LINEX Support Vector Machine for Large-Scale Classification

Traditional soft margin support vector machine usually uses hinge loss to build a classifier with the “maximum-margin” principle. However, C-SVM depends on support vectors causing the loss of data information. Then, least square support vector machine is proposed with square loss (
$l_{2}$
-loss). It establishes equality constraints instead of inequalities and considering all the instances. However, the square loss is still not the perfect one, since it gives equivalent punishment to the instances at both sides of the center plane. It does not match the reality considering the instances between two center planes deserve heavier penalty than the others. To this end, we propose a novel SVM method with the adoption of the asymmetry LINEX (linear-exponential) loss, which we called it LINEX-SVM. The LINEX loss gives different treatments to instances based on the importance of each point. It gives a heavier penalty to the points between two center planes while drawing light penalty to the points outside of the corresponding center planes. The comprehensive experiments have been implemented to validate the effectiveness of the LINEX-SVM.