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Graph convolutional networks (GCNs) successfully generalize convolutional neural networks to handle the graphs with high-order arbitrary structures. However, most existing GCNs variants consider only the local geometry of row vectors of high-dimensional data via example graph Laplacian, while neglecting the manifold structure information of column vectors. To address this problem, we propose the example-feature graph convolutional networks (EFGCNs) for semi-supervised classification. Particularly, we introduce the definition of the spectral example-feature graph (EFG) convolution that simultaneously utilizes the example graph Laplacian and feature graph Laplacian to better preserve the local geometry distributions of data. After optimizing the spectral EFG convolution with the first-order approximation, a single-layer EFGCNs is obtained. It is then further extended to build a multi-layer EFGCNs. Extensive experiments on remote sensing and citation networks datasets demonstrate the proposed EFGCNs show superior performance in semi-supervised classification compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Deep learning has shown superiority to extract more representative features from multimedia data in recent years. Recently, the most typical graph convolutional networks (GCN) has achieved excellent performance in the semi-supervised framework-based data representation learning tasks. GCN successfully generalizes traditional convolutional neural networks to encode arbitrary graphs by exploiting the graph Laplacian-based sample structure information. However, GCN only fuses the static structure information. It is difficult to guarantee that its structure information is optimal during the training process and applicable for all practical applications. To tackle the above problem, in this paper, we propose a manifold regularized dynamic graph convolutional network (MRDGCN). The proposed MRDGCN automatically updates the structure information by manifold regularization until model fitting. In particular, we build an optimization convolution layer formulation to acquire the optimal structure information. Thus, MRDGCN can automatically learn high-level sample features to improve the performance of data representation learning. To demonstrate the effectiveness of our proposed model, we apply MRDGCN on the semi-supervised classification tasks. The extensive experiment results on human activity datasets and citation network datasets validate the performance of MRDGCN compared with GCN and other semi-supervised learning methods. [ABSTRACT FROM AUTHOR]