MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing

TL;DR

MixHop introduces a novel graph neural network architecture that learns complex neighborhood relationships through repeated feature mixing at various distances, outperforming existing methods without added complexity.

Contribution

The paper presents MixHop, a new GNN model capable of learning higher-order neighborhood mixing relationships, including difference operators, with no extra computational cost.

Findings

MixHop outperforms baseline models on challenging datasets.

Sparsity regularization enables visualization of neighborhood prioritization.

Neighborhood mixing patterns vary across datasets.

Abstract

Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.