Unsupervised Ground Metric Learning
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911061486075904 |
|---|---|
| author | Auffenberg, Janis Bresch, Jonas Melnyk, Oleh Steidl, Gabriele |
| author_facet | Auffenberg, Janis Bresch, Jonas Melnyk, Oleh Steidl, Gabriele |
| contents | Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyré proposed to simultaneously learn optimal transport (OT) cost matrices between samples and features of the dataset. This leads to the task of finding positive eigenvectors of a certain nonlinear function that maps cost matrices to OT distances. Having this basic idea in mind, we consider both the algorithmic and the modeling part of unsupervised metric learning. First, we examine appropriate algorithms and their convergence. In particular, we propose to use the stochastic random function iteration algorithm and prove that it converges linearly for our setting, although our operators are not paracontractive as it was required for convergence so far. Second, we ask the natural question if the OT distance can be replaced by other distances. We show how Mahalanobis-like distances fit into our considerations. Further, we examine an approach via graph Laplacians. In contrast to the previous settings, we have just to deal with linear functions in the wanted matrices here, so that simple algorithms from linear algebra can be applied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unsupervised Ground Metric Learning Auffenberg, Janis Bresch, Jonas Melnyk, Oleh Steidl, Gabriele Optimization and Control Machine Learning Numerical Analysis Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyré proposed to simultaneously learn optimal transport (OT) cost matrices between samples and features of the dataset. This leads to the task of finding positive eigenvectors of a certain nonlinear function that maps cost matrices to OT distances. Having this basic idea in mind, we consider both the algorithmic and the modeling part of unsupervised metric learning. First, we examine appropriate algorithms and their convergence. In particular, we propose to use the stochastic random function iteration algorithm and prove that it converges linearly for our setting, although our operators are not paracontractive as it was required for convergence so far. Second, we ask the natural question if the OT distance can be replaced by other distances. We show how Mahalanobis-like distances fit into our considerations. Further, we examine an approach via graph Laplacians. In contrast to the previous settings, we have just to deal with linear functions in the wanted matrices here, so that simple algorithms from linear algebra can be applied. |
| title | Unsupervised Ground Metric Learning |
| topic | Optimization and Control Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2507.13094 |