Pointspectrum：图表示学习的等方差满足拉普拉斯滤波
Pointspectrum: Equivariance Meets Laplacian Filtering for Graph Representation Learning
摘要：
图表示学习（GRL）已成为现代图数据采掘和学习任务的基本要求。GRL的目标是捕获图的结构信息，并将其与节点和边属性相结合，以计算低维表示。虽然图神经网络（GNN）已被用于最先进的GRL架构中，但当需要堆叠许多GNN层时，它们已被证明存在过度平滑的问题。在不同的GRL方法中，基于图滤波的谱方法已经出现了解决平滑问题的方法;然而，到目前为止，它们采用传统的神经网络，无法有效地利用图数据的结构。出于这一动机，我们提出了PointSpectrum，一种谱方法，它采用了一组等变网络来解释图的结构。PointSpectrum增强了谱方法的效率和表现力，同时优于最先进的GRL方法或与之竞争。总的来说，PointSpectrum通过使用图滤波器来解决平滑问题，并通过集合等方差来捕获图的结构，位于GNN和谱方法的交叉点上。我们的研究结果是有希望的频谱方法和GRL的这种架构转变的好处和适用性。
英文摘要：
Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. GRL aims to capture the graph's structural information and exploit it in combination with node and edge attributes to compute low-dimensional representations. While Graph Neural Networks (GNNs) have been used in state-of-the-art GRL architectures, they have been shown to suffer from over smoothing when many GNN layers need to be stacked. In a different GRL approach, spectral methods based on graph filtering have emerged addressing over smoothing; however, up to now, they employ traditional neural networks that cannot efficiently exploit the structure of graph data. Motivated by this, we propose PointSpectrum, a spectral method that incorporates a set equivariant network to account for a graph's structure. PointSpectrum enhances the efficiency and expressiveness of spectral methods, while it outperforms or competes with state-of-the-art GRL methods. Overall, PointSpectrum addresses over smoothing by employing a graph filter and captures a graph's structure through set equivariance, lying on the intersection of GNNs and spectral methods. Our findings are promising for the benefits and applicability of this architectural shift for spectral methods and GRL.
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。
