一种新的高维小样本情况下的线性判别分析  

New Linear Discriminant Analysis in High-dimensional and Small Sample Size Case

作　　者：黄国宏[1] 刘东峰[1] 

机构地区：[1]广东工业大学信息工程学院,广州510006

出　　处：《科学技术与工程》2008年第10期2575-2578,共4页Science Technology and Engineering

基　　金：广东省自然科学基金(5001835)资助

摘　　要：针对高维小样本问题,对传统的"PCA+LDA"处理方法进行了两方面改进:首先,在降维过程中,选取主元的原则是使得Fisher准则函数取得较大值,而不是使得投影后样本在投影空间里的方差最小;其次,根据训练样本在模式空间的几何分布情况,重新定义了类内散度矩阵Sw,使之更准确地反映类内样本间的分布关系,提高了准则模型的精确性。实验结果证明了本文方法的有效性,和同类方法相比,就识别率而言,有较大提高。For the high-dimensional and small sample size problem, a different ＂ PCA ＋ LDA＂ method is adopted. Firstly, in the process of reducing the dimensionality of the feature space using PCA, the way selecting the principal components of PCA is that the principal components have stronger Fisher discrimination capabilities than the rest. Secondly, a new definition of within-class scatter matrix is presented according to the geometrical distribution of samples, which can more exactly reflect the inherent distributing relation of samples in same class and improve the accuracy of Fisher criterion. Experimental results show that new optimal discriminant vectors have more powerful ability of feature extraction in terms of rates of classification.

关 键 词：特征提取 Fisher准则函数 高维小样本 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]