Multi-scale Directed Graph Convolution Neural Network for Node Classification Task

The existence of problems and objects in the real world which can be naturally modeled by complex graph structure has motivated researchers to combine deep learning techniques with graph theory. Despite the proposal of various spectral-based graph neural networks (GNNs), they still have shortcomings in dealing with directed graph-structured data and aggregating neighborhood information of nodes at larger scales. In this paper, we first improve the Lanczos algorithm by orthogonality checking method and Modified Gram-Schmidt orthogonalization technique. Then, we build a long-scale convolution filter based on the improved Lanczos algorithm and combine it with a short-scale filter based on Chebyshev polynomial truncation to construct a multi-scale directed graph convolution neural network (MSDGCNN) which can aggregate multi-scale neighborhood information of directed graph nodes in larger scales. We validate our improved Lanczos algorithm on the atom classification task of the QM8 quantum chemistry dataset. We also apply the MSDGCNN on various real-world directed graph datasets (including WebKB, Citeseer, Telegram and Cora-ML) for node classification task. The result shows that our improved Lanczos algorithm has much better stability, and the MSDGCNN outperforms other state-of-the-art GNNs on such task of real-world datasets.