Generalizing Graph Convolutional Neural Networks with Edge-Variant Recursions on Graphs
This work addresses the need for more flexible and efficient GCNNs in graph-based machine learning, offering a general framework that can guide the development of new methods, but it appears incremental as it builds on existing state-of-the-art solutions.
The paper tackles the problem of generalizing graph convolutional neural networks (GCNNs) by introducing a framework based on edge-variant graph filters, which allows nodes to weigh neighbor information differently. It presents a novel approach that shows superior performance in graph signal classification problems, though no specific numbers are provided.
This paper reviews graph convolutional neural networks (GCNNs) through the lens of edge-variant graph filters. The edge-variant graph filter is a finite order, linear, and local recursion that allows each node, in each iteration, to weigh differently the information of its neighbors. By exploiting this recursion, we formulate a general framework for GCNNs which considers state-of-the-art solutions as particular cases. This framework results useful to i) understand the tradeoff between local detail and the number of parameters of each solution and ii) provide guidelines for developing a myriad of novel approaches that can be implemented locally in the vertex domain. One of such approaches is presented here showing superior performance w.r.t. current alternatives in graph signal classification problems.