用最优传输保持多视图数据结构，提升融合效果。
Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport
- 基于最优传输构建视图间关系对齐，不依赖线性假设。
- 在合成流形与真实数据集上，结构保留率显著优于传统方法。
- 适合处理几何异质或非线性扭曲的多视图数据任务。
多视图数据分析旨在整合同一样本的多种表示以恢复一致的低维结构。传统方法常依赖特征拼接或显式对齐假设，在异构几何或非线性失真下表现受限。本文提出两种基于格罗莫夫-沃瑟斯坦（Gromov-Wasserstein, GW）最优传输的几何感知多视图嵌入策略。第一种称为Mean-GWMDS，通过平均各视图的距离矩阵，并应用基于GW的多维缩放获得代表性嵌入；第二种称为Multi-GWMDS，采用选择式范式，通过GW对齐生成多个几何一致的候选嵌入并择优选取。在合成流形和真实数据集上的实验表明，所提方法能有效保持跨视图的内在关系结构。结果验证了基于GW的方法在多视图表示学习中具备灵活性与理论一致性。
原文摘要 · Abstract (English)
Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions, which become restrictive under heterogeneous geometries or nonlinear distortions. In this work, we propose two geometry-aware multi-view embedding strategies grounded in Gromov-Wasserstein (GW) optimal transport. The first, termed Mean-GWMDS, aggregates view-specific relational information by averaging distance matrices and applying GW-based multidimensional scaling to obtain a representative embedding. The second strategy, referred to as Multi-GWMDS, adopts a selection-based paradigm in which multiple geometry-consistent candidate embeddings are generated via GW-based alignment and a representative embedding is selected. Experiments on synthetic manifolds and real-world datasets show that the proposed methods effectively preserve intrinsic relational structure across views. These results highlight GW-based approaches as a flexible and principled framework for multi-view representation learning.
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