The support vector machine (SVM) is a popularly used classifier in applications such as pattern recognition, texture mining and image retrieval owing to its flexibility and interpretability. However, its performance deteriorates when the response classes are imbalanced. To enhance the performance of the support vector machine classifier in the imbalanced cases we investigate a new two stage method by adaptively scaling the kernel function. Based on the information obtained from the standard SVM in the first stage, we conformally rescale the kernel function in a data adaptive fashion in the second stage so that the separation between two classes can be effectively enlarged with incorporation of observation imbalance. The proposed method takes into account the location of the support vectors in the feature space, therefore is especially appealing when the response classes are imbalanced. The resulting algorithm can efficiently improve the classification accuracy, which is confirmed by intensive numerical studies as well as a real prostate cancer imaging data application.

支持向量机（SVM）由于具有灵活性和可解释性，因此在诸如模式识别，纹理挖掘和图像检索等应用中被广泛使用。但是，当响应类不平衡时，其性能会下降。为了提高不平衡情况下支持向量机分类器的性能，我们通过自适应缩放内核函数来研究一种新的两阶段方法。根据第一阶段从标准SVM获得的信息，我们在第二阶段以数据自适应方式共形缩放内核函数，以便在合并观察不平衡的情况下有效地扩大两类之间的距离。所提出的方法考虑了支持向量在特征空间中的位置，因此，当响应类不平衡时，它尤其有吸引力。由此产生的算法可以有效地提高分类精度，这已通过深入的数值研究以及实际的前列腺癌成像数据应用得到了证实。