求解统计不相关的最佳鉴别矢量的统一算法

A Unified Algorithm for the Computation of Statistically Uncorrelated Optimal Discriminant Vectors

Fisher最佳鉴别准则是高维模式分析中的有效方法 ,其关键是求解最佳鉴别矢量。统计不相关的最佳鉴别矢量保证模式矢量投影后得到的特征是统计不相关的 ,已有的计算统计不相关的最佳鉴别矢量算法不能计算小样本的情形 (类内散布矩阵是奇异的 ) ,针对这种情形 ,该文给出了一种对大小样本都能精确计算统计不相关最佳鉴别矢量的统一算法。在大样本情形下 ,该方法得到的结果与已有的方法相同。为验证算法的有效性 ,将其用于人脸识别实验 。

Fisher optimal discriminant criterion is an efficient method to extract classifying information of high dimensional patterns.The key of the method is how to calculate the optimal discriminant vectors.The statistically uncorrelated optimal discriminant vectors ensure that the projected features of the pattern vectors are statistically uncorrelated.The existed algorithm computing the statistically uncorrelated optimal discriminant vectors is ineffective for the case of the small samples (the within class scatter matrix is singular).This paper presented a unified algorithm that can calculate the statistically uncorrelated optimal discriminant vectors exactly both for the small samples and large ones.In the case of large samples,the result of our method is the same as the existed method.In order to test the efficiency of our method,it is used to recognize human faces.Experimental results have shown that our method has better recognition performance than existed method.