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中文摘要：
考虑样本为图像矩阵的图像鉴别分析问题，将Foley—Sammon鉴别分析问题转化为一类带约束条件的两目标优化问题，给出了有效投影向量的概念．利用多目标优化的必要条件，得到有效投影向量应满足的条件，它为广义特征方程的最大特征值所对应的特征向量，从而得到了求有效投影向量集的方法，其中类内散布矩阵不必是非奇异的．实验结果表明：该方法节省了特征抽取的时间，并且识别性能要优于其他方法．
英文摘要：
The paper concerns the image discriminant analysis problem where image matrices are taken as samples. Foley-Sammon discriminant analysis is transformed into a class of bi-objective constrained optimization problem, and the efficient projection vector is defined. By the necessary conditions for multiobjective optimization, we shown that the efficient projection vector is the eigenvector of eigen-equation corresponding to the largest eigenvalue. As a result, a method to find the set of efficient projection vectors is obtained. Here, the non-singularity of the within-scatter matrix is not essential. The experiments show that the computational time could be greatly reduced if our proppsed method is used for feature extraction, and the performance of its recognition is superior to the others.
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