Feature Construction Using Network Control Theory and Rank Encoding for Graph Machine Learning

TL;DR

This paper introduces a novel feature construction method using network control theory and rank encoding to enhance graph neural network performance in social network classification, especially when node features are scarce.

Contribution

It proposes a new approach combining average controllability and rank encoding to create expressive node features for GNNs, improving their classification accuracy.

Findings

Rank encoding outperforms one-hot degree encoding.

Incorporating average controllability improves GNN ROC AUC scores.

Method achieves significant performance gains on benchmark datasets.

Abstract

In this article, we utilize the concept of average controllability in graphs, along with a novel rank encoding method, to enhance the performance of Graph Neural Networks (GNNs) in social network classification tasks. GNNs have proven highly effective in various network-based learning applications and require some form of node features to function. However, their performance is heavily influenced by the expressiveness of these features. In social networks, node features are often unavailable due to privacy constraints or the absence of inherent attributes, making it challenging for GNNs to achieve optimal performance. To address this limitation, we propose two strategies for constructing expressive node features. First, we introduce average controllability along with other centrality metrics (denoted as NCT-EFA) as node-level metrics that capture critical aspects of network topology. Building on this, we develop a rank encoding method that transforms average controllability or any other graph-theoretic metric into a fixed-dimensional feature space, thereby improving feature representation. We conduct extensive numerical evaluations using six benchmark GNN models across four social network datasets to compare different node feature construction methods. Our results demonstrate that incorporating average controllability into the feature space significantly improves GNN performance. Moreover, the proposed rank encoding method outperforms traditional one-hot degree encoding, improving the ROC AUC from 68.7% to 73.9% using GraphSAGE on the GitHub Stargazers dataset, underscoring its effectiveness in generating expressive and efficient node representations.