HYPERSAGE: GENERALIZING INDUCTIVE REPRESENTATION LEARNING ON HYPERGRAPHS

Abstract

Graphs are the most ubiquitous form of structured data representation used in machine learning. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations found in many real-world datasets. To model such complex relations, hypergraphs have proven to be a natural representation. Learning the node representations in a hypergraph is more complex than in a graph as it involves information propagation at two levels: within every hyperedge and across the hyperedges. Most current approaches first transform a hypergraph structure to a graph for use in existing geometric deep learning algorithms. This transformation leads to information loss, and sub-optimal exploitation of the hypergraph's expressive power. We present HyperSAGE, a novel hypergraph learning framework that uses a two-level neural message passing strategy to accurately and efficiently propagate information through hypergraphs. The flexible design of HyperSAGE facilitates different ways of aggregating neighborhood information. Unlike the majority of related work which is transductive, our approach, inspired by the popular GraphSAGE method, is inductive. Thus, it can also be used on previously unseen nodes, facilitating deployment in problems such as evolving or partially observed hypergraphs. Through extensive experimentation, we show that HyperSAGE outperforms state-of-the-art hypergraph learning methods on representative benchmark datasets. We also demonstrate that the higher expressive power of HyperSAGE makes it more stable in learning node representations as compared to the alternatives.

1. INTRODUCTION

Graphs are considered the most prevalent structures for discovering useful information within a network, especially because of their capability to combine object-level information with the underlying inter-object relations (Wu et al., 2020) . However, most structures encountered in practical applications form groups and relations that cannot be properly represented using pairwise connections alone, hence a graph may fail to capture the collective flow of information across objects. In addition, the underlying data structure might be evolving and only partially observed. Such dynamic higher-order relations occur in various domains, such as social networks (Tan et al., 2011 ), computational chemistry (Gu et al., 2020) , neuroscience (Gu et al., 2017) and visual arts (Arya et al., 2019), among others. These relations can be readily represented with hypergraphs, where an edge can connect an arbitrary number of vertices as opposed to just two vertices in graphs. Hypergraphs thus provide a more flexible and natural framework to represent such multi-way relations (Wolf et al., 2016) , however, this requires a representation learning technique that exploits the full expressive power of hypergraphs and can generalize on unseen nodes from a partially observed hypergraph. Recent work in the field of geometric deep learning have presented formulations on graph structured data for the tasks of node classification (Kipf & Welling, 2016) , link prediction (Zhang & Chen, 2018), or the classification of graphs (Zhang et al., 2018b) . Subsequently, for data containing higher-order relations, a few recent papers have presented hypergraph-based learning approaches on similar tasks (Yadati et al., 2019; Feng et al., 2019) . A common implicit premise in these papers is that a hypergraph can be viewed as a specific type of regular graph. Therefore, reduction of hypergraph learning problem to that of a graph should suffice. Strategies to reduce a hypergraph to a graph include transforming the hyperedges into multiple edges using clique expansion (Feng et al., 2019; Jiang et al., 2019; Zhang et al., 2018a) , converting to a heterogeneous graph using star 1

