Simplified PCNet with Robustness

Graph Neural Networks (GNNs) have garnered significant attention for their success in learning the representation of homophilic or heterophilic graphs. However, they cannot generalize well to real-world graphs with different levels of homophily. In response, the Possion-Charlier Network (PCNet) \cite{li2024pc}, the previous work, allows graph representation to be learned from heterophily to homophily. Although PCNet alleviates the heterophily issue, there remain some challenges in further improving the efficacy and efficiency. In this paper, we simplify PCNet and enhance its robustness. We first extend the filter order to continuous values and reduce its parameters. Two variants with adaptive neighborhood sizes are implemented. Theoretical analysis shows our model's robustness to graph structure perturbations or adversarial attacks. We validate our approach through semi-supervised learning tasks on various datasets representing both homophilic and heterophilic graphs.

Provable Filter for Real-world Graph Clustering

Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods.

Robust Graph Structure Learning under Heterophily

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.

CDC: A Simple Framework for Complex Data Clustering

In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid knowledge from data, is extremely useful in practice. However, existing methods are independently developed to handle one particular challenge at the expense of the others. In this work, we propose a simple but effective framework for complex data clustering (CDC) that can efficiently process different types of data with linear complexity. We first utilize graph filtering to fuse geometry structure and attribute information. We then reduce the complexity with high-quality anchors that are adaptively learned via a novel similarity-preserving regularizer. We illustrate the cluster-ability of our proposed method theoretically and experimentally. In particular, we deploy CDC to graph data of size 111M.