Tverberg's theorem and multi-class support vector machines
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916223084658688 |
|---|---|
| author | Soberón, Pablo |
| author_facet | Soberón, Pablo |
| contents | We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions to classify sets of points, and can be computed using existing binary SVM algorithms in higher-dimensional spaces, including soft-margin SVM algorithms. We describe how the theoretical guarantees of standard support vector machines transfer to these new classes of multi-class support vector machines. We give a new simple proof of a geometric characterization of support vectors for largest margin SVMs by Veelaert. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tverberg's theorem and multi-class support vector machines Soberón, Pablo Machine Learning 52A35, 52C35, 62R07, 62R40 We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions to classify sets of points, and can be computed using existing binary SVM algorithms in higher-dimensional spaces, including soft-margin SVM algorithms. We describe how the theoretical guarantees of standard support vector machines transfer to these new classes of multi-class support vector machines. We give a new simple proof of a geometric characterization of support vectors for largest margin SVMs by Veelaert. |
| title | Tverberg's theorem and multi-class support vector machines |
| topic | Machine Learning 52A35, 52C35, 62R07, 62R40 |
| url | https://arxiv.org/abs/2404.16724 |