Support vector machine (SVM) is one of well-known supervised machine learning classifier and is used widely in image classification, pattern recognition, disease diagnosis, etc. However, the high computational complexity is a major issue for large-scale classification problems. To address this issue, we propose a new truncated fraction loss function to construct a new sparse and robust SVM model (Ltf-SVM). By newly developed support vectors and a working set based on the proximal operator of truncated fraction loss, we prove the sparsity and robustness to outliers of Ltf-SVM from a theoretical perspective. When it comes to solve Ltf-SVM problems, we develop an alternating direction method of multipliers with a working set for addressing Ltf-SVM. The proposed algorithm is proven to converge globally and enjoys very low computational complexity. Moreover, numerical experiments verify its superior performance with respect to its high accuracy and high computational speed in comparison with other leading solvers.
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