A safe double screening strategy for elastic net support vector machine

Abstract

Elastic net support vector machine (ENSVM) is an effective and popular classification technique. It has been widely used in many practical applications. However, solving large-scale problems still remains challenging. Inspired by its sparsity, a safe double screening rule (DSR) is proposed for accelerating ENSVM. Its main idea is to reduce the scale of the model by discarding the inactive features and samples simultaneously. In this way, the computational speed can be accelerated. Another superiority of DSR is safety, i.e., the discarded features and samples must be inactive. Its key strategy is to estimate the region containing optimal solution based on the feasible solution and duality gap. Thus, the DSR can be embedded into the process of solving the model until the algorithm converges. In addition, the safe keeping rule is constructed to identify the active features and samples. So, the DSR only needs to work on the remaining set after safe keeping. In this way, the screening process of DSR can be accelerated. Moreover, the Stochastic Dual Coordinate Ascent (SDCA) method is employed as an efficient solver. Numerical experiments on an artificial dataset and eighteen benchmark datasets demonstrate the feasibility and validity of our proposed method.