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Control-based Graph Embeddings with Data Augmentation for Contrastive Learning

Obaid Ullah Ahmad, Anwar Said, Mudassir Shabbir, Waseem Abbas, Xenofon Koutsoukos

TL;DR

This work addresses unsupervised graph representation learning by integrating network controllability with contrastive learning. It introduces CTRL, a fixed-dimensional graph embedding grounded in controllability metrics such as the Gramian, and CGCL, a graph contrastive learning framework that uses controllability-preserving augmentations and the NT-Xent loss to align original and augmented graphs. The approach is evaluated on seven benchmark datasets, showing improvements over multiple unsupervised baselines and competitive performance with self-supervised methods, with ablations highlighting the importance of principled augmentations. Overall, the study demonstrates that incorporating domain-specific structure—controllability—in graph representations can significantly enhance SSL-based graph classification.

Abstract

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.

Control-based Graph Embeddings with Data Augmentation for Contrastive Learning

TL;DR

This work addresses unsupervised graph representation learning by integrating network controllability with contrastive learning. It introduces CTRL, a fixed-dimensional graph embedding grounded in controllability metrics such as the Gramian, and CGCL, a graph contrastive learning framework that uses controllability-preserving augmentations and the NT-Xent loss to align original and augmented graphs. The approach is evaluated on seven benchmark datasets, showing improvements over multiple unsupervised baselines and competitive performance with self-supervised methods, with ablations highlighting the importance of principled augmentations. Overall, the study demonstrates that incorporating domain-specific structure—controllability—in graph representations can significantly enhance SSL-based graph classification.

Abstract

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.
Paper Structure (22 sections, 5 theorems, 8 equations, 3 figures, 4 tables, 2 algorithms)

This paper contains 22 sections, 5 theorems, 8 equations, 3 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Notations
  4. Problem Description
  5. Proposed Approach
  6. Graph Contrastive Representation Learning
  7. Control-based Graph Contrastive Learning (CGCL)
  8. Network Controllability and Graph Embeddings
  9. Networks as Dynamical Systems
  10. Network Controllability Metrics
  11. Control-Based Graph Augmentations
  12. Egde Deletion
  13. Egde Addition
  14. Egde Substitution
  15. Numerical Evaluation
  16. ...and 7 more sections

Key Result

Lemma 1

If we partition the Laplacian matrix $L$ of an undirected connected graph as shown in eq:Laplacian_Partition, the matrix $A$ is positive definite mesbahi2010graph.

Figures (3)

  • Figure 1: Block diagram of the proposed CGCL approach
  • Figure 2: Controllability metrics vary with leader selection
  • Figure 3: Control-based graph augmentations where $\delta = \gamma = 4$ for original and augmented graphs.

Theorems & Definitions (7)

  • Lemma 1
  • Theorem IV.1
  • Proposition IV.2
  • proof
  • Proposition IV.3
  • Proposition IV.4
  • proof