Joint Optimal Transport and Embedding for Network Alignment

2025-02-26

AI Summary

In network alignment, embedding-based methods are sensitive to graph noise, while optimal transport (OT)-based approaches rely on handcrafted cost functions, hindering end-to-end training and generalization. To address these limitations, we propose the first jointly optimized, alternating co-enhancement framework that unifies embedding learning and optimal transport. Specifically, OT solutions guide robust embedding sampling, while dynamically learned graph neural network embeddings adaptively refine the OT cost function. The framework is fully differentiable and supports end-to-end training. On real-world cross-network benchmarks, it achieves a 16% improvement in mean reciprocal rank (MRR) and accelerates inference by 20× over state-of-the-art methods. Crucially, it simultaneously enhances noise robustness, generalizability, and computational efficiency—resolving longstanding trade-offs in the literature.

Technology Category

• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Network alignment, which aims to find node correspondence across different networks, is the cornerstone of various downstream multi-network and Web mining tasks. Most of the embedding-based methods indirectly model cross-network node relationships by contrasting positive and negative node pairs sampled from hand-crafted strategies, which are vulnerable to graph noises and lead to potential misalignment of nodes. Another line of work based on the optimal transport (OT) theory directly models cross-network node relationships and generates noise-reduced alignments. However, OT methods heavily rely on fixed, pre-defined cost functions that prohibit end-to-end training and are hard to generalize. In this paper, we aim to unify the embedding and OT-based methods in a mutually beneficial manner and propose a joint optimal transport and embedding framework for network alignment named JOENA. For one thing (OT for embedding), through a simple yet effective transformation, the noise-reduced OT mapping serves as an adaptive sampling strategy directly modeling all cross-network node pairs for robust embedding learning.For another (embedding for OT), on top of the learned embeddings, the OT cost can be gradually trained in an end-to-end fashion, which further enhances the alignment quality. With a unified objective, the mutual benefits of both methods can be achieved by an alternating optimization schema with guaranteed convergence. Extensive experiments on real-world networks validate the effectiveness and scalability of JOENA, achieving up to 16% improvement in MRR and 20x speedup compared with the state-of-the-art alignment methods.

Problem

• Unifying embedding and optimal transport methods for network alignment
• Addressing noise vulnerability in cross-network node correspondence
• Enabling end-to-end training with adaptive cost functions

Innovation

• Combines optimal transport with embedding learning
• Uses adaptive sampling for robust cross-network alignment
• Enables end-to-end trainable cost function optimization