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 the 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.
In this section we describe existing approaches to the problems of semi-supervised learning, graph classification, and edge classification, and discuss their relationship to DCNNs. Other researchers have investigated how CNNs can be extended from grid-structured to more general graph-structured data. @cite_9 propose a spatial method with ties to hierarchical clustering, where the layers of the network are defined via a hierarchical partitioning of the node set. In the same paper, the authors propose a spectral method that extends the notion of convolution to graph spectra. Later, @cite_1 applied these techniques to data where a graph is not immediately present but must be inferred. DCNNs, which fall within the spatial category, are distinct from this work because their parameterization makes them transferable; a DCNN learned on one graph can be applied to another. A related branch of work that has focused on extending convolutional neural networks to domains where the structure of the graph itself is of direct interest @cite_15 @cite_10 @cite_5 . For example, @cite_14 construct a deep convolutional model that learns real-valued fingerprint representation of chemical compounds.
@cite_14 @cite_9 @cite_1 @cite_5 @cite_15 @cite_10
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Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches. 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. We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of an inferred graph structure. In more details, we introduce a three-step methodology to create convolutional layers that are adapted to the signals to process: 1) From a training set of signals, infer a graph representing the topology on which they evolve; 2) Identify translation operators in the vertex domain; 3) Emulate a convolution operator by translating a localized kernel on the graph. Using these layers, a convolutional neural network is built, and is trained on the initial signals to perform a classification task. Contributions are twofold. First, we adapt a definition of translations on graphs to make them more robust to irregularities, and to take into account locality of the kernel. Second, we introduce a procedure to build CNNs from data. We apply our methodology on a scrambled version of the CIFAR-10 and Haxby datasets. Without using any knowledge on the signals, we significantly outperform existing methods. Moreover, our approach extends classical CNNs on images in the sense that such networks are a particular case of our approach when the inferred graph is a grid. Deep convolutional networks (DCNNs) are achieving previously unseen performance in object classification, raising questions about whether DCNNs operate similarly to human vision. In biological vision, shape is arguably the most important cue for recognition. We tested the role of shape information in DCNNs trained to recognize objects. In Experiment 1, we presented a trained DCNN with object silhouettes that preserved overall shape but were filled with surface texture taken from other objects. Shape cues appeared to play some role in the classification of artifacts, but little or none for animals. In Experiments 2–4, DCNNs showed no ability to classify glass figurines or outlines but correctly classified some silhouettes. Aspects of these results led us to hypothesize that DCNNs do not distinguish object’s bounding contours from other edges, and that DCNNs access some local shape features, but not global shape. In Experiment 5, we tested this hypothesis with displays that preserved local features but disrupted global shape, and vice versa. With disrupted global shape, which reduced human accuracy to 28 , DCNNs gave the same classification labels as with ordinary shapes. Conversely, local contour changes eliminated accurate DCNN classification but caused no difficulty for human observers. These results provide evidence that DCNNs have access to some local shape information in the form of local edge relations, but they have no access to global object shapes.