Fisher大间距线性分类器

Fisher Large Margin Linear Classifier

作为一种著名的特征抽取方法,Fisher线性鉴别分析的基本思想是选择使得Fisher准则函数达到最大值的向量(称为最优鉴别向量)作为最优投影方向,以便使得高维输入空间中的模式样本在该向量投影后,在类间散度达到最大的同时,类内散度最小。大间距线性分类器是寻找一个最优投影矢量(最优分隔超平面的法向量),它可使得投影后的两类样本之间的分类间距(Margin)最大。为了获得更佳的识别效果,结合Fisher线性鉴别分析和大间距分类器的优点,提出了一种新的线性投影分类算法——Fisher大间距线性分类器。该分类器的主要思想就是寻找最优投影矢量wbest(最优超平面的法向量),使得高维输入空间中的样本模式在wbest上投影后,在使类间间距达到最大的同时,使类内离散度尽可能地小。并从理论上讨论了与其他线性分类器的联系。在ORL人脸库和FERET人脸数据库上的实验结果表明,该线性投影分类算法的识别率优于其他分类器。

Fisher linear discriminant analysis（LDA） , a well-known feature extraction method, searches for the projection axes on which the data samples from different classes are far from each other while requiring data samples of the same class to be close to each other. Large margin classifier（LMC） , also referred as linear support vector machine, de finds a project direction onto which two classes of the samples projected reach maximal margin. With combination of advantages of both LDA and LMC, the paper develops a novel linear projection classfication algorithm, called Fisher large margin linear classifier. The underlying idea is that an optimal discrimiant vector w^best is found along which the samples of high dimensional input space are projected such that the margin is maximized while within-class scatter is kept as small as possible. In addition, relations to other classifiers are explored in theory in this paper. Finally, the proposed method is tested on ORL face database and FERET face database. The experimental results show that the proposed classifier outperforms other linear classifiers.