# Optimizing Sparse Generalized Singular Vectors for Feature Selection in Proximal Support Vector Machines with Application to Breast and Ovarian Cancer Detection

arXiv: https://arxiv.org/abs/2410.03978 · HTML: https://mlsanity.com/paper/2410.03978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 33 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [Sparse Generalized Eigenvalue Problem via Smooth Optimization](https://mlsanity.com/paper/1408.6686/) (2014)

## Abstract (arXiv)

This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by ℓ1-norm and ℓq-penalty for 0<q<1, resulting in the ℓ1-GSVP and ℓq-GSVP formulations. The solutions of these problems are determined by applying the proximal gradient descent algorithm with a fixed step size. The inherent sparsity levels within the computed solutions are exploited for feature selection, and subsequently, binary classification with non-parallel Support Vector Machines (SVM). For our feature selection task, SVM is integrated into the ℓ1-GSVP and ℓq-GSVP frameworks to derive the ℓ1-GSVPSVM and ℓq-GSVPSVM variants. Machine learning applications to cancer detection are considered. We remarkably report near-to-perfect balanced accuracy across breast and ovarian cancer datasets using a few selected features.