# Generalizing Graph Convolutional Neural Networks with Edge-Variant Recursions on Graphs

## TL;DR

This paper introduces a generalized framework for graph convolutional neural networks using edge-variant recursions, enabling more flexible node-wise weighting of neighbor information and demonstrating superior classification performance.

## Contribution

It formulates a unifying framework for GCNNs based on edge-variant filters, offering insights into tradeoffs and guiding the development of new local graph processing methods.

## Key findings

- Superior performance in graph signal classification
- Framework unifies and generalizes existing GCNN solutions
- Provides guidelines for designing novel local graph filters

## Abstract

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.