# Effective Eigendecomposition based Graph Adaptation for Heterophilic Networks

arXiv: https://arxiv.org/abs/2107.13312 · HTML: https://mlsanity.com/paper/2107.13312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [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)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification](https://mlsanity.com/paper/1802.08888/) (2018)

## Abstract (arXiv)

Graph Neural Networks (GNNs) exhibit excellent performance when graphs have strong homophily property, i.e. connected nodes have the same labels. However, they perform poorly on heterophilic graphs. Several approaches address the issue of heterophily by proposing models that adapt the graph by optimizing task-specific loss function using labelled data. These adaptations are made either via attention or by attenuating or enhancing various low-frequency/high-frequency signals, as needed for the task at hand. More recent approaches adapt the eigenvalues of the graph. One important interpretation of this adaptation is that these models select/weigh the eigenvectors of the graph. Based on this interpretation, we present an eigendecomposition based approach and propose EigenNetwork models that improve the performance of GNNs on heterophilic graphs. Performance improvement is achieved by learning flexible graph adaptation functions that modulate the eigenvalues of the graph. Regularization of these functions via parameter sharing helps to improve the performance even more. Our approach achieves up to 11% improvement in performance over the state-of-the-art methods on heterophilic graphs.