# Fused Partial Gromov-Wasserstein for Structured Objects

arXiv: https://arxiv.org/abs/2502.09934 · HTML: https://mlsanity.com/paper/2502.09934/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2025.

## Built on by (most cited first, 3 of 3)

- [REMAP: Regularized Matching and Partial Alignment of Video Embeddings](https://mlsanity.com/paper/2509.24382/) (2025)
- [Generalized Sobolev IPM for Graph-Based Measures](https://mlsanity.com/paper/2510.25591/) (2025)
- [Passive Dementia Screening via Facial Temporal Micro-Dynamics Analysis of In-the-Wild Talking-Head Video](https://mlsanity.com/paper/2511.13802/) (2025)

## Abstract (arXiv)

Structured data, such as graphs, is vital in machine learning due to its capacity to capture complex relationships and interactions. In recent years, the Fused Gromov-Wasserstein (FGW) distance has attracted growing interest because it enables the comparison of structured data by jointly accounting for feature similarity and geometric structure. However, as a variant of optimal transport (OT), classical FGW assumes an equal mass constraint on the compared data. In this work, we relax this mass constraint and propose the Fused Partial Gromov-Wasserstein (FPGW) framework, which extends FGW to accommodate unbalanced data. Theoretically, we establish the relationship between FPGW and FGW and prove the metric properties of FPGW. Numerically, we introduce Frank-Wolfe solvers and Sinkhorn solvers for the proposed FPGW framework. Finally, we evaluate the FPGW distance through graph matching, graph classification and graph clustering experiments, demonstrating its robust performance.