Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they are highly diverse or even not well defined. Under some circumstances, e.g. chemical molecular data, clustering or coarsening for simplifying the graphs is hard to be justified chemically. In this paper, we propose a more general and flexible graph convolution network (EGCN) fed by batch of arbitrarily shaped data together with their evolving graph Laplacians trained in supervised fashion. Extensive experiments have been conducted to demonstrate the superior performance in terms of both the acceleration of parameter fitting and the significantly improved prediction accuracy on multiple graph-structured datasets.
Besides above papers on constructing convolution layer on graphs, many others studied the problem from a different angle. @cite_31 first investigated learning a network from a set of heterogeneous graphs to predict node-level feature as well as to do graph completion, although it is based on node sequence selection. @cite_25 introduced a graph diffusion process, which delivers equivalent effect as convolution has, but @cite_25 's DCNN has no dependency on the indexing of nodes. Its constrains are the highly restricted locality by diffusion process and the expensive dense matrix multiplication.
@cite_31 @cite_25
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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. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. A number of recent studies have shown that a Deep Convolutional Neural Network (DCNN) pretrained on a large dataset can be adopted as a universal image descriptor, and that doing so leads to impressive performance at a range of image classification tasks. Most of these studies, if not all, adopt activations of the fully-connected layer of a DCNN as the image or region representation and it is believed that convolutional layer activations are less discriminative. This paper, however, advocates that if used appropriately, convolutional layer activations constitute a powerful image representation. This is achieved by adopting a new technique proposed in this paper called cross-convolutional-layer pooling. More specifically, it extracts subarrays of feature maps of one convolutional layer as local features, and pools the extracted features with the guidance of the feature maps of the successive convolutional layer. Compared with existing methods that apply DCNNs in the similar local feature setting, the proposed method avoids the input image style mismatching issue which is usually encountered when applying fully connected layer activations to describe local regions. Also, the proposed method is easier to implement since it is codebook free and does not have any tuning parameters. By applying our method to four popular visual classification tasks, it is demonstrated that the proposed method can achieve comparable or in some cases significantly better performance than existing fully-connected layer based image representations. Deep Convolutional Neural Networks (DCNNs) commonly use generic 'max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic con-volution as a building block alternative to the common convolution-MP cascade of DCNNs; while having identical complexity to MP, Epitomic Convolution allows for pa-rameter sharing across different filters, resulting in faster convergence and better generalization. Second, we introduce a Multiple Instance Learning approach to explicitly accommodate global translation and scaling when training a DCNN exclusively with class labels. For this we rely on a 'patchwork' data structure that efficiently lays out all image scales and positions as candidates to a DCNN. Factoring global and local deformations allows a DCNN to 'focus its resources' on the treatment of non-rigid defor-mations and yields a substantial classification accuracy improvement. Third, further pursuing this idea, we develop an efficient DCNN sliding window object detector that employs explicit search over position, scale, and aspect ratio. We provide competitive image classification and localization results on the ImageNet dataset and object detection results on the Pascal VOC 2007 benchmark.