Tao Qian

Qian Tao, Zhen Wang, Wenyuan Yu et al.

In recent years, a plethora of spectral graph neural networks (GNN) methods have utilized polynomial basis with learnable coefficients to achieve top-tier performances on many node-level tasks. Although various kinds of polynomial bases have been explored, each such method adopts a fixed polynomial basis which might not be the optimal choice for the given graph. Besides, we identify the so-called over-passing issue of these methods and show that it is somewhat rooted in their less-principled regularization strategy and unnormalized basis. In this paper, we make the first attempts to address these two issues. Leveraging Jacobi polynomials, we design a novel spectral GNN, LON-GNN, with Learnable OrthoNormal bases and prove that regularizing coefficients becomes equivalent to regularizing the norm of learned filter function now. We conduct extensive experiments on diverse graph datasets to evaluate the fitting and generalization capability of LON-GNN, where the results imply its superiority.

Jianpeng Liao, Jun Yan, Qian Tao

Graph-based semi-supervised node classification has been shown to become a state-of-the-art approach in many applications with high research value and significance. Most existing methods are only based on the original intrinsic or artificially established graph structure which may not accurately reflect the "true" correlation among data and are not optimal for semi-supervised node classification in the downstream graph neural networks. Besides, while existing graph-based methods mostly utilize the explicit graph structure, some implicit information, for example, the density information, can also provide latent information that can be further exploited. To address these limitations, this paper proposes the Dual Hypergraph Neural Network (DualHGNN), a new dual connection model integrating both hypergraph structure learning and hypergraph representation learning simultaneously in a unified architecture. The DualHGNN first leverages a multi-view hypergraph learning network to explore the optimal hypergraph structure from multiple views, constrained by a consistency loss proposed to improve its generalization. Then, DualHGNN employs a density-aware hypergraph attention network to explore the high-order semantic correlation among data points based on the density-aware attention mechanism. Extensive experiments are conducted in various benchmark datasets, and the results demonstrate the effectiveness of the proposed approach.

Jianpeng Liao, Qian Tao, Jun Yan

Graph-based semi-supervised learning, which can exploit the connectivity relationship between labeled and unlabeled data, has been shown to outperform the state-of-the-art in many artificial intelligence applications. One of the most challenging problems for graph-based semi-supervised node classification is how to use the implicit information among various data to improve the performance of classifying. Traditional studies on graph-based semi-supervised learning have focused on the pairwise connections among data. However, the data correlation in real applications could be beyond pairwise and more complicated. The density information has been demonstrated to be an important clue, but it is rarely explored in depth among existing graph-based semi-supervised node classification methods. To develop a flexible and effective model for graph-based semi-supervised node classification, we propose a novel Density-Aware Hyper-Graph Neural Networks (DA-HGNN). In our proposed approach, hyper-graph is provided to explore the high-order semantic correlation among data, and a density-aware hyper-graph attention network is presented to explore the high-order connection relationship. Extensive experiments are conducted in various benchmark datasets, and the results demonstrate the effectiveness of the proposed approach.