Hyperparameter-free and Explainable Whole Graph Embedding

TL;DR

This paper introduces DHC-E, a simple, hyperparameter-free, and explainable whole graph embedding method that effectively balances simplicity and quality for classification and visualization tasks across various network types.

Contribution

The paper proposes a novel graph embedding approach based on DHC and Shannon Entropy that eliminates the need for parameter tuning and enhances interpretability.

Findings

Performs well in molecular, social, and brain network classification.

Effective in low-dimensional graph visualization.

Offers a good trade-off between simplicity and embedding quality.

Abstract

Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention. However, most graph embedding methods have problems such as tedious parameter tuning or poor explanation. This paper presents a simple and hyperparameter-free whole graph embedding method based on the DHC (Degree, H-index, and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The DHC-E can provide a trade-off between simplicity and quality for supervised classification learning tasks involving molecular, social, and brain networks. Moreover, it performs well in lower-dimensional graph visualization. Overall, the DHC-E is simple, hyperparameter-free, and explainable for whole graph embedding with promising potential for exploring graph classification and lower-dimensional graph visualization.