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Towards Effective and Efficient Graph Alignment without Supervision

Songyang Chen, Youfang Lin, Yu Liu, Shuai Zheng, Lei Zou

TL;DR

This work formalizes the exploitation of local and global graph information as the ``local representation, global alignment''paradigm, and presents a new ``global representation and alignment''paradigm to resolve the mismatch between the two phases in the alignment process.

Abstract

Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport (OT)-based approaches, we observe their limitations in terms of model accuracy-efficiency tradeoff. By focusing on the exploitation of local and global graph information, we formalize them as the ``local representation, global alignment'' paradigm, and present a new ``global representation and alignment'' paradigm to resolve the mismatch between the two phases in the alignment process. We then propose \underline{Gl}obal representation and \underline{o}ptimal transport-\underline{b}ased \underline{Align}ment (\texttt{GlobAlign}), and its variant, \texttt{GlobAlign-E}, for better \underline{E}fficiency. Our methods are equipped with the global attention mechanism and a hierarchical cross-graph transport cost, able to capture long-range and implicit node dependencies beyond the local graph structure. Furthermore, \texttt{GlobAlign-E} successfully closes the time complexity gap between representative embedding and OT-based methods, reducing OT's cubic complexity to quadratic terms. Through extensive experiments, our methods demonstrate superior performance, with up to a 20\% accuracy improvement over the best competitor. Meanwhile, \texttt{GlobAlign-E} achieves the best efficiency, with an order of magnitude speedup against existing OT-based methods.

Towards Effective and Efficient Graph Alignment without Supervision

TL;DR

This work formalizes the exploitation of local and global graph information as the ``local representation, global alignment''paradigm, and presents a new ``global representation and alignment''paradigm to resolve the mismatch between the two phases in the alignment process.

Abstract

Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport (OT)-based approaches, we observe their limitations in terms of model accuracy-efficiency tradeoff. By focusing on the exploitation of local and global graph information, we formalize them as the ``local representation, global alignment'' paradigm, and present a new ``global representation and alignment'' paradigm to resolve the mismatch between the two phases in the alignment process. We then propose \underline{Gl}obal representation and \underline{o}ptimal transport-\underline{b}ased \underline{Align}ment (\texttt{GlobAlign}), and its variant, \texttt{GlobAlign-E}, for better \underline{E}fficiency. Our methods are equipped with the global attention mechanism and a hierarchical cross-graph transport cost, able to capture long-range and implicit node dependencies beyond the local graph structure. Furthermore, \texttt{GlobAlign-E} successfully closes the time complexity gap between representative embedding and OT-based methods, reducing OT's cubic complexity to quadratic terms. Through extensive experiments, our methods demonstrate superior performance, with up to a 20\% accuracy improvement over the best competitor. Meanwhile, \texttt{GlobAlign-E} achieves the best efficiency, with an order of magnitude speedup against existing OT-based methods.
Paper Structure (32 sections, 2 theorems, 17 equations, 9 figures, 4 tables, 1 algorithm)

This paper contains 32 sections, 2 theorems, 17 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Challenges
  3. Our Contributions
  4. Preliminary and Problem
  5. The Alignment Paradigm: Local vs. Global
  6. Formalizing Existing Alignment Paradigms
  7. Local Representation/Propagation
  8. Global Comparison/Transport
  9. Mismatch between Local Representation and Global Alignment
  10. Global Representation and Alignment
  11. Our GlobAlign Model
  12. Model Overview
  13. Global Representation via Self-Attention
  14. Hierarchical Cross-Graph Transport Cost
  15. Improving Model Efficiency
  16. ...and 17 more sections

Key Result

Lemma 1

Local representation (e.g., using GNNs) is insufficient for embedding-based alignment.

Figures (9)

  • Figure 1: Running time (s) vs. accuracy (Hits@1) on three widely-adopted datasets slotaligngwlwaligngtcaligndhot. Existing embedding and OT-based methods show similar performance in terms of efficiency-accuracy tradeoff. Our GlobAlign model significantly surpasses existing solutions in accuracy, while our GlobAlign-E model achieves up to one order of magnitude speedup with comparable performance
  • Figure 2: A toy example to show the limitation of local representation for graph alignment
  • Figure 3: Illustration of node alignment from OT perspective
  • Figure 4: The GlobAlign model framework
  • Figure 5: Running time comparison. Vertical bars with diagonal lines represent methods that exceed the 3-hour time limit
  • ...and 4 more figures

Theorems & Definitions (8)

  • Definition 1: Unsupervised Graph Alignment
  • Definition 2: Local Representation
  • Definition 3: Global Alignment
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 4: Global Representation