Dual graph convolutional neural network for predicting chemical networks

Abstract

Background: Predicting of chemical compounds is one of the fundamental tasks in bioinformatics and chemoinformatics, because it contributes to various applications in metabolic engineering and drug discovery. The recent rapid growth of the amount of available data has enabled applications of computational approaches such as statistical modeling and machine learning method. Both a set of chemical interactions and chemical compound structures are represented as graphs, and various graph-based approaches including graph convolutional neural networks have been successfully applied to chemical network prediction. However, there was no efficient method that can consider the two different types of graphs in an end-to-end manner.

Results: We give a new formulation of the chemical network prediction problem as a link prediction problem in a graph of graphs (GoG) which can represent the hierarchical structure consisting of compound graphs and an inter-compound graph. We propose a new graph convolutional neural network architecture called dual graph convolutional network that learns compound representations from both the compound graphs and the inter-compound network in an end-to-end manner.

Conclusions: Experiments using four chemical networks with different sparsity levels and degree distributions shows that our dual graph convolution approach achieves high prediction performance in relatively dense networks, while the performance becomes inferior on extremely-sparse networks.

Keywords: Chemical network prediction; Graph convolutional neural network; Graph of graphs.

Fig. 1

Chemical network. A chemical network is represented as a graph of graphs consisting of an external graph and a set of internal graphs. Each node of the external graph corresponds to a chemical compound, and each compound has its own internal graph structure representing chemical bonds among its atoms

Fig. 2

Dual graph convolutional neural network. The internal convolution layer extracts features from the molecular compound graphs, which are followed by the external convolutions layer to incorporate structural information of the inter-compound network

Fig. 3

Node degree distribution of the drug-drug interaction network. The network is dense and very heavy-tailed

Fig. 4

Node degree distribution of the drug indication network. The network is dense and heavy-tailed

Fig. 5

Node degree distribution of the drug function network. The network is sparse and light-tailed

Fig. 6

Node degree distribution of the metabolic reaction network. The network is extremely sparse and light-tailed

Fig. 7

Prediction performance for the drug-drug interaction network. The performance is given in both ROC-AUC (left) and PR-AUC (right). The proposed dual graph convolution method performs well for this dense network with the very heavy-tailed degree distribution

Fig. 8

Prediction performance for the drug indication network. The performance is given in both ROC-AUC (left) and PR-AUC (right). The proposed dual graph convolution method performs well for this dense network with the heavy-tailed degree distribution

Fig. 9

Prediction performance for the drug function network. The performance is given in both ROC-AUC (left) and PR-AUC (right). The advantage of the proposed method is limited for this sparse network with the light-tailed degree distribution

Fig. 10

Prediction performance for the metabolic reaction network. The performance is given in both ROC-AUC (left) and PR-AUC (right). The proposed method shows the limited performance for this extremely sparse network with the light-tailed degree distribution. Inter-compound links are almost useless as features, and therefore the domain specific features (i.e., Morgan indices) perform the best. The internal convolution also suffers from the lack of the links as the training data