The predictive power and overall computational efficiency of Diffusion-convolutional neural networks make them an attractive choice for node classification tasks. However, a naive dense-tensor-based implementation of DCNNs leads to @math memory complexity which is prohibitive for large graphs. In this paper, we introduce a simple method for thresholding input graphs that provably reduces memory requirements of DCNNs to O(N) (i.e. linear in the number of nodes in the input) without significantly affecting predictive performance.
Neural networks for graphs were introduced by @cite_1 and followed by @cite_2 , in departure from the traditional approach of transforming the graph into a simpler representation which could then be tackled by conventional machine learning algorithms. Both the works used recursive neural networks for processing graph data, requiring repeated application of contraction maps until node representations reach a stable state. @cite_3 proposed two generalizations of CNNs to signals defined on general domains; one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. This was followed by @cite_10 , which used these techniques to address a setting where the graph structure is not known a priori, and needs to be inferred. However, the parametrization of CNNs developed in @cite_3 @cite_10 are dependent on the input graph size, while that of DCNNs or sDCNNs are not, making the technique transferable, i.e., a DCNN or sDCNN learned on one graph can be applied to another. @cite_7 proposed a CNN approach which extracts locally connected regions of the input graph, requiring the definition of node ordering as a pre-processing step.
@cite_7 @cite_1 @cite_3 @cite_2 @cite_10
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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. This paper presents a new approach for learning in structured domains (SDs) using a constructive neural network for graphs (NN4G). The new model allows the extension of the input domain for supervised neural networks to a general class of graphs including both acyclic cyclic, directed undirected labeled graphs. In particular, the model can realize adaptive contextual transductions, learning the mapping from graphs for both classification and regression tasks. In contrast to previous neural networks for structures that had a recursive dynamics, NN4G is based on a constructive feedforward architecture with state variables that uses neurons with no feedback connections. The neurons are applied to the input graphs by a general traversal process that relaxes the constraints of previous approaches derived by the causality assumption over hierarchical input data. Moreover, the incremental approach eliminates the need to introduce cyclic dependencies in the definition of the system state variables. In the traversal process, the NN4G units exploit (local) contextual information of the graphs vertices. In spite of the simplicity of the approach, we show that, through the compositionality of the contextual information developed by the learning, the model can deal with contextual information that is incrementally extended according to the graphs topology. The effectiveness and the generality of the new approach are investigated by analyzing its theoretical properties and providing experimental results. 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. Automatically detecting illustrations is needed for the target system.Deep Convolutional Neural Networks have been successful in computer vision tasks.DCNN with fine-tuning outperformed the other models including handcrafted features. Systems for aggregating illustrations require a function for automatically distinguishing illustrations from photographs as they crawl the network to collect images. A previous attempt to implement this functionality by designing basic features that were deemed useful for classification achieved an accuracy of only about 58 . On the other hand, deep neural networks had been successful in computer vision tasks, and convolutional neural networks (CNNs) had performed good at extracting such useful image features automatically. We evaluated alternative methods to implement this classification functionality with focus on deep neural networks. As the result of experiments, the method that fine-tuned deep convolutional neural network (DCNN) acquired 96.8 accuracy, outperforming the other models including the custom CNN models that were trained from scratch. We conclude that DCNN with fine-tuning is the best method for implementing a function for automatically distinguishing illustrations from photographs.