线性判别分析的迭代解法及其应用  

The Iterative Solution of Linear Discriminant Analysis and Its Application

作　　者：张建文[1] 刘新国[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2015年第11期119-124,共6页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11371333)资助

摘　　要：线性判别分析(LDA)作为一种降维技术,已成功应用于许多分类问题中,如语音识别、人脸识别、信息提取等领域。本文研究并改进求解迹比问题的两种主要方法:二分法、迭代迹比法(ITR法)。主要研究成果有:给出了一种基于线性插值的求解非线性方程二分法的改进算法;对这两种迭代方法与基于比迹准则的方法进行比较;对于ITR算法,选择好的初始迭代矩阵使得算法的收敛速度有明显的提高;分析了组内样本的相关性对识别精度的影响。Linear discriminant analysis（LDA）has been successfully used as a dimensionality reduction technique to many classification problems,such as speech recognition,face recognition and information retrieval.We study some efficient iterative procedures to directly solve the trace ratio optimization problem,namely,bisection method,iterative trace ratio.We made some improvements to these methods.The main research achievement are as follows：we present an improved bisection method based on linear interpolation for solving nonlinear equation;we compare these two methods against ratio trace solution to LDA;for the ITR algorithm,agood choice of initial iterative matrix makes the convergence speed of our method improved significantly;we analyze the influence of the correlation of sample to recognition accuracy.

关 键 词：线性判别分析 迭代解 迹比问题 

分 类 号：O212.5[理学—概率论与数理统计]