Graph2DMatrix: Exploring Graph Neural Networks Ability to Visualize Multivariate Graphs with Reordered Matrices

Abstract

Previous research in graph embedding concentrates mainly on using embeddings for downstream machine learning tasks such as node classification, edge prediction and, to a lesser extent, on visualizing these embeddings for analytical examination. This study aims to determine whether high dimensional graph embeddings can be used to uncover structures in graphs, and visualize these in two dimensional matrices. We propose a framework that embeds a graph in high dimensions; calculates the pairwise distance matrix; reorders rows and columns in this matrix; and visualizes the original graph in a new matrix exploration tool. The goal of this framework is to supply individuals with high level knowledge on relational data. We test the framework by analyzing visual quality by feeding in basic pre-generated graphs. The random walk algorithms (e.g. DeepWalk, Walkets and attentionWalk) are able to accurately visualize 4 out of 6 of the canonical data patterns for a high level understanding of the data. Nevertheless, these basic graphs do not reflect complex relational data used in many real world applications, and therefore, we introduce two novel algorithms for embedding numerical node-attributed graphs (i.e. featPMI and featWalk). These algorithms are tested on a subset of the attributed Slovakian social network Pokec, in which both the algorithms show increasing information retention over the naive embedding of DeepWalk. Furthermore, featWalk is found to be preferred over featPMI with a clearer separation of patterns, and better feature preservation. Our findings indicate the potentiality of embeddings to generate valuable high level matrix visualizations.