# Deep Node Ranking for Neuro-symbolic Structural Node Embedding and Classification

## TL;DR

This paper introduces Deep Node Ranking, a scalable and efficient method for network node embedding and classification that outperforms existing approaches in speed, space efficiency, and accuracy, while providing insights into node representations.

## Contribution

The novel Deep Node Ranking algorithm combines node ranking with autoencoder neural networks to improve classification performance and scalability in large networks.

## Key findings

- Achieves competitive or better classification accuracy than state-of-the-art methods.
- Significantly faster learning speed and lower memory usage.
- Scales effectively to networks with tens of millions of links.

## Abstract

Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Deep Node Ranking (DNR) algorithm are competitive or better classification performance, significantly higher learning speed and lower space requirements when compared to state-of-the-art approaches on 15 real-life node classification benchmarks. Furthermore, it enables exploration of the relationship between symbolic and the derived sub-symbolic node representations, offering insights into the learned node space structure. To avoid the space complexity bottleneck in a direct node classification setting, DNR computes stationary distributions of personalized random walks from given nodes in mini-batches, scaling seamlessly to larger networks. The scaling laws associated with DNR were also investigated on 1488 synthetic Erd\H{o}s-R\'enyi networks, demonstrating its scalability to tens of millions of links.