# Graph Neural Networks with Feature and Structure Aware Random Walk

arXiv: https://arxiv.org/abs/2111.10102 · HTML: https://mlsanity.com/paper/2111.10102/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 49 references that are in the map.
- First posted on arXiv 19 Nov 2021.

## Builds on (most cited first, 27 of 27)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (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)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Adversarial Attacks on Graph Neural Networks via Meta Learning](https://mlsanity.com/paper/1902.08412/) (2019)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [New Benchmarks for Learning on Non-Homophilous Graphs](https://mlsanity.com/paper/2104.01404/) (2021)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have received increasing attention for representation learning in various machine learning tasks. However, most existing GNNs applying neighborhood aggregation usually perform poorly on the graph with heterophily where adjacent nodes belong to different classes. In this paper, we show that in typical heterphilous graphs, the edges may be directed, and whether to treat the edges as is or simply make them undirected greatly affects the performance of the GNN models. Furthermore, due to the limitation of heterophily, it is highly beneficial for the nodes to aggregate messages from similar nodes beyond local neighborhood.These motivate us to develop a model that adaptively learns the directionality of the graph, and exploits the underlying long-distance correlations between nodes. We first generalize the graph Laplacian to digraph based on the proposed Feature-Aware PageRank algorithm, which simultaneously considers the graph directionality and long-distance feature similarity between nodes. Then digraph Laplacian defines a graph propagation matrix that leads to a model called em DiglacianGCN. Based on this, we further leverage the node proximity measured by commute times between nodes, in order to preserve the nodes' long-distance correlation on the topology level. Extensive experiments on ten datasets with different levels of homophily demonstrate the effectiveness of our method over existing solutions in the task of node classification.