提出了用于手写字符识别的非线性主动判别函数，是线性主动判别函数在手写字符非线性变化情况下的推广。该方法利用Kernel PCA分析捕捉和表示这种非线性变化。将输入空间非线性映射为特征空间，在特征空间的主子空间中生成最优主动原型模板，其与字符特征向量在特征空间主子空间的投影之间的距离即为非线性主动判别函数；同时，基于最小分类错误准则对该函数进行了优化。实验结果表明，非线性主动判别函数获得了比线性主动判别函数更高的识别率。

A generalization of Linear Active Discriminant Functions named as Nonlinear Active Discriminant Functions (nonlinear ADF) to deal with nonlinear deformations of handwritten character is proposed. In Nonlinear ADF, Kernel PCA is applied to capture and represent the nonlinear deformations. Input space is mapped to feature space through nonlinear mapping. Then an optimal active prototype model is produced in principal subspace of the feature space and the distance between it and the projection of character feature vector in the principal subspace is defined as Nonlinear ADF. In addition, the Nonlinear ADF is further optimized using Minimum Classification Error criterion. Experimental results demonstrated that Nonlinear ADF has achieved a higher recognition rate than that of Linear ADF.