BIGCN: A BI-DIRECTIONAL LOW-PASS FILTERING GRAPH NEURAL NETWORK

Abstract

Graph convolutional networks have achieved great success on graph-structured data. Many graph convolutional networks can be regarded as low-pass filters for graph signals. In this paper, we propose a new model, BiGCN, which represents a graph neural network as a bi-directional low-pass filter. Specifically, we not only consider the original graph structure information but also the latent correlation between features, thus BiGCN can filter the signals along with both the original graph and a latent feature-connection graph. Our model outperforms previous graph neural networks in the tasks of node classification and link prediction on most of the benchmark datasets, especially when we add noise to the node features.

1. INTRODUCTION

Graphs are important research objects in the field of machine learning as they are good carriers for structural data such as social networks and citation networks. Recently, graph neural networks (GNNs) received extensive attention due to their great performances in graph representation learning. A graph neural network takes node features and graph structure (e.g. adjacency matrix) as input, and embeds the graph into a lower-dimensional space. With the success of GNNs (Kipf & Welling, 2017; Veličković et al., 2017; Hamilton et al., 2017; Chen et al., 2018) in various domains, more and more efforts are focused on the reasons why GNNs are so powerful (Xu et al., 2019) . Li et al (Li et al., 2018) re-examined graph convolutional networks (GCNs) and connected it with Laplacian smoothing. NT and Maehara et al (NT & Maehara, 2019) revisited GCNs in terms of graph signal processing and explained that many graph convolutions can be considered as low-pass filters (e.g. (Kipf & Welling, 2017; Wu et al., 2019) ) which can capture low-frequency components and remove some feature noise by making connective nodes more similar. In fact, these findings are not new. Since its first appearance in Bruna et al. ( 2014), spectral GCNs have been closely related to graph signal processing and denoising. The spectral graph convolutional operation is derived from Graph Fourier Transform, and the filter can be formulated as a function with respect to the graph Laplacian matrix, denoted as g(L). In general spectral GCNs, the forward function is: H (l+1) = σ(g(L)H (l) ). Kipf and Welling (Kipf & Welling, 2017) approximated g(L) using first-order Chebyshev polynomials, which can be simplified as multiplying the augmented normalized adjacency matrix to the feature matrix. Despite the efficiency, this first-order graph filter is found sensitive to changes in the graph signals and the underlying graph structure (Isufi et al., 2016; Bianchi et al., 2019) . For instance, on isolated nodes or small single components of the graph, their denoising effect is quite limited due to the lack of reliable neighbors. The potential incorrect structure information will also constrain the power of GCNs and cause more negative impacts with deeper layers. As noisy/incorrect information is inevitable in real-world graph data, more powerful and robust GCNs are needed to solve this problem. In this work, we propose a new graph neural network with more powerful denoising effects from the perspective of graph signal processing and higher fault tolerance to the graph structure. Different from image data, graph data usually has high dimensional features, and there may be some latent connection/correlation between each dimensions. Noting this, we take this connection information into account to offset the efforts of certain unreliable structure information, and remove extra noise by applying a smoothness assumption on such a "feature graph". Derived from the additional Laplacian smoothing regularization in this feature graph, we obtain a novel variant of 1

