Abstract: In this paper，a novel nonlinear feature extraction method，parameterized direct linear discriminant analysis in hidden space（PD-LDA-HS） is proposed.The main idea of PD-LDA-HS is that a kernel function is used to nonlinearly map the original input space into a hidden space，in which problems such as that within-class scatter is always singular are conducted by using PD-LDA in feature extraction.Different from the existing kernel feature extraction methods，the kernel function used in the proposed one is not required to satisfy Mercer’s theorem so that they can be chosen from a wide range.It is more important that due to the adoption of PD-LDA in hidden space，not only the advantages of PD-LDA are preserved，but also nonlinear feature of samples is effectively extracted.A more rational weight coefficient matrix is proposed to improve the classification performance.The experimental results based on the sub-set of FERET face database show the effectiveness of PD-LDA-HS.

Key words: hidden space, direct Linear Discriminant Analysis（LDA）, weight coefficient, feature extraction

摘要： 提出了一种新的非线性特征抽取方法——隐空间中参数化直接鉴别分析。其主要思想是利用一核函数将原始输入空间非线性变换到隐空间，针对在该隐空间中类内散布矩阵总是奇异等问题，利用参数化直接鉴别分析进行特征抽取。与现有的核特征抽取方法不同的是，该方法不需要核函数满足Mercer 定理，从而增加了核函数的选择范围。更为重要的是，由于在隐空间中采用了参数化直接鉴别分析，不仅保留了参数化直接鉴别分析的优点，而且有效地抽取了样本的非线性特征；在该方法中提出了一个更为合理的加权系数矩阵，提高了分类性能。在FERET人脸数据库子库上的实验结果验证了该方法的有效性。

关键词: 隐空间, 直接鉴别分析, 加权系数, 特征抽取