Abstract：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.
康倩, 周水生. 光滑有下界的奖惩结合损失函数的最大间隔双球模型[J]. 模式识别与人工智能, 2021, 34(10): 885-897.
KANG Qian, ZHOU Shuisheng. Maximum Margin of Twin Sphere Model via Combined Smooth Reward-Penalty Loss Function with Lower Bound. , 2021, 34(10): 885-897.
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