A new method to minimize the recognition risk of ballistic targets with rejection options is proposed to focus on the unsymmetry problem of different misclassification costs in ballistic targets recognition. The receiver operating characteristic(ROC)curve is applied to analyze the relationship between the true positive rate and false alarm rate and the decision threshold from the perspective of probability distribution. Loss functions of a cost-sensitive model and a cost-sensitive model with rejection options are defined
and the condition to be met for minimizing the loss function is derived. The optimal rejection thresholds are obtained via the tangent of ROC curve. The proposed method is validated on high resolution range profile(HRRP)datasets of two kinds of targets. The results show that the proposed method obtains the unique optimal rejection threshold
and minimizes the classification risk as well. The weaknesses of traditional methods are overcome and the reliability and stability are improved. It shows that the method has good values in theoretical analysis and realistic applications.
HU Xiaosheng, ZHONG Yong. Support vector machine imbalanced data classification based on weighted clustering centroid [J]. CAAI Transactions on Intelligent Systems, 2013, 8(3): 261-265.
DATTA S, DAS S. Near-Bayesian support vector machines for imbalanced data classification with equal or unequal misclassification costs [J]. Neural Networks, 2015, 70(12): 39-52.
JIANG L, LI C, WANG S S. Cost-sensitive Bayesian network classifiers [J]. Pattern Recognition Letters, 2014, 45(2): 211-216.
IBANEZ A, BIELZA C, LARRANAGA P. Cost-sensitive selective naïve Bayes classifiers for predicting the increase of the h-index for scientific journals [J]. Neurocomputing, 2014, 135(4): 42-52.
XIONG Bingyan, WANG Guoyin, DENG Weibin. Hierarchical cost sensitive decision tree and its application in the prediction of the mobile phone replacement [J]. Journal of Shandong University, 2015, 45(5): 36-42.
SUN Y M, KARNEL M S, WONG A, et al. Cost-sensitive boosting for classification of imbalanced data [J]. Pattern Recognition, 2007, 40(12): 3358-3378.
LIU Chuanwu, ZHANG Zhijun, BI Duyan. Novel refuse-recognition algorithm of radar automatic target recognition system [J]. Systems Engineering and Electronics, 2009, 31(8): 1846-1850.
HUANG Yao, LIU Sisong, KONG Rui. SVM-based hand-written character recognition with reject option [J]. Electronics Quality, 2011(4): 5-7.
FUMERA G, ROLI F, GIACINTO G. Multiple reject thresholds for improving classification reliability [C]∥Proceedings of the Joint International Workshops on Advances in Pattern Recognition. Berlin, Germany: Springer-Verlag, 2000: 863-871.
FUMERA G, ROLI F, GIACINTO G. Reject option with multiple thresholds [J]. Pattern Recognition, 2000, 33(12): 2099-2101.
ZHENG Enhui, XU Huan. Binary classification algorithm with class-dependent reject cost [J]. Control and Decision, 2013, 28(6): 855-860.
TORTORELLA F. An optimal reject rule for binary classifiers [C]∥ Proceedings of the Joint International Workshops on Advances in Pattern Recognition. Berlin, Germany: Springer-Verlag, 2000: 611-620.