—Support Vector Machine (SVM) has shown better performance than other methods in real world classification applications, because it gives mathematical tractability and geometrical interpretation. However, the standard SVM can suffer from outliers in either the response or the predictor space. SVM can be viewed as a penalized method with the hinge loss function and penalty functions. Instead of í µí°¿ 2 penalty function we considered the Smoothly Clipped Absolute Deviation (SCAD) function, because it has two advantages, sparse learning and unbiasedness. However, it has drawbacks of non-robustness when there are outliers in the data. We develop a robust algorithm for SVM using a weight function of the SCAD with a Local Linear Approximation (LLA) method and a Local Quadratic Approximation (LQA). We compare the performance of the proposed algorithm with the standard SVM using í µí°¿ 1 and í µí°¿ 2 penalty functions.
Paper
Full text
Robust Algorithm for Multiclass Weighted Support Vector Machine
Semantic Scholar · Computer Science · 2016
Abstract
—Support Vector Machine (SVM) has shown better performance than other methods in real world classification applications, because it gives mathematical tractability and geometrical interpretation. However, the standard SVM can suffer from outliers in either the response or the predictor space. SVM can be viewed as a penalized method with the hinge loss function and penalty functions. Instead of í µí°¿ 2 penalty function we considered the Smoothly Clipped Absolute Deviation (SCAD) function, because it has two advantages, sparse learning and unbiasedness. However, it has drawbacks of non-robustness when there are outliers in the data. We develop a robust algorithm for SVM using a weight function of the SCAD with a Local Linear Approximation (LLA) method and a Local Quadratic Approximation (LQA). We compare the performance of the proposed algorithm with the standard SVM using í µí°¿ 1 and í µí°¿ 2 penalty functions.