# Quadratic GCN for Graph Classification

arXiv: https://arxiv.org/abs/2104.06750 · HTML: https://mlsanity.com/paper/2104.06750/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Fast Interactive Object Annotation with Curve-GCN](https://mlsanity.com/paper/1903.06874/) (2019)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [Contrastive Self-supervised Learning for Graph Classification](https://mlsanity.com/paper/2009.05923/) (2020)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Edge Contraction Pooling for Graph Neural Networks](https://mlsanity.com/paper/1905.10990/) (2019)
- [Universal Graph Transformer Self-Attention Networks](https://mlsanity.com/paper/1909.11855/) (2019)
- [GCN-GAN: A Non-linear Temporal Link Prediction Model for Weighted Dynamic Networks](https://mlsanity.com/paper/1901.09165/) (2019)
- [Optimization of Graph Neural Networks with Natural Gradient Descent](https://mlsanity.com/paper/2008.09624/) (2020)
- [On Multi-Relational Link Prediction with Bilinear Models](https://mlsanity.com/paper/1709.04808/) (2017)
- [Improving Attention Mechanism in Graph Neural Networks via Cardinality Preservation](https://mlsanity.com/paper/1907.02204/) (2019)
- [Clique pooling for graph classification](https://mlsanity.com/paper/1904.00374/) (2019)
- [Graph Star Net for Generalized Multi-Task Learning](https://mlsanity.com/paper/1906.12330/) (2019)
- [DAGCN: Dual Attention Graph Convolutional Networks](https://mlsanity.com/paper/1904.02278/) (2019)
- [When Work Matters: Transforming Classical Network Structures to Graph CNN](https://mlsanity.com/paper/1807.02653/) (2018)
- [Regional based query in graph active learning](https://mlsanity.com/paper/1906.08541/) (2019)
- [Topological based classification of paper domains using graph convolutional networks](https://mlsanity.com/paper/1904.07787/) (2019)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have been extensively used to classify vertices in graphs and have been shown to outperform other vertex classification methods. GCNs have been extended to graph classification tasks (GCT). In GCT, graphs with different numbers of edges and vertices belong to different classes, and one attempts to predict the graph class. GCN based GCT have mostly used pooling and attention-based models. The accuracy of existing GCT methods is still limited. We here propose a novel solution combining GCN, methods from knowledge graphs, and a new self-regularized activation function to significantly improve the accuracy of the GCN based GCT. We present quadratic GCN (QGCN) - A GCN formalism with a quadratic layer. Such a layer produces an output with fixed dimensions, independent of the graph vertex number. We applied this method to a wide range of graph classification problems, and show that when using a self regularized activation function, QGCN outperforms the state of the art methods for all graph classification tasks tested with or without external input on each graph. The code for QGCN is available at: https://github.com/Unknown-Data/QGCN .