data Clustering](https://mlsanity.com/paper/2403.03670/) (2024)
- [Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering](https://mlsanity.com/paper/2106.09874/) (2021)
- [Multiple Kernel Clustering with Dual Noise Minimization](https://mlsanity.com/paper/2207.06041/) (2022)
- [RobGC: Towards Robust Graph Condensation](https://mlsanity.com/paper/2406.13200/) (2024)
- [Deep Contrastive Graph Learning with Clustering-Oriented Guidance](https://mlsanity.com/paper/2402.16012/) (2024)
- [Sparse Graph Learning Under Laplacian-Related Constraints](https://mlsanity.com/paper/2111.08161/) (2021)
- [Spacecraft Anomaly Detection with Attention Temporal Convolution Network](https://mlsanity.com/paper/2303.06879/) (2023)
- [Efficient Multi-View Graph Clustering with Local and Global Structure Preservation](https://mlsanity.com/paper/2309.00024/) (2023)
- [Smoothed Multi-View Subspace Clustering](https://mlsanity.com/paper/2106.09875/) (2021)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Towards Lightweight Graph Neural Network Search with Curriculum Graph Sparsification](https://mlsanity.com/paper/2406.16357/) (2024)
- [Self-paced Principal Component Analysis](https://mlsanity.com/paper/2106.13880/) (2021)
- [LyAm: Robust Non-Convex Optimization for Stable Learning in Noisy Environments](https://mlsanity.com/paper/2507.11262/) (2025)
- [Decentralized Learning of Tree-Structured Gaussian Graphical Models from Noisy Data](https://mlsanity.com/paper/2109.10642/) (2021)
- [Non-Linear Spectral Dimensionality Reduction Under Uncertainty](https://mlsanity.com/paper/2202.04678/) (2022)
- [Balanced Self-Paced Learning for AUC Maximization](https://mlsanity.com/paper/2207.03650/) (2022)
- [Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering](https://mlsanity.com/paper/2210.12638/) (2022)
- [Energy Guided smoothness to improve Robustness in Graph Classification](https://mlsanity.com/paper/2412.08419/) (2024)
- [TiGer: Self-Supervised Purification for Time-evolving Graphs](https://mlsanity.com/paper/2503.06990/) (2025)
- [RANA: Robust Active Learning for Noisy Network Alignment](https://mlsanity.com/paper/2507.22434/) (2025)

## Abstract (arXiv)

Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.