Graph Based Convolutional Neural Network

By Michael Edwards, Xianghua Xie. 2016

52 citations recorded by the source corpus.

The benefit of localized features within the regular domain has given rise to the use of Convolutional Neural Networks (CNNs) in machine learning, with great proficiency in the image classification. The use of CNNs becomes problematic within the irregular spatial domain due to design and convolution of a kernel filter being non-trivial. One solution to this problem is to utilize graph signal processing techniques and the convolution theorem to perform convolutions on the graph of the irregular domain to obtain feature map responses to learnt filters. We propose graph convolution and pooling operators analogous to those in the regular domain. We also provide gradient calculations on the input data and spectral filters, which allow for the deep learning of an irregular spatial domain problem. Signal filters take the form of spectral multipliers, applying convolution in the graph spectral domain. Applying smooth multipliers results in localized convolutions in the spatial domain, with smoother multipliers providing sharper feature maps. Algebraic Multigrid is presented as a graph pooling method, reducing the resolution of the graph through agglomeration of nodes between layers of the network. Evaluation of performance on the MNIST digit classification problem in both the regular and irregular domain is presented, with comparison drawn to standard CNN. The proposed graph CNN provides a deep learning method for the irregular domains present in the machine learning community, obtaining 94.23% on the regular grid, and 94.96% on a spatially irregular subsampled MNIST.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017, positive): “This is exactly the same accuracy as reported by Defferrard et al. [11] and better than what is offered by other spectral-based approaches (98.2 [6], 94.96 [15]).”
3D shape segmentation via shape fully convolutional networks (2017, positive): “Common pooling operations are those of taking the average and maximum of receptive ﬁelds over the input map [11].”
Discovering objects and their relations from entangled scene representations (2017, methodology): “Our model is also related to various other approaches that apply neural networks directly to graphs (Scarselli et al., 2009; Bruna et al., 2013; Li et al., 2015; Duvenaud et al., 2015; Henaff et al., 2015; Defferrard et al., 2016; Kipf & Welling, 2016; Edwards & Xie, 2016).”
Mining Point Cloud Local Structures by Kernel Correlation and Graph Pooling (2017, unknown): “Therefore, a graph e.g. a connectivity graph or a polygon mesh can be used to represent a 3D point cloud, convert to the spectral representation and apply convolution in spectral domain [4, 8, 10, 13, 19, 22].”
Adversarial Examples on Graph Data: Deep Insights into Attack and Defense (2019, background): “The graph convolutional networks [Bruna et al. , 2013; Edwards and Xie, 2016] and its recent variants [Kipf and Welling, 2017] perform convolution operations in the graph domain by aggregating and combining the information of neighbor nodes.”
FoldingNet: Interpretable Unsupervised Learning on 3D Point Clouds (2017, background): “There are tremendous amount of works on applying deep learning onto irregular data such as graphs and point sets [2,5,6,12,14,15,22,23,27,30,33,36,37,41,44,49, 56].”
FoldingNet: Point Cloud Auto-Encoder via Deep Grid Deformation (2017, background): “There are tremendous amount of works on applying deep learning onto irregular data such as graphs and point sets [2,5,6,12,14,15,23,24,28,32,35,38,39,43,47,52, 59].”