Abstract: Kernel Fisher discriminant method performs well in classification; however, the fact that the classification efficiency associated with KFD descends when the number of training samples increases makes against its application. In this paper an optimized scheme on kernel Fisher discriminant method is proposed, which is with superiority in classification efficiency. The corresponding algorithms are developed for two-class problems and multi-class problems, respectively. In the scheme, only a part of training patterns, called “significant nodes”, are necessary to be adopted in classifying one test pattern. A recursive algorithm for selecting “significant nodes” is also presented in detail. The experiment on benchmarks and face image databases show that the novel method is effective and much efficient in classifying.

Key words: Fisher discriminant analysis, Kernel function, Pattern recognition, Feature space

摘要： 核Fisher鉴别分析方法是一类性能较优的方法,但 对测试样本的分类效率随着训练样本数增多而描写下降的特点使其在实际应用中受到较大限制.本文提出了一种核Fisher鉴别分析方法优化方案,并分别给出了解决两类分类和解决多于两类的分类问题的算法,该方案具有明显的分类效率上的优势.在这种方案的实现中,首先从总体训练样本中选择出”显著”训练样本,对测试样本的分类只依赖于测试样本与”显著”训练样本之间的核函数.本文还设计出了一种选择”显著”训练样本的递归算法,以降低算法的计算复杂度. 将本文算法应用于人脸图象数据库与”基准”数据集,得到了很好的实验效果.

关键词: Fisher鉴别分析, 核函数, 模式识别, 特征空间