求解广义最佳鉴别矢量集的一种迭代算法及人脸识别

广义最佳鉴别矢量集是Foley-Sammon最佳鉴别矢量集的一种推广，它与Foley-Sammon最佳鉴别矢量集的不同之处在于广义最佳鉴别矢量集从整体上考虑投影集的可分性，即样本在广义最佳鉴别矢量上的投影集从整体上具有最佳的可分性。该文给出了广义最佳鉴别矢量的定义，对求解广义最佳鉴别矢量集的已有算法从理论上作了分析，指出了其中的不足之处，给出了一种迭代算法，从理论上证明了迭代结果收敛于精确解，并对其误差作了分析。最后，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。

An Iterative Algorithm for the Generalized Optimal Set of Discriminant Vectors and Its Application to Face Recognition

The generalized optimal set of discriminant vectors is a generalized version of Foley-Sammon optimal set of discriminant vectors. The main difference between the generalized optimal set of discriminant vectors and Foley-Sammon optimal set of discriminant vectors is that the separability of the projected set of the samples is considered from global view when calculating the generalized optimal set of discriminant vectors, that is, the projected set of the samples on the generalized optimal set of discriminant vectors have the best separability in global sense. This paper presents the definition of generalized optimal discriminant vectors, analyzes the shortcomings of the old algorithm, and puts forward a new iterative algorithm, which is proven theoretically to converge to the precise solution while the errors are also taken into consider. And lastly, the algorithm is applied to face recognition, the results of which show that it is more effective than the old method.