求解广义最佳鉴别矢量集的一种改进算法

An Improved Algorithm for the General Optimal Set of Discriminant Vectors

鉴于广义最佳鉴别矢量集是 Foley- Sam mon最佳鉴别矢量集的一种推广 ,给出了广义最佳鉴别矢量的定义 ,并从理论上对已有的求解广义最佳鉴别矢量集的算法作了分析 ,指出了其中的不足之处 ,并给出了一种改进的算法 .将此方法用于人脸识别 ,结果显示 ,新方法比已有的方法更有效 .

The general optimal set of discriminant vectors is the extension of the Foley Sammon optimal set of discriminant vectors. First, this paper gives the definition and existed calculating method in theory, through which it is found that the existed method has two principal problems:(1)The general optimal discriminant vectors are calculated step by step, which can not make sure that the corresponding general Fisher discriminant function can reach the maximum;(2)When the popular scatter matrix is singular, it is possible that there exists one discriminant vector on which the between\|class distance of the projected set of the training sample set is equal to zero, which is meaningless for classification. To solve the above two problems, a new method for calculating the general optimal set of discriminant vectors is presented. In the end, our method is applied to human face recognition. Experimental result shows that the new method is superior to the existed method in terms of correct classification rate and stability.