GRAPH NEURAL NETOWRK POOLING BY EDGE CUT

Abstract

Graph neural networks (GNNs) are very efficient at solving several tasks in graphs such as node classification or graph classification. They come from an adaptation of convolutional neural networks on images to graph structured data. These models are very effective at finding patterns in images that can discriminate images from each others. Another aspect leading to their success is their ability to uncover hierarchical structures. This comes from the pooling operation that produces different versions of the input image at different scales. The same way, we want to identify patterns at different scales in graphs in order to improve the classification accuracy. Compared to the case of images, it is not trivial to develop a pooling layer on graphs. This is mainly due to the fact that in graphs nodes are not ordered and have irregular neighborhoods. To aleviate this issue, we propose a pooling layer based on edge cuts in graphs. This pooling layer works by computing edge scores that correspond to the importance of edges in the process of information propagation of the GNN. Moreover, we define a regularization function that aims at producing edge scores that minimize the minCUT problem. Finally, through extensive experiments we show that this architecture can compete with state-ofthe-art methods.

1. INTRODUCTION

Convolution neural networks (LeCun et al., 1995) have been proven to be very efficient at learning meaningful patterns for many articificial intelligence tasks. They convey the ability to learn hierarchical informations in data with Euclidean grid-like structures such as images and textual data. Convolutional Neural Networks (CNNs) have rapidly become state-of-the-art methods in the fields of computer vision (Russakovsky et al., 2015) and natural language processing (Devlin et al., 2018) . However in many scientific fields, studied data have an underlying graph or manifold structure such as communication networks (whether social or technical) or knowledge graphs. Recently there have been many attempts to extend convolution to such non-Euclidean structured data (Hammond et al., 2011; Kipf & Welling, 2016; Defferrard et al., 2016) . In these new approaches, the authors propose to compute node embeddings in a semi-supervised fashion in order to perform node classification. Those node embeddings can also be used for link prediction by computing distances between each node of the graph (Hammond et al., 2011; Kipf & Welling, 2016 ). An image can be seen as a special case of graph that lies on a 2D grid and where nodes are pixels and edges are weighted according to the difference of intensity and to the distance between two pixels (Zhang et al., 2015; Achanta & Susstrunk, 2017; Van den Bergh et al., 2012; Stutz et al., 2018) . In the emerging field of graph analysis based on convolutions and deep neural networks, it is appealing to try to apply models that worked best in the field of computer vision. In this effort, several ways to perform convolutions in graphs have been proposed (Hammond et al., 2011; Kipf & Welling, 2016; Defferrard et al., 2016; Gilmer et al., 2017; Veličković et al., 2017; Xu et al., 2018; Battaglia et al., 2016; Kearnes et al., 2016) . Moreover, when dealing with image classification, pooling is an important step (Gao & Ji, 2019; Ying et al., 2018; Defferrard et al., 2016; Diehl, 2019) . It allows us to extract hierarchical features in images in order to make the classification more accuracte. While it is easy to apply coarsening to an image, it isn't obvious how to coarsen a graph since nodes in graphs are not ordered like pixels in images. In this work we present a novel pooling layer based on edge scoring and related to the minCUT problem. The main contributions of this work are summarized below: 1

