基于PSO的Fisher准则下小样本最佳鉴别变换  

Small Sample Optimal Discriminant Transform Based on PSO under Fisher Criterion

作　　者：芮挺[1] 周游[2] Qi Tian 方虎生[1] 戎晓力[1] 

机构地区：[1]解放军理工大学工程兵工程学院,南京210007 [2]江苏经贸职业技术学院会计系,南京210007 [3]Deptartment of Computer Science, University of Texas at San Antonio, San Antonio, TX 78249

出　　处：《模式识别与人工智能》2009年第2期288-292,共5页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目资助(No.50608069)

摘　　要：小样本条件下,Fisher准则中类内散布矩阵一般是奇异的,无法直接求解.本文提出利用粒子群优化理论,在无需求类内散布矩阵逆的情况下求解Fisher准则下小样本最佳鉴别变换的方法.讨论了通过粒子群优化算法的位置——速度搜索模型获取最佳鉴别投影向量的方法和步骤.实验对比类内散布矩阵非奇异时,采用计算特征向量方法和本文方法的差异.分析验证小样本条件下类内散布矩阵奇异时,通过本文方法进行最佳鉴别变换的分类效果.实验证实本文算法的有效性.The within-class scatter matrix Fisher criterion is singular under small samples. Therefore, it can not be solved directly. A method based on PSO is proposed to get optimal discriminant transform under small samples without calculating inverse of the within-class scatter matrix. The methods and steps are discussed to get optimal discriminant projection vector by velocity-position search model of particle swarm optimization. The eigenvectors method and the proposed method are compared, when within-class scatter matrix is non-singular. Experimental results on both small and large samples demonstrate the accuracy of the proposed method.

关 键 词：模式识别 FISHER准则 最佳鉴别变换 粒子群优化(PSO) 

分 类 号：TP391.43[自动化与计算机技术—计算机应用技术]