Graph Prolongation Convolutional Networks (GPCNs) are a type of graph convolutional network model. In my 2020 IOP: Machine Learning, Science, and Technology paper “Graph Prolongation Convolutional Networks” (with Eric Mjolsness), I define this type of GCN model, and compare it to other types of GCN ensemble models.
Recent successes of deep learning have demonstrated that the inductive bias of Convolutional Neural Networks (CNNs) makes them extremely efficient for analyzing data with an inherent grid structure, such as images or video. In particular, many applications use these models to make per-node (per-pixel) predictions over grid graphs: examples include image segmentation, optical flow prediction, anticipating motion of objects in a scene, and facial detection/identification. These models learn a set of local filters whose size is much smaller than the size of the domain – these filters may then be applied simultaneously across the entire domain, leveraging the fact that at a given scale the local behavior of the neighborhood around a pixel (voxel) is likely to be similar at all grid points.
Graph Convolutional Networks (GCNs) are a natural extension of the above idea of image ‘filters’ to arbitrary graphs rather than grids, which may be more suitable in some scientific contexts. Intuitively, GCNs replace the image filtering operation of CNNs with repeated passes of: 1) aggregation of information between nodes according to some structure matrix 2) nonlinear processing of data at each node according to some rule (most commonly a flat neural network which takes as separate input(s) the current vector at each node). We refer the reader to a recent survey by Bacciu et al (Bacciu et al. 2019) for a more complete exploration of the taxonomy graph neural networks.
