Geometric Graph Convolutional Neural Networks

Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the ordering of node neighbors, even when there is a geometric interpretation of the graph vertices that provides an order based on their spatial positions. To remedy this issue, we propose Geometric Graph Convolutional Network (geo-GCN) which uses spatial features to efficiently learn from graphs that can be naturally located in space. Our contribution is threefold: we propose a GCN-inspired architecture which (i) leverages node positions, (ii) is a proper generalisation of both GCNs and Convolutional Neural Networks (CNNs), (iii) benefits from augmentation which further improves the performance and assures invariance with respect to the desired properties. Empirically, geo-GCN outperforms state-of-the-art graph-based methods on image classification and chemical tasks. Introduction Convolutional Neural Networks (CNNs) outperform humans on visual learning tasks, such as image classification (Krizhevsky, Sutskever, and Hinton 2012), object detection (Seferbekov et al. 2018) or image captioning (Y ang et al. 2017). They have also been successfully applied to text processing (Kim 2014) and time series analysis (Y ang et al. 2015). Nevertheless, CNNs cannot be easily adapted to irregular entities, such as graphs, where data representation is not organised in a grid-like structure. Graph Convolutional Networks (GCNs) attempt to mimic CNNs by operating on spatially close neighbors. Motivated by spectral graph theory, Kipf and Welling (Kipf and Welling 2016) use fixed weights determined by the adjacency matrix of a graph to aggregate labels of the neighbors.