小样本情况下Fisher线性鉴别分析的理论及其验证

Theory of Fisher Linear Discriminant Analysis for Small Sample Size Problem and Its Verification

线性鉴别分析是特征抽取中最为经典和广泛使用的方法之一。近几年,在小样本情况下如何抽取F isher最优鉴别特征一直是许多研究者关心的问题。本文应用投影变换和同构变换的原理,从理论上解决了小样本情况下最优鉴别矢量的求解问题,即最优鉴别矢量可在一个低维空间里求得;给出了特征抽取模型,并给出求解模型的PPCA+LDA算法;在ORL人脸库3种分辨率灰度图像上进行实验。实验结果表明,PPCA+LDA算法抽取的鉴别向量有较强的特征抽取能力,在普通的最小距离分类器下能达到较高的正确识别率,而且识别结果十分稳定。

Linear discriminant analysis is one of the classical and popular methods used for feature extraction. In recent years many researchers have been absorbed in the problem of how to extract the optimal Fisher discriminant feature in small sample size case. By making use of the principle of projection transformation and isomorphic transformation, in this paper,we have solved the problem of how to gain the optimal discriminant vectors in the singular case. In fact these optimal discriminant vectors can be derived from a low dimension transformed subspace. Fulfilling the need of application, a new model for feature extraction has been put forward and a corresponding algorithm, called PPCA ＋ LDA in this paper, has been established. The experiments on three kinds of resolution grayscale image for ORL face image database have been performed. The results of experiments show that the set of the discriminant vectors extracted by the proposed algorithm has powerful ability of feature extraction and the recognition results are very robust by the general minimum distance classifier.