  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.
