Dimension Reduction by Support Vector Machine

Motivated by the support vector machine (SVM), we propose a novel dimensionality reduction method that reduces data dimensionality while preserving maximal cluster separation. Unlike existing methods, our approach leverages the geometric properties of data points and does not impose distributional assumptions. Furthermore, we introduce a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{l}_{0}$</tex> -norm constraint, a form of nonconvex regularization, to promote sparsity, thereby enhancing model identifiability and interpretability. Numerical studies and an real-data analysis demonstrate the effectiveness of our method.