DYHCN: DYNAMIC HYPERGRAPH CONVOLUTIONAL NETWORKS

Abstract

Hypergraph Convolutional Network (HCN) has become a default choice for capturing high-order relations among nodes, i.e., encoding the structure of a hypergraph. However, existing HCN models ignore the dynamic evolution of hypergraphs in the real-world scenarios, i.e., nodes and hyperedges in a hypergraph change dynamically over time. To capture the evolution of high-order relations and facilitate relevant analytic tasks, we formulate dynamic hypergraph and devise the Dynamic Hypergraph Convolutional Networks (DyHCN). In general, DyHCN consists of a Hypergraph Convolution (HC) to encode the hypergraph structure at a time point and a Temporal Evolution module (TE) to capture the varying of the relations. The HC is delicately designed by equipping inner attention and outer attention, which adaptively aggregate nodes' features to hyperedge and estimate the importance of each hyperedge connected to the centroid node, respectively. Extensive experiments on the Tiigo and Stocktwits datasets show that DyHCN achieves superior performance over existing methods, which implies the effectiveness of capturing the property of dynamic hypergraphs by HC and TE modules.

1. INTRODUCTION

Graph Convolutional Network (GCN) Scarselli et al. (2008) extends deep neural networks to process graph data, which encodes the relations between nodes via propagating node features over the graph structure. GCN has become a promising solution in a wide spectral of graph analytic tasks, such as relation detection Schlichtkrull et al. (2018) and recommendation Ying et al. (2018) . An emergent direction of GCN research is extending the graph covolution operations to hypergraphs, i.e., hypergraph convolutional networks Zhu et al. (2017); Zhou et al. (2007); Zhang et al. (2017); Feng et al. (2019b); Yadati et al. (2019) , where high-order node relations are represented as hyperedges (one hyperedge can connect multiple nodes). For instance, in a hypergraph of stocks, an financial event relevant to several stocks is represented as a hyperedge. While a surge of attention paid on hypergraph convolutional networks, most of them discard the dynamic property of hypergraphs in real-world applications, e.g., new hyperedges (i.e., events) emerge in the hypergraph of stocks (see Fig. 1 ), where the evolution of the hypergraph is crucial for the analytic tasks (e.g., stock price prediction). Aiming to bridge the gap, this work explore the central theme of dynamic hypergraph and the corresponding GCN. Formally, a hypergraph with n nodes and m hyperedges is represented as G = (V, E, A, H, X) where V and E denote the set of nodes and hyperedges respectively; A ∈ R n×m is an incidence matrix with binary value indicating the connectedness of nodes; H ∈ R m×c and X ∈ R n×d are features represent the hyperedges and nodes respectively. In order to account for the evolution, we first extend the concept of static hypergraph to dynamic hypergraph, which has two different formulations when treating the time as continuous value or discrete value. 1) Discrete-time formulation. A straightforward solution is to treat a time window with length of T (e.g., T days) as a sequence of time-steps and get a snapshot at each time-step. In this way, a dynamic hypergraph is defined as G D = [G 1 , • • • , G t , • • • , G T ] T where G t is a hypergraph dumped at time-step t. 2) Continuous formulation. By treating time as a continuous variable, the dynamic hypergraph can be defined as G C = (G 0 , U ) where G 0 is the initial status (a hypergraph) and U = {(p t , v t , a t )|t <= T } is a streaming of updates. p t denotes the target variable (e.g., a row of X) changed at time t; v t denotes the latest value of the target variable, a t denotes the action of change, including add, delete,

