Improving Graph Machine Learning Performance Through Feature Augmentation Based on Network Control Theory

TL;DR

This work tackles the problem of degraded GNN performance when node features are missing by introducing NCT-EFA, a feature augmentation framework that injects network control theory metrics into node representations. It leverages average controllability $\mathcal{C}_a = \operatorname{tr}(\mathcal{W})$, alongside centrality measures, and a histogram-based rank encoding to enrich features before applying various GNNs for graph classification. Across two social-network datasets and six GNN architectures, NCT-EFA consistently improves predictive performance, achieving up to 11.69% ROC AUC gains on GitHub Stargazers, with substantial gains even when only average controllability is used (e.g., 9.98% for GAT). The results demonstrate that integrating NCT with feature construction extends the applicability of GNNs in settings with limited node attributes and highlights a promising direction for fusion of network control theory and graph ML.

Abstract

Network control theory (NCT) offers a robust analytical framework for understanding the influence of network topology on dynamic behaviors, enabling researchers to decipher how certain patterns of external control measures can steer system dynamics towards desired states. Distinguished from other structure-function methodologies, NCT's predictive capabilities can be coupled with deploying Graph Neural Networks (GNNs), which have demonstrated exceptional utility in various network-based learning tasks. However, the performance of GNNs heavily relies on the expressiveness of node features, and the lack of node features can greatly degrade their performance. Furthermore, many real-world systems may lack node-level information, posing a challenge for GNNs.To tackle this challenge, we introduce a novel approach, NCT-based Enhanced Feature Augmentation (NCT-EFA), that assimilates average controllability, along with other centrality indices, into the feature augmentation pipeline to enhance GNNs performance. Our evaluation of NCT-EFA, on six benchmark GNN models across two experimental setting. solely employing average controllability and in combination with additional centrality metrics. showcases an improved performance reaching as high as 11%. Our results demonstrate that incorporating NCT into feature enrichment can substantively extend the applicability and heighten the performance of GNNs in scenarios where node-level information is unavailable.

Figures (2)

• Figure 1: Illustration of the proposed NCT-EFA framework. Starting with a simple graph, NCT-EFA utilizes network control theory and network science metrics to enhance the graph by node features. These graphs with enriched features are subsequently fed into GNN module for training and the downstream classification task.
• Figure 2: Comparison of ROC AUC scores of the encoded ranks (average controllability) against degree one-hot-encoding.