# Joint Optimal Transport and Embedding for Network Alignment

arXiv: https://arxiv.org/abs/2502.19334 · HTML: https://mlsanity.com/paper/2502.19334/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 87 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 30 of 32)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Multilingual Knowledge Graph Embeddings for Cross-lingual Knowledge Alignment](https://mlsanity.com/paper/1611.03954/) (2016)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Relation-Aware Entity Alignment for Heterogeneous Knowledge Graphs](https://mlsanity.com/paper/1908.08210/) (2019)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [EE-Net: Exploitation-Exploration Neural Networks in Contextual Bandits](https://mlsanity.com/paper/2110.03177/) (2021)
- [REGAL: Representation Learning-based Graph Alignment](https://mlsanity.com/paper/1802.06257/) (2018)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [AceKG: A Large-scale Knowledge Graph for Academic Data Mining](https://mlsanity.com/paper/1807.08484/) (2018)
- [Ensuring User-side Fairness in Dynamic Recommender Systems](https://mlsanity.com/paper/2308.15651/) (2023)
- [Towards Unified Multi-Modal Personalization: Large Vision-Language Models for Generative Recommendation and Beyond](https://mlsanity.com/paper/2403.10667/) (2024)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [COPT: Coordinated Optimal Transport for Graph Sketching](https://mlsanity.com/paper/2003.03892/) (2020)
- [COIN: Co-Cluster Infomax for Bipartite Graphs](https://mlsanity.com/paper/2206.00006/) (2022)
- [APEX2: Adaptive and Extreme Summarization for Personalized Knowledge Graphs](https://mlsanity.com/paper/2412.17336/) (2024)
- [Unsupervised Belief Representation Learning with Information-Theoretic Variational Graph Auto-Encoders](https://mlsanity.com/paper/2110.00210/) (2021)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [Privacy-Preserving Graph Machine Learning from Data to Computation: A Survey](https://mlsanity.com/paper/2307.04338/) (2023)
- [A Collaborative Ensemble Framework for CTR Prediction](https://mlsanity.com/paper/2411.13700/) (2024)
- [Optimal Transport-based Alignment of Learned Character Representations for String Similarity](https://mlsanity.com/paper/1907.10165/) (2019)
- [WL-Align: Weisfeiler-Lehman Relabeling for Aligning Users across Networks via Regularized Representation Learning](https://mlsanity.com/paper/2212.14182/) (2022)
- [Neural Exploitation and Exploration of Contextual Bandits](https://mlsanity.com/paper/2305.03784/) (2023)

## Built on by (most cited first, 10 of 10)

- [Pave Your Own Path: Graph Gradual Domain Adaptation on Fused Gromov-Wasserstein Geodesics](https://mlsanity.com/paper/2505.12709/) (2025)
- [PLANETALIGN: A Comprehensive Python Library for Benchmarking Network Alignment](https://mlsanity.com/paper/2505.21366/) (2025)
- [Harnessing Consistency for Robust Test-Time LLM Ensemble](https://mlsanity.com/paper/2510.13855/) (2025)
- [Prune as You Generate: Online Rollout Pruning for Faster and Better RLVR](https://mlsanity.com/paper/2603.24840/) (2026)
- [Graph Data Selection for Domain Adaptation: A Model-Free Approach](https://mlsanity.com/paper/2505.17293/) (2025)
- [Predict, Don't Iterate: Efficient Adaptive-Length Infilling for Diffusion Language Models](https://mlsanity.com/paper/2609.02108/) (2026)
- [Graph homophily booster: Reimagining the role of discrete features in heterophilic graph learning](https://mlsanity.com/paper/2602.07256/) (2026)
- [AvAtar: Learning to Align via Active Optimal Transport](https://mlsanity.com/paper/2605.24395/) (2026)
- [Scalable Optimal Transport Algorithm for Network Alignment](https://mlsanity.com/paper/2607.11952/) (2026)
- [From Inference to Adaptation: A Unified Optimal Transport View of Vision Language Model](https://mlsanity.com/paper/2608.18339/) (2026)

## Abstract (arXiv)

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.