Parameterized Pseudo-Differential Operators for Graph Convolutional Neural Networks
We present a novel graph convolutional layer that is fast, conceptually simple, 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. 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 datasets. When compared to the best published results, the new layer achieves greater than 15% reduction in error rate on the MNIST dataset and greater than 8% reduction in error rate for the CIFAR-100 dataset. For the FAUST node correspondence task, our layer is competitive with other recent results without extensive hyperparameter tuning. 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.