Robust Graph Structure Learning under Heterophily

TL;DR

This paper introduces a robust graph structure learning method designed to handle heterophilic data, improving graph quality for tasks like clustering and classification despite noise and sparsity.

Contribution

It proposes a novel approach combining high-pass filtering, adaptive norm-based graph learning, and a new regularizer to effectively learn from heterophilic graphs.

Findings

Improves graph quality in heterophilic settings

Enhances clustering and classification accuracy

Demonstrates robustness against noise and sparsity

Abstract

Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real data is inevitably noisy and sparse, which will lead to inferior results. Despite the remarkable success of recent graph representation learning methods, they inherently presume that the graph is homophilic, and largely overlook heterophily, where most connected nodes are from different classes. In this regard, we propose a novel robust graph structure learning method to achieve a high-quality graph from heterophilic data for downstream tasks. We first apply a high-pass filter to make each node more distinctive from its neighbors by encoding structure information into the node features. Then, we learn a robust graph with an adaptive norm characterizing different levels of noise. Afterwards, we propose a novel regularizer to further refine the graph structure. Clustering and semi-supervised classification experiments on heterophilic graphs verify the effectiveness of our method.