论文标题
图形池用于降低图形上信号和卷积运算符的维度
Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs
论文作者
论文摘要
在本文中，我们提出了一种依赖图形理论和密集图序列限制的图表上的卷积信息处理的合并方法。我们提出了三种方法，可以利用图形空间中[0，1] 2的分区上的图形和图信号的诱导图形表示。结果，我们得出了卷积运算符的低维表示，而信号的尺寸降低是通过简单的L2（[0，1]）功能的局部插值来实现的。我们证明，这些低维表示分别构成了图和图信号的收敛序列。提出的方法和理论确保我们提供的方法表明，还原的图和信号继承了原始数量的光谱结构特性。我们通过在依靠Graphon池的图形神经网络（GNN）上执行的一组数值实验来评估我们的方法。我们观察到，当层之间的降低比率较大时，Graphon合并的性能要比文献中提出的其他方法的表现明显好。我们还观察到，当使用Graphon合并时，通常我们的计算成本较低，计算成本较低。
In this paper we propose a pooling approach for convolutional information processing on graphs relying on the theory of graphons and limits of dense graph sequences. We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. As a result we derive low dimensional representations of the convolutional operators, while a dimensionality reduction of the signals is achieved by simple local interpolation of functions in L2([0, 1]). We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals, respectively. The methods proposed and the theoretical guarantees that we provide show that the reduced graphs and signals inherit spectral-structural properties of the original quantities. We evaluate our approach with a set of numerical experiments performed on graph neural networks (GNNs) that rely on graphon pooling. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large. We also observe that when graphon pooling is used we have, in general, less overfitting and lower computational cost.
