核不相关鉴别分析以及它在字符识别中的应用

核不相关鉴别分析是在线性不相关鉴别分析的基础上发展起来的．然而，由于核函数的运用，计算核不相关矢量集变得更加复杂．为了解决这个问题，提出一种解决核不相关鉴别分析的有效算法．该算法巧妙地利用了矩阵的分解，然后在一个矩阵对上进行广义奇异值分解．与此同时，提出了几个相关的定理．最重要的是，提出的算法能克服核不相关鉴别分析中矩阵的奇异问题．在某种意义上，提出的算法拓宽了已有的算法，即从线性问题到非线性问题．最后，用手写数字字符识别实验来验证提出的算法是可行和有效的．

Kernel Uncorrelated Discriminant Analysis and Its Application to Handwritten Character Recognition

Based on uncorrelated discriminant analysis, kernel uncorrelated discriminant analysis is developed. However, computing kernel uncorrelated vectors is computationally expensive due to the utilization of kernel functions. In order to overcome this problem, an effective method for solving kernel uncorrelated discriminant analysis is proposed in this paper. Firstly, the proposed algorithm smartly uses the decomposition of matrices. Then the generalized singular value decomposition on the matrix pair is carried out. At the same time, several related theorems are proposed. Most importantly, the proposed method can overcome the singular problem of matrices in kernel uncorrelated discriminant analysis. In some sense, the proposed method extends existing methods, namely, from linear problems to non-linear problems. Finally, experimental results on handwritten numeral characters show that the proposed method is effective and feasible.