# Deconvolutional Networks on Graph Data

arXiv: https://arxiv.org/abs/2110.15528 · HTML: https://mlsanity.com/paper/2110.15528/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 58 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Symmetric Graph Convolutional Autoencoder for Unsupervised Graph Representation Learning](https://mlsanity.com/paper/1908.02441/) (2019)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding](https://mlsanity.com/paper/1910.02370/) (2019)
- [Predicting Path Failure In Time-Evolving Graphs](https://mlsanity.com/paper/1905.03994/) (2019)
- [Graph Convolutional Networks for Graphs Containing Missing Features](https://mlsanity.com/paper/2007.04583/) (2020)
- [Dirichlet Graph Variational Autoencoder](https://mlsanity.com/paper/2010.04408/) (2020)
- [Deep Graph Generators: A Survey](https://mlsanity.com/paper/2012.15544/) (2020)
- [Enhancing Geometric Deep Learning via Graph Filter Deconvolution](https://mlsanity.com/paper/1810.00661/) (2018)

## Built on by (most cited first, 16 of 16)

- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport](https://mlsanity.com/paper/2301.12721/) (2023)
- [Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning](https://mlsanity.com/paper/2206.12933/) (2022)
- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [Deep Insights into Noisy Pseudo Labeling on Graph Data](https://mlsanity.com/paper/2310.01634/) (2023)
- [Learning Graph Structure from Convolutional Mixtures](https://mlsanity.com/paper/2205.09575/) (2022)
- [A Contrastive Variational Graph Auto-Encoder for Node Clustering](https://mlsanity.com/paper/2312.16830/) (2023)
- [Sampling-guided Heterogeneous Graph Neural Network with Temporal Smoothing for Scalable Longitudinal Data Imputation](https://mlsanity.com/paper/2411.04899/) (2024)
- [Data Imputation from the Perspective of Graph Dirichlet Energy](https://mlsanity.com/paper/2304.04474/) (2023)
- [GRASPED: Graph Anomaly Detection using Autoencoder with Spectral Encoder and Decoder (Full Version)](https://mlsanity.com/paper/2508.15633/) (2025)
- [Graph-based Neural Modules to Inspect Attention-based Architectures: A Position Paper](https://mlsanity.com/paper/2210.07117/) (2022)
- [Decision Support System for Chronic Diseases Based on Drug-Drug Interactions](https://mlsanity.com/paper/2303.02405/) (2023)
- [A Graph Encoder-Decoder Network for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2308.07774/) (2023)
- [Enhancing Missing Data Imputation through Combined Bipartite Graph and Complete Directed Graph](https://mlsanity.com/paper/2411.04907/) (2024)

## Abstract (arXiv)

In this paper, we consider an inverse problem in graph learning domain -- ``given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional Network (GDN) and motivate the design of GDN via a combination of inverse filters in spectral domain and de-noising layers in wavelet domain, as the inverse operation results in a high frequency amplifier and may amplify the noise. We demonstrate the effectiveness of the proposed method on several tasks including graph feature imputation and graph structure generation.