中文摘要：

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．

英文摘要：

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.