In this paper, we develop a novel Aligned-Spatial Graph Convolutional Network (ASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized aligned grid structures, and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed ASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Moreover, the proposed ASGCN model can adaptively discriminate the importance between specified vertices during the process of spatial graph convolution, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.
Eq.) indicates that the spatial graph convolution operation of the DGCNN model cannot discriminate the importance between specified vertices in the convolution operation process. This is because the required filter weights @math are shared by each vertex, i.e., the feature transformations of the vertices are all based on the same trainable function. Thus, the DGCNN model cannot directly influence the aggregation process of the vertex features. In fact, this problem also arises in other spatially-based GCN models, e.g., the Neural Graph Fingerprint Network (NGFN) model @cite_13 , the Diffusion Convolution Neural Network (DCNN) model @cite_18 , etc. Since the associated spatial graph convolution operations of these models also take the similar form with that of the DGCNN model, i.e., the trainable parameters of their spatial graph convolution operations are also shared by each vertex. This drawback influences the effectiveness of the existing spatially-based GCN models for graph classification. In this paper, we aim to propose a new spatially-based GCN model to overcome the above problems. @math
@cite_18 @cite_13
2963984147 2964113829
We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks. We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.