Abstract: A balance method for the offset of separation hyperplane of biclassification imbalanced data is proposed.Firstly，the principal eigenvalues are found respectively of the two classes of samples in feature space by using Kernel Principal Component Analysis（KPCA）.Secondly，one penalty proportion is given based on the information provided by the sizes of the two sample data and their eigenvalues.Finally，a new separation hyperplane is generated by the optimization training.The hyperplane revises the error of the standard Support Vector Machines.Experiments show the efficiency of proposed method，i.e.comparing with standard Support Vector Machines the classification error can be balanced and be also decreased.

Key words: imbalanced data, Kernel Principal Component Analysis（KPCA）, Support Vector Machines（SVM）, offset

摘要： 针对两类不平衡数据的分离超平面的偏移问题提出一种平衡方法。首先，对两类样本数据在核空间中进行核主成分分析，分别求出两类样本数据的在特征空间中的主要特征值；然后，根据两样本容量以及各自的特征值所提供的信息，对两类数据给出惩罚因子比例；最后，通过优化训练，产生一个新的分离超平面。该分类面校正了标准的支持向量机的分类误差。实验显示了所提出方法的有效性，即与标准的支持向量机相比，不仅平衡了错分率而且还能减少错分率。

关键词: 不平衡数据, 核主成分分析, 支持向量机, 偏移