样本典型性分析与线性鉴别分析

Representative samples and linear discriminant analysis

首先分析了经典LDA方法的物理意义及其局限性,然后提出了一个新的LDA方法。该方法强调训练样本的典型性与代表性,并认为相同类别中与一个样本距离较远的若干样本是同一类别中对这个样本有典型意义的样本,而不同类别中与这个样本距离较近的若干样本也是对该样本而言有典型代表意义的样本。该新的LDA方法基于定义在这些典型样本上的类间散布矩阵与类内散布矩阵实现特征提取。方法的物理意义体现为:特征提取过程中最大化样本与不同类中的典型样本间距离与最小化样本与同类中的典型样本间距离这一思路的实现,可使抽取出的不同类别的样本特征具有更大的线性可分离性。充分的理论与实验分析表明本文方法可优于经典LDA方法。

In this paper,the physical meaning and shortcomings of Fisher Linear Discriminant Analysis（CLDA）are analyzed firstly.Then,a novel LDA method is proposed.This method considers that,for a sample,the samples which are from the same class and the farthest away from this sample,are the representative samples in its own category.On the other hand,for the same sample,the samples which are from other classes and the nearest to this sample,have indicative meaning.The novel LDA method defines its between-class and within-class scatter matrices based on these representative samples.As a result,the feature extraction process associated with this method will maximize the distance between one sample and the corresponding representative samples in other categories,while minimizing the distance between this sample and those representative samples in its own class.This process can be more effective than the feature extraction process associated with classical LDA to achieve feature space with larger linear separability.A number of experiments also show that the method proposed in this paper outperforms classical LDA.