发表机构
Instituto Federal do Ceará (IFCE); Federal University of Ceará (UFC); Sigma Nova（塞阿拉联邦学院; 塞阿拉联邦大学; Sigma Nova）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于重心蒸馏的归纳式框架，将转导式GW-MDS嵌入转化为显式神经映射，在未见样本上保持几何结构并优于直接神经GW训练。
AI 中文摘要
Gromov-Wasserstein多维缩放（GW-MDS）从关系数据中学习低维表示，但仍是转导式的，无法为未见样本提供显式映射。我们提出了一种基于重心蒸馏的归纳式框架。GW-MDS教师从训练数据中学习潜在支撑集和最优传输计划，重心投影将所得耦合转换为样本对齐的目标。神经学生网络随后学习显式的样本外映射，避免在推理时构建额外的关系矩阵和进行GW优化。我们将该方法公式化用于单视图数据，并通过多视图学生网络（具有视图特定编码器）学习共识目标和选择性投影目标，将其扩展到均值GW-MDS（Mean-GWMDS）和多GW-MDS（Multi-GWMDS）教师。我们还研究了一个仅以GW目标训练的直接神经基线。在合成和真实数据上使用欧几里得、测地线和余弦关系的实验表明，蒸馏模型在未见样本上保持了教师的几何结构，并且在样本索引的关系保持方面始终优于直接神经GW训练。这些结果确立了重心投影作为转导式GW嵌入与归纳式神经映射之间的有效桥梁。
英文摘要
Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.
CommentsThis paper was accepted at the GDDL (Geometric Distributional Deep Learning) Workshop at NeurIPS 2026
