L2P-Norm Distance Twin Support Vector Machine

A twin support vector machine (TWSVM) is an effective classifier, especially for binary data, which is defined by squared l
₂
-norm distance in the objective function. Since squared l
₂
-norm distance is susceptible to outliers, it is desirable to develop a revised TWSVM. In this paper, a new robust TWSVM via l
_2,p
-norm formulations was proposed, because it suppress the influence of outliers better than l
₁
-norm or squared l
₂
-norm minimizations. However, the resulted objective is challenging to solve, because it is non-smooth and non-convex. As an important work, we systematically derive an efficient iterative algorithm to minimize the pth order of l
₂
-norm distances. Theoretical support shows that the iterative algorithm is effective in the resolution to improve TWSVM via l
_2,p
-norm instead of squared l
₂
-norm distances. A large number of experiments show that l
_2,p
-norm distances twin support vector machine can treat the noise data effectively and has a better accuracy.