Graph neural network is a popular modelling approach developed in recent years. They take into account the relationship information that exists in data to build better-performing models. However, when relationship information is of a single direction, most state-of-the-art graph neural networks may ignore this important direction information. The SVD-Framelet algorithms we introduce in this paper take care of this type of information. With a good increase in classification accuracy after adopting our algorithms over other existing approaches, the proposed modelling method is ready to support practitioners in a wide variety of applications including the retailer industry (customer segmentation), financial markets (stock classification), and the social networks (community identification). Moreover,?the proposed technology could offer an alternative way of molecule classifications in drug design for the pharmaceutical industry.

In this work, we propose a spectral-based graph convolutional network for directed graphs. The proposed model employs the classic singular value decomposition (SVD) to perform signal decomposition directly on the asymmetric adjacency matrix. This strategy is simple, which allows many existing spectral-based methods to be adapted to directed graphs. We particularly utilize framelets-based filtering, which significantly enhances the learning capacity due to the separated modeling of information at different frequencies. We empirically observe the proposed model achieves the state-of-the-art results on various datasets. We also show that the model is robust to feature perturbation.