Adaptive loss function based least squares one-class support vector machine

Abstract

• Adaptive loss function based least squares one-class support vector machine is proposed. • Fisher consistency of the adaptive loss function is proved. • Iteratively reweighted least squares (IRLS) method is used to solve the optimization problem. • Efficiency of the proposed method is verified in comparison with its related methods. Least squares one-class support vector machine (LS-OCSVM) can accurately describe the similarity between new sample and training set. However, LS-OCSVM is very sensitive to the outliers among training samples, which means that the separating hyperplane of LS-OCSVM may deviate from the normal data even with a few outliers. To enhance the anti-outlier performance of LS-OCSVM, a novel adaptive loss function based LS-OCSVM is proposed. In the proposed method, an adaptive loss function is utilized to substitute the square loss function in the objective function of LS-OCSVM. The property of Fisher consistency for the adaptive loss function is validated from the theoretical viewpoint. The optimization problem of the proposed method is solved by the iteratively reweighted least squares (IRLS) method. In comparison with its nine related methods, the proposed method demonstrates better anti-outlier and generalization abilities on synthetic and benchmark data sets.