Parameterized Pseudo-Differential Operators for Graph Convolutional Neural Networks.

We present a novel graph convolutional layer that is conceptually simple, fast, and provides high accuracy with reduced overfitting. Based on pseudo-differential operators, our layer operates on graphs with relative position information available for each pair of connected nodes. Our layer represents a generalization of parameterized differential operators (previously shown effective for shape correspondence, image segmentation, and dimensionality reduction tasks) to a larger class of graphs. We evaluate our method on a variety of supervised learning tasks, including 2D graph classification using the MNIST and CIFAR-100 datasets and 3D node correspondence using the FAUST dataset. We also introduce a superpixel graph version of the lesion classification task using the ISIC 2016 challenge dataset and evaluate our layer versus other state-of-the-art graph convolutional network architectures. The new layer outperforms multiple recent architectures on graph classification tasks using the MNIST and CIFAR-100 superpixel datasets. For the ISIC dataset, we outperform all other graph neural networks examined as well as all of the submissions to the original ISIC challenge despite the best of those models having more than 200 times as many parameters as our model.