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T-GAE: Transferable Graph Autoencoder for Network Alignment

Jiashu He, Charilaos I. Kanatsoulis, Alejandro Ribeiro

TL;DR

T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining is proposed and it is proved that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods.

Abstract

Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form. Existing optimization algorithms do not scale up as the size of the graphs increases. While being able to reduce the matching complexity, current GNN approaches fit a deep neural network on each graph and requires re-train on unseen samples, which is time and memory inefficient. To tackle both challenges we propose T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining. We prove that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods. Our experiments on real-world benchmarks demonstrate that T-GAE outperforms the state-of-the-art optimization method and the best GNN approach by up to 38.7% and 50.8%, respectively, while being able to reduce 90% of the training time when matching out-of-distribution large scale networks. We conduct ablation studies to highlight the effectiveness of the proposed encoder architecture and training objective in enhancing the expressiveness of GNNs to match perturbed graphs. T-GAE is also proved to be flexible to utilize matching algorithms of different complexities. Our code is available at https://github.com/Jason-Tree/T-GAE.

T-GAE: Transferable Graph Autoencoder for Network Alignment

TL;DR

T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining is proposed and it is proved that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods.

Abstract

Network alignment is the task of establishing one-to-one correspondences between the nodes of different graphs. Although finding a plethora of applications in high-impact domains, this task is known to be NP-hard in its general form. Existing optimization algorithms do not scale up as the size of the graphs increases. While being able to reduce the matching complexity, current GNN approaches fit a deep neural network on each graph and requires re-train on unseen samples, which is time and memory inefficient. To tackle both challenges we propose T-GAE, a transferable graph autoencoder framework that leverages transferability and stability of GNNs to achieve efficient network alignment on out-of-distribution graphs without retraining. We prove that GNN-generated embeddings can achieve more accurate alignment compared to classical spectral methods. Our experiments on real-world benchmarks demonstrate that T-GAE outperforms the state-of-the-art optimization method and the best GNN approach by up to 38.7% and 50.8%, respectively, while being able to reduce 90% of the training time when matching out-of-distribution large scale networks. We conduct ablation studies to highlight the effectiveness of the proposed encoder architecture and training objective in enhancing the expressiveness of GNNs to match perturbed graphs. T-GAE is also proved to be flexible to utilize matching algorithms of different complexities. Our code is available at https://github.com/Jason-Tree/T-GAE.
Paper Structure (39 sections, 2 theorems, 29 equations, 5 figures, 9 tables, 1 algorithm)

This paper contains 39 sections, 2 theorems, 29 equations, 5 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Network Alignment
  4. Spectral Decomposition of the Graph
  5. Graph Neural Networks (GNNs) Upper-Bounds Spectral Methods for Network Alignment
  6. GNNs and Network Alignment
  7. Proposed Method
  8. Learning Network Geometry with Transferable Graph Auto-encoders
  9. Robust and Generalizable Node representations with self-supervised learning (data augmentation)
  10. Alignment and Complexity analysis
  11. Experiments
  12. Experiments Setup
  13. Graph Matching Experiments
  14. Sub-graph Matching Experiments
  15. Ablation study
  16. ...and 24 more sections

Key Result

Theorem 3.1

Let $\phi\left(\bm X; \bm S, \mathcal{H} \right):\mathbb{R}^{N\times D}\to\mathbb{R}^{N\times D^{L}}$ be a GNN with parameters $\mathcal{H}$. For $\tilde{\bm X} = \bm P\bm X$ and $\tilde{\bm S} = \bm P\bm S\bm P^T$ that correspond to node relabelling according to the permutation matrix $\bm P$, the

Figures (5)

  • Figure 1: To enhance the expressiveness of GNNs to align the unseen graphs, our proposed encoder processes the input features by a local MLP, we then incorporate attention mechanism on (1) input to each message-passing layer by attending to the output of the last layer and processed input feature. (2) output of the encoder by attending to the output of each message passing layer.
  • Figure 2: Proposed training objective: For each of the training graph, we generate a number of augmented samples by randomly adding or removing edges. The node embedding of these augmented samples are decoded non-parametrically, and compared with the corresponding original graph to train the T-GAE encoder.
  • Figure 3: The pre-trained encoder operates on out-of-distribution samples. The generated node embeddings are then matched greedily.
  • Figure 4: Graph matching performance comparison of T-GAE,T-GAE trained on a single graph(T-GAE single), the untrained T-GAE (T-GAE untrained), and GAE. The proposed training objective and encoder structure helps to prompt the expressiveness of GNN thus achieve higher accuracy as we introduce more perturbations.
  • Figure 5: Training time comparison (20 epoches) between T-GAE and WAlign for graph-matching. $\text{TGAE}\_{\text{s}}$ is the specific setting where we train the encoder GNN according to Equation (7), whereas $\text{TGAE}\_{\text{t}}$ means training according to Equation (8) on a family of graphs. (Celegans, Arenas, Cora, Douban)

Theorems & Definitions (4)

  • Definition 2.1: Network Alignment
  • Theorem 3.1: xu2018howmaron2018invariant
  • Theorem 3.2
  • Remark 4.1