光滑有下界的奖惩结合损失函数的最大间隔双球模型

在极度不平衡分类问题中,球形分类器将分类正确样本的损失计为零,仅使用误分样本构造决策函数.文中提出光滑有下界的奖惩结合损失函数,将分类正确样本的损失计为负,实现对目标函数的奖励,避免边界附近噪声的干扰.基于最大间隔双球面支持向量机,利用损失函数,建立奖惩结合的最大间隔双球模型.通过牛顿法构造两个同心球.小球体在覆盖多数类样本的同时抛弃多余的空隙.大球通过增加两个同心球之间的间隔,排除少数类.实验表明,文中模型分类效果较优.

Maximum Margin of Twin Sphere Model via Combined Smooth Reward-Penalty Loss Function with Lower Bound

The loss of the correctly classified samples is counted as zero by classical spherical classifier in extremely imbalanced classification. The decision function is constructed only by misclassified samples. In this paper, a smooth reward-penalty loss function with lower bound is proposed. The loss of the correctly classified samples is counted as negative in the proposed loss function. Therefore, the reward of the objective function can be realized and the interference of noise near the boundary can be avoided. Based on maximum margin of twin spheres support vector machine, a maximum margin of twin sphere model via combined reward-penalty loss function with lower bound(RPMMTS) is established. Two concentric spheres are constructed by RPMMTS using Newton's method. The majority samples are captured in the small sphere and the extra space are eliminated at the same time. By increasing the margin between two concentric spheres, the minority samples are pushed out of the large sphere as many as possible. Experimental results show that the proposed loss function makes RPMMTS better than other unbalanced classification algorithms in classification performance.