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

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.