Joint Optimal Transport and Embedding for Network Alignment

TL;DR

JOENA tackles the network alignment problem by unifying two complementary paradigms: embedding-based learning and optimal transport. It introduces a joint objective that couples a learnable OT cost with an adaptive sampling mechanism, enabling end-to-end training and mitigating embedding collapse via a learnable transformation g_\lambda on the OT mapping. The framework uses RWR-encoded structure, a shared MLP for embeddings, and FGW-based OT optimization, with an alternating scheme that guarantees convergence. Empirically, JOENA achieves up to 16-31% improvements in MRR over state-of-the-art methods and up to 20x faster inference, while remaining robust to both structural and attribute noises. The work demonstrates that end-to-end, learnable OT costs and adaptive sampling substantially enhance both accuracy and scalability in cross-network node alignment, offering a practical, scalable solution for real-world multi-network mining tasks.

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.

Figures (7)

• Figure 1: An example of embedding-based methods with hand-crafted sampling strategies. Due to edge noise, $(a_1,b_1)$ is identified as a false negative intra-network pair, pushing $(b_1,b_2)$ that should be aligned far apart. Likewise, $(d_1,d_2)$ fails to align due to attribute noise on $d_1$. Best viewed in color.
• Figure 2: An overview of JOENA, including RWR encoding, embedding learning and OT optimization. RWR encoding and raw node attributes are processed by a shared MLP, supervised by the ranking loss based on the OT-based sampling strategy. The OT mapping is optimized via cost matrices derived from the learned embeddings, further transformed into a sampling strategy by the learnable transformation $g_\lambda$.
• Figure 3: Scalability results. JOENA achieves the best scalability results with up to 20$\times$ speed-up in inference time and up to 5$\times$ scale-up in network size.
• Figure 4: Performance comparison of five alignment methods under different levels of structure and attribute noise.
• Figure 5: MRR with different $\lambda$. Our learned $\lambda$ consistently achieves the best MRR on both datasets.

Theorems & Definitions (8)

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