Graph Neural Networks as a combination of Graph Signal Processing and Deep Convolutional Networks shows great power in pattern recognition in non-Euclidean domains. In this paper, we propose a new method to deploy two pipelines based on the duality of a graph to improve accuracy. By exploring the primal graph and its dual graph where nodes and edges can be treated as one another, we have exploited the benefits of both vertex features and edge features. As a result, we have arrived at a framework that has great potential in both semisupervised and unsupervised learning. Convolutional Neural Networks (CNNs) (Lecun et al. (1998) ) has been very successfully used for automated feature extraction in Euclidean domains, especially for computer vision, such as 2D image classification, object detection, etc. However, many real-life data has a non-Euclidean graph structure in nature, from which we want to investigate the underlying relations among different objects by utilizing the representation of nodes and edges. Recently, research on applying the generalization of Convolutional Neural Networks to the non-Euclidean domains has attracted growing attention. As a result, a branch of research on Geometric Deep Learning (Bruna et al. (2013) ) based on that has been ignited. Previous works including ChebNet (Defferrard et al. (2016) ) and GCN (Kipf & Welling (2017) ) have demonstrated strong results in solving problems in semi-supervised learning where the labels of only a few objects are given, and we want to find out the labels of other objects through their inner connections. Current methods generalizing convolution operations include both spatial and spectral domains (Bruna et al. (2013) ). The spatial one deals with each node directly in the vertex domain while the spectral one takes a further step in converting signals via graph Fourier transform into the spectral domain. However, one critical weakness would be the fact that the interchangeable and complementary nature between nodes and edges are generally ignored in previous research. As a result, the duality of the graph is not fully utilized. If we treat those edges in the original, or known as the primal graph, as the nodes in the new graph, and original nodes as edges, we can arrive at a new graph that further exploits the benefits of edge features. In such a way, we are able to get both the primal graph and the dual graph (Monti et al. (2018) ). By combining both the vertex features and the edge features, we will be able to solve wider range of problems and achieve better performance. In this paper, we propose a new approach to transform the primal graph into its dual form and have implemented two pipelines based on these two forms of graph to improve the accuracy and the performance. With two pipelines, we also exploited a path to make the model wider instead of merely deeper. Meanwhile, we have developed a new framework that can be applied later on both semi-supervised learning and unsupervised learning. In this work, we propose the TwinGCN with parallel pipelines working on both the primal graph and its dual graph, respectively. TwinGCN achieves the state-of-the-art performance in semisupervised learning tasks. Moreover, TwinGCN's ability is not limited to this, we can extend its power/utilization into unsupervised learning by altering its loss functions.
A primal dual graph neural network model for semi-supervised learning
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