从谱小波到顶点传播：基于Taylor近似的图卷积网络
From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation
摘要：
图卷积网络（GCN）最近被用来提取具有一些标记数据和高维特征的数据集的底层结构。现有的GCN主要依赖于图小波核的一阶Chebyshev近似。这种通用的传播模型并不总是适合各种数据集及其特征。这项工作重温了图小波的基本原理，并探讨了在顶点域的信号传播近似的频谱小波核的效用。首先，我们推导出通过顶点传播表示图小波核的条件。接下来，我们提出了基于泰勒展开的GCN层的替代传播模型。我们进一步分析了TGCN的详细图形表示的选择。在引文网络、多媒体数据集和合成图上的实验表明，基于泰勒的GCN（TGCN）在节点分类问题上优于传统的GCN方法。
英文摘要：
Graph convolutional networks (GCN) have been recently utilized to extract the underlying structures of datasets with some labeled data and high-dimensional features. Existing GCNs mostly rely on a first-order Chebyshev approximation of graph wavelet-kernels. Such a generic propagation model does not always suit the various datasets and their features. This work revisits the fundamentals of graph wavelet and explores the utility of signal propagation in the vertex domain to approximate the spectral wavelet-kernels. We first derive the conditions for representing the graph wavelet-kernels via vertex propagation. We next propose alternative propagation models for GCN layers based on Taylor expansions. We further analyze the choices of detailed graph representations for TGCNs. Experiments on citation networks, multimedia datasets and synthetic graphs demonstrate the advantage of Taylor-based GCN (TGCN) in the node classification problems over the traditional GCN methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
