一种基于核的快速非线性鉴别分析方法

基于“核技巧”提出的新的非线性鉴别分析方法在最小二乘意义上与基于核的Fisher鉴别分析方法等效，相应鉴别方向通过一个线性方程组得出，计算代价较小，相应分类实现极其简便．该方法的最大优点是，对训练数据进行筛选，可使构造鉴别矢量的“显著”训练模式数大大低于总训练模式数，从而使得测试集的分类非常高效；同时，设计出专门的优化算法以加速“显著”训练模式的选取．实验表明，这种非线性方法不仅具有明显的效率上的优势，且具有不低于基于核的Fisher鉴别分析方法的性能．

A Fast Kernel-Based Nonlinear Discriminant Analysis Method

The least squares solution of novel discriminant analysis method, based on kernel trick, is equivalent to kernel-based Fisher discriminant analysis. The discriminant vector of the novel method is efficiently solved from linear equations. Moreover, corresponding classifying strategy is very simple. The most striking advantage of the novel method is that only a few original training samples are sorted as "significant" nodes for constructing discriminant vector. As a result, corresponding testing is much more efficient than the naive kernel Fisher discriminant analysis. In addition an appropriative, optimized algorithm is developed to improve the efficiency of selecting " significant" nodes. Experiments on benchmarks and face databases show that the performance of the novel method is comparative to kernel-based Fisher discriminant analysis, with superiority in efficiency.