Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or features are useful or not. Recent methods have improved solutions by sampling a fixed size set of neighbors, or assigning different weights to different neighbors in the aggregation process, but features within a feature vector are still treated equally in the aggregation process. In this paper, we introduce a new convolution operation on regular size feature maps constructed from features of a fixed node bandwidth via sampling to get the first-level node representation, which is then passed to a standard GCN to learn the second-level node representation. Experiments show that our method outperforms competing methods in semi-supervised node classification tasks. Furthermore, our method opens new doors for exploring new GCN architectures, particularly deeper GCN models.
The above graph representation methods mainly consider the graph structure (node and edge) information but they do not use the node feature matrix @math in the learning process. proposed the graph convolutional networks (GCN) as an effective graph representation model that can naturally combine structure information and node features in the learning process. It is derived from conducting graph convolution in the spectral domain @cite_22 @cite_12 . It represents a node by aggregating feature vectors from its neighbors (including itself), which is similar with the convolution operation in CNN. The propagation rule of GCN can be summarized by the following expression: where is a normalized adjacency matrix of the undirected graph @math with added self-connections . @math is an identity matrix. The diagonal entries of @math is @math is a layer-specific trainable weight matrix, @math denotes an activation function such as the @math , and @math is the matrix of activation in the @math layer. @math is the node feature matrix.
@cite_22 @cite_12
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Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures. In this paper, we propose a novel neural network model called RNN Encoder-Decoder that consists of two recurrent neural networks (RNN). One RNN encodes a sequence of symbols into a fixed-length vector representation, and the other decodes the representation into another sequence of symbols. The encoder and decoder of the proposed model are jointly trained to maximize the conditional probability of a target sequence given a source sequence. The performance of a statistical machine translation system is empirically found to improve by using the conditional probabilities of phrase pairs computed by the RNN Encoder-Decoder as an additional feature in the existing log-linear model. Qualitatively, we show that the proposed model learns a semantically and syntactically meaningful representation of linguistic phrases.