一种加权核鉴别分析方法

Kernel Fisher Discriminant Analysis with Weighted Schemes

基于Fisher准则的核鉴别分析法(KDA)是最常用的非线性特征提取方法之一,但对于多类识别问题,就分类率而言Fisher准则并不是最优。本文提出了一种加权核鉴别分析方法(KIDA)。首先利用非线性映射将原始样本隐式地映射到高维隐特征空间;在此特征空间内使用权函数重新估计类间离散度矩阵得到优化的准则函数;最后采用同时对角化方案求解最优鉴别矢量。在ORL和Yale人脸数据库上的实验结果验证了本文方法的有效性。

Kernel fisher discriminant analysis （KDA） is one of the most used tools for nonlinear feature extraction. However, in multiclass case, the fisher criterion is non-optimal for the classification rate. A kernel based improved discriminant analysis （KIDA） is presented to solve the problem. In the proposed framework, origin samples are firstly projected into a feature space by an implicit nonlinear projection. After reconstructing class scatter matrix in the feature space by weighted schemes, the kernel method is used to obtain a modified fisher criterion. Finally, the simultaneous diagonalization is employed to find lower-dimensional nonlinear features with significant discrimination power. Experiments on the ORL and Yale face databases show that the proposed method is efficient in nonlinear feature extracting.