Sparse and robust support vector machine with capped squared loss for large-scale pattern classification

Support vector machine (SVM), being considered one of the most efficient tools for classification, has received widespread attention in various fields. However, its performance is hindered when dealing with large-scale pattern classification tasks due to high memory requirements and running very slow. To address this challenge, we construct a novel sparse and robust SVM based on our newly proposed capped squared loss (named as L-csl-SVM). To solve L-csl-SVM, we first focus on establishing optimality theory of L-csl-SVM via our defined proximal stationary point, which is convenient for us to efficiently characterize the L-csl support vectors of L-csl-SVM. We subsequently demonstrate that the L-csl support vectors comprise merely a minor fraction of entire training data. This observation leads us to introduce the concept of the working set. Furthermore, we design a novel subspace fast algorithm with working set (named as L-csl-ADMM) for solving L-csl-SVM, which is proven that L-csl-ADMM has both global convergence and relatively low computational complexity. Finally, numerical experiments show that L-csl-ADMM has excellent performances in terms of getting the best classification accuracy, using the shortest time and presenting the smallest numbers of support vectors when solving large-scale pattern classification problems.