线性判别分析（LDA）是监督式的特征提取方法，在人脸识别等领域得到了广泛应用。为了提高特征提取速度，提出了基于无穷范数的线性判别分析方法。传统LDA方法将目标函数表示为类内散布矩阵和类间散布矩阵之差的或者商的L2范数，且通常需要涉及到矩阵求逆和特征值分解问题。与传统方法不同，这里所提方法将目标函数表示为类内散布矩阵和类间散布矩阵之差的无穷范数，而且最优解是以迭代形式得到，避免了耗时的特征值分解。无穷范数使得到的基向量实现了二值化，即元素仅在-1和1两个数字内取值，避免了特征提取时的浮点型点积运算，从而降低了测试时间，提高了效率。在ORL人脸数据库和Yale数据库上的实验表明所提算法是有效的。%The linear discriminant analysis(LDA)is a method of supervised feature extraction. It has been widely used in the field of computer vision such as face recognition. An infinite norm based LDA method is proposed this paper to improve the efficiency of feature extraction. Traditional LDA methods express their objective functions as either difference of between-class scattering matrix and within-class scattering matrix or quotient in the L2 norm. Consequently,these methods need to involve in matrix inversion and eigen-value decomposition. By contrast,the proposed method utilizes L-norm(infinite norm)instead of L2 norm to formulate the objective function with respect to the difference between between-class scatter matrix and within-class scat-ter matrix. Because the solution is obtained iteratively,this method avoids time-consuming eigen-decomposition. Moreover,the projection vector realizes binarization,and the value of elements is -1 or 1,resulting in high efficiency because it avoids compu-ting the inner product between a sample and the projection vector. The results of experiments in ORL database and Yale data-base demonstrate the efficiency and effectiveness of the proposed method.
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