Revisiting Heterophily in Graph Convolution Networks by Learning Representations Across Topological and Feature Spaces

Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the homophily assumption and have shown limited performance on the heterophilous graphs. While several methods have been developed with new architectures to address heterophily, we argue that by learning graph representations across two spaces i.e., topology and feature space GCNs can address heterophily. In this work, we experimentally demonstrate the performance of the proposed GCN framework over semi-supervised node classification task on both homophilous and heterophilous graph benchmarks by learning and combining representations across the topological and the feature spaces.Comment: Under Review Project Page: https://sites.google.com/iitgn.ac.in/hetgcn/hom

GPNet: Simplifying Graph Neural Networks via Multi-channel Geometric Polynomials

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing, over-fitting, difficult to train, and strong homophily assumption. For example, Simple Graph Convolution (SGC) is known to suffer from the first and fourth limitations. To tackle these limitations, we identify a set of key designs including (D1) dilated convolution, (D2) multi-channel learning, (D3) self-attention score, and (D4) sign factor to boost learning from different types (i.e. homophily and heterophily) and scales (i.e. small, medium, and large) of networks, and combine them into a graph neural network, GPNet, a simple and efficient one-layer model. We theoretically analyze the model and show that it can approximate various graph filters by adjusting the self-attention score and sign factor. Experiments show that GPNet consistently outperforms baselines in terms of average rank, average accuracy, complexity, and parameters on semi-supervised and full-supervised tasks, and achieves competitive performance compared to state-of-the-art model with inductive learning task.Comment: 15 pages, 15 figure

Hetero2^2Net: Heterophily-aware Representation Learning on Heterogenerous Graphs

Real-world graphs are typically complex, exhibiting heterogeneity in the global structure, as well as strong heterophily within local neighborhoods. While a growing body of literature has revealed the limitations of common graph neural networks (GNNs) in handling homogeneous graphs with heterophily, little work has been conducted on investigating the heterophily properties in the context of heterogeneous graphs. To bridge this research gap, we identify the heterophily in heterogeneous graphs using metapaths and propose two practical metrics to quantitatively describe the levels of heterophily. Through in-depth investigations on several real-world heterogeneous graphs exhibiting varying levels of heterophily, we have observed that heterogeneous graph neural networks (HGNNs), which inherit many mechanisms from GNNs designed for homogeneous graphs, fail to generalize to heterogeneous graphs with heterophily or low level of homophily. To address the challenge, we present Hetero$^2$Net, a heterophily-aware HGNN that incorporates both masked metapath prediction and masked label prediction tasks to effectively and flexibly handle both homophilic and heterophilic heterogeneous graphs. We evaluate the performance of Hetero$^2$Net on five real-world heterogeneous graph benchmarks with varying levels of heterophily. The results demonstrate that Hetero$^2$Net outperforms strong baselines in the semi-supervised node classification task, providing valuable insights into effectively handling more complex heterogeneous graphs.Comment: Preprin

From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigm

Existing Graph Neural Networks (GNNs) follow the message-passing mechanism that conducts information interaction among nodes iteratively. While considerable progress has been made, such node interaction paradigms still have the following limitation. First, the scalability limitation precludes the wide application of GNNs in large-scale industrial settings since the node interaction among rapidly expanding neighbors incurs high computation and memory costs. Second, the over-smoothing problem restricts the discrimination ability of nodes, i.e., node representations of different classes will converge to indistinguishable after repeated node interactions. In this work, we propose a novel hop interaction paradigm to address these limitations simultaneously. The core idea of hop interaction is to convert the target of message-passing from nodes into multi-hop features inside each node. Specifically, it first pre-computed multi-hop features of nodes to reduce computation costs during training and inference. Then, it conducts a non-linear interaction among multi-hop features to enhance the discrimination of nodes. We design a simple yet effective HopGNN framework that can easily utilize existing GNNs to achieve hop interaction. Furthermore, we propose a multi-task learning strategy with a self-supervised learning objective to enhance HopGNN. We conduct extensive experiments on 12 benchmark datasets in a wide range of domains, scales, and smoothness of graphs. Experimental results show that our methods achieve superior performance while maintaining high scalability and efficiency

Diffusion-Jump GNNs: Homophiliation via Learnable Metric Filters

High-order Graph Neural Networks (HO-GNNs) have been developed to infer consistent latent spaces in the heterophilic regime, where the label distribution is not correlated with the graph structure. However, most of the existing HO-GNNs are hop-based, i.e., they rely on the powers of the transition matrix. As a result, these architectures are not fully reactive to the classification loss and the achieved structural filters have static supports. In other words, neither the filters' supports nor their coefficients can be learned with these networks. They are confined, instead, to learn combinations of filters. To address the above concerns, we propose Diffusion-jump GNNs a method relying on asymptotic diffusion distances that operates on jumps. A diffusion-pump generates pairwise distances whose projections determine both the support and coefficients of each structural filter. These filters are called jumps because they explore a wide range of scales in order to find bonds between scattered nodes with the same label. Actually, the full process is controlled by the classification loss. Both the jumps and the diffusion distances react to classification errors (i.e. they are learnable). Homophiliation, i.e., the process of learning piecewise smooth latent spaces in the heterophilic regime, is formulated as a Dirichlet problem: the known labels determine the border nodes and the diffusion-pump ensures a minimal deviation of the semi-supervised grouping from a canonical unsupervised grouping. This triggers the update of both the diffusion distances and, consequently, the jumps in order to minimize the classification error. The Dirichlet formulation has several advantages. It leads to the definition of structural heterophily, a novel measure beyond edge heterophily. It also allows us to investigate links with (learnable) diffusion distances, absorbing random walks and stochastic diffusion

On the Exploitation of Heterophily in Graph-Based Multimodal Remote Sensing Data Analysis

The field of Earth observation is dealing with increasingly large, multimodal data sets. An important processing step consists of providing these data sets with labels. However, standard label propagation algorithms cannot be applied to multimodal remote sensing data for two reasons. First, multimodal data is heterogeneous while classic label propagation algorithms assume a homogeneous network. Second, real-world data can show both homophily ('birds of a feather flock together') and heterophily ('opposites attract') during propagation, while standard algorithms only consider homophily. Both shortcomings are addressed in this work and the result is a graph-based label propagation algorithm for multimodal data that includes homophily and/or heterophily. Furthermore, the method is also able to transfer information between uni- and multimodal data. Experiments on the remote sensing data set of Houston, which contains a LiDAR and a hyperspectral image, show that our approach ties state-of-the-art methods for classification with an OA of 91.4%, while being more flexible and not constrained to a specific data set or a specific combination of modalities.</p