A Rank-One-Update Method for the Training of Support Vector Machines
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912315620720640 |
|---|---|
| author | Jarre, Florian |
| author_facet | Jarre, Florian |
| contents | This paper considers convex quadratic programs
associated with the training of support vector machines (SVM).
Exploiting the special structure of the SVM problem a new
type of active set method with long cycles and stable rank-one-updates
is proposed and tested (CMU: cycling method with updates).
The structure of the problem allows for a repeated simple increase
of the set of inactive constraints while controlling its size. This is
followed by minimization steps with cheap updates of a matrix factorization.
A widely used approach for solving SVM problems is the
alternating direction method SMO,
a method that is very efficient for low accuracy.
The new active set approach allows for higher accuracy
results at moderate computational cost. To relate both approaches,
the effect of the accuracy on the running time and on the
predictive quality of the SVM is compared with some numerical examples.
A surprising result of the numerical examples is that only a
very small number of cycles (each consisting of less than 2n
steps) was used for CMU. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Rank-One-Update Method for the Training of Support Vector Machines Jarre, Florian Optimization and Control 90-04, 90-08, 90C20 G.4 This paper considers convex quadratic programs associated with the training of support vector machines (SVM). Exploiting the special structure of the SVM problem a new type of active set method with long cycles and stable rank-one-updates is proposed and tested (CMU: cycling method with updates). The structure of the problem allows for a repeated simple increase of the set of inactive constraints while controlling its size. This is followed by minimization steps with cheap updates of a matrix factorization. A widely used approach for solving SVM problems is the alternating direction method SMO, a method that is very efficient for low accuracy. The new active set approach allows for higher accuracy results at moderate computational cost. To relate both approaches, the effect of the accuracy on the running time and on the predictive quality of the SVM is compared with some numerical examples. A surprising result of the numerical examples is that only a very small number of cycles (each consisting of less than 2n steps) was used for CMU. |
| title | A Rank-One-Update Method for the Training of Support Vector Machines |
| topic | Optimization and Control 90-04, 90-08, 90C20 G.4 |
| url | https://arxiv.org/abs/2503.10482 |