Abstract: Fisher criterion assumes that each sample has a unimodal,symmetric distribution for each class.However,when the training sample size is large and their distributions are multimodal or skewed,the definition of classical Fisher criterion can not correctly reflect the distribution of the data in the sample space,in that case,the sets of discriminant vectors are not optimal virtually.Aiming at this case,this paper generalizes the Fisher criterion by introducing the idea of Gaussian mixture model and proposes a new linear discriminant analysis,at same time,a direct algorithm is proposed.The method is applied to letter image recognition,and the experimental result shows that the present method is superior to the existing methods in terms of correct classification rate.

Key words: linear discriminant analysis, feature extraction, Fisher criterion, Gaussian mixture model

摘要： Fisher准则函数的前提条件就是假设每类样本数据满足单峰高斯分布,即各类样本在模式空间的分布近似椭球状,但是当训练样本数据较多且呈多峰分布时,传统的Fisher准则函数并不能准确反映样本数据的分布,显然基于Fisher准则函数的线性判别分析得到的最优判别矢量集也不是最优的。针对这种情况,通过引入高斯混合模型的概念,提出了一种新的基于高斯混合模型的线性判别分析方法,同时也给出了在该模型下的最优判别矢量集的直接求解方法,并通过实验证明了该算法的有效性。

关键词: 线性判别分析, 特征提取, Fisher准则函数, 高斯混合模型