Data Imputation from the Perspective of Graph Dirichlet Energy
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Abstract (arXiv)
Data imputation is a crucial task due to the widespread occurrence of missing data. Many methods adopt a two-step approach: initially crafting a preliminary imputation (the "draft") and then refining it to produce the final missing data imputation result, commonly referred to as "draft-then-refine". In our study, we examine this prevalent strategy through the lens of graph Dirichlet energy. We observe that a basic "draft" imputation tends to decrease the Dirichlet energy. Therefore, a subsequent "refine" step is necessary to restore the overall energy balance. Existing refinement techniques, such as the Graph Convolutional Network (GCN), often result in further energy reduction. To address this, we introduce a new framework, the Graph Laplacian Pyramid Network (GLPN). GLPN incorporates a U-shaped autoencoder and residual networks to capture both global and local details effectively. Through extensive experiments on multiple real-world datasets, GLPN consistently outperforms state-of-the-art methods across three different missing data mechanisms. The code is available at https://github.com/liguanlue/GLPN.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 30 of its 62 references that are in the map. First posted on arXiv 10 Apr 2023.
Builds on
30 of 62 references.
References · 30
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2019Simplifying Graph Convolutional Networkscited by 1,470
- 2016Variational Graph Auto-Encoderscited by 1,373
- 2019Graph U-Netscited by 489
- 2017Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolutioncited by 452
- 2019Self-Attention Graph Poolingcited by 421
- 2018GAIN: Missing Data Imputation using Generative Adversarial Netscited by 349
- 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
- 2020A Note on Over-Smoothing for Graph Neural Networkscited by 245
- 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
- 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 145
- 2020Handling Missing Data with Graph Representation Learningcited by 132
18 more
- 2014Matrix Completion and Low-Rank SVD via Fast Alternating Least Squarescited by 104
- 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
- 2019Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learningcited by 94
- 2020Inductive Graph Neural Networks for Spatiotemporal Krigingcited by 90
- 2020Tackling Over-Smoothing for General Graph Convolutional Networkscited by 66
- 2018Deep Bidirectional and Unidirectional LSTM Recurrent Neural Network for Network-wide Traffic Speed Predictioncited by 61
- 2021What's a good imputation to predict with missing values?cited by 61
- 2019Densely Residual Laplacian Super-Resolutioncited by 57
- 2020Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networkscited by 57
- 2019Semi-Supervised Graph Classification: A Hierarchical Graph Perspectivecited by 55
- 2021MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanismscited by 50
- 2020Graph Convolutional Networks for Graphs Containing Missing Featurescited by 46
- 2016Faster Kernels for Graphs with Continuous Attributes via Hashingcited by 31
- 2021Deconvolutional Networks on Graph Datacited by 16
- 2016Using Fuzzy Logic to Leverage HTML Markup for Web Page Representationcited by 15
- 2022Handling Missing Data via Max-Entropy Regularized Graph Autoencodercited by 12
- 2014Multiple imputation for continuous variables using a Bayesian principal component analysiscited by 11
- 2022Differentiable and Scalable Generative Adversarial Models for Data Imputationcited by 5
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