Graph convolutional network (GCN) is generalization of convolutional neural network (CNN) to work with arbitrarily structured graphs. A binary adjacency matrix is commonly used in training a GCN. Recently, the attention mechanism allows the network to learn a dynamic and adaptive aggregation of the neighborhood. We propose a new GCN model on the graphs where edges are characterized in multiple views or precisely in terms of multiple relationships. For instance, in chemical graph theory, compound structures are often represented by the hydrogen-depleted molecular graph where nodes correspond to atoms and edges correspond to chemical bonds. Multiple attributes can be important to characterize chemical bonds, such as atom pair (the types of atoms that a bond connects), aromaticity, and whether a bond is in a ring. The different attributes lead to different graph representations for the same molecule. There is growing interests in both chemistry and machine learning fields to directly learn molecular properties of compounds from the molecular graph, instead of from fingerprints predefined by chemists. The proposed GCN model, which we call edge attention-based multi-relational GCN (EAGCN), jointly learns attention weights and node features in graph convolution. For each bond attribute, a real-valued attention matrix is used to replace the binary adjacency matrix. By designing a dictionary for the edge attention, and forming the attention matrix of each molecule by looking up the dictionary, the EAGCN exploits correspondence between bonds in different molecules. The prediction of compound properties is based on the aggregated node features, which is independent of the varying molecule (graph) size. We demonstrate the efficacy of the EAGCN on multiple chemical datasets: Tox21, HIV, Freesolv, and Lipophilicity, and interpret the resultant attention weights.
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