# Learning Backtrackless Aligned-Spatial Graph Convolutional Networks for Graph Classification

## TL;DR

This paper introduces BASGCN, a novel graph convolutional network that transforms graphs into fixed-sized grid structures, improving information retention and bridging CNN and GCN models for better graph classification.

## Contribution

The paper proposes a new BASGCN model that transforms graphs into backtrackless aligned grids and defines a spatial convolution, addressing information loss and tottering issues in existing GCNs.

## Key findings

- BASGCN outperforms existing models on standard datasets.
- The model effectively reduces information loss and tottering problems.
- Experimental results validate the model's superiority in graph classification.

## Abstract

In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.