IEEE Trans Cybern. 2014 Jun;44(6):828-42. doi: 10.1109/TCYB.2013.2273355. Epub 2013 Jul 30.
Fisher linear discriminant analysis (LDA) is a classical subspace learning technique of extracting discriminative features for pattern recognition problems. The formulation of the Fisher criterion is based on the L2-norm, which makes LDA prone to being affected by the presence of outliers. In this paper, we propose a new method, termed LDA-L1, by maximizing the ratio of the between-class dispersion to the within-class dispersion using the L1-norm rather than the L2-norm. LDA-L1 is robust to outliers, and is solved by an iterative algorithm proposed. The algorithm is easy to be implemented and is theoretically shown to arrive at a locally maximal point. LDA-L1 does not suffer from the problems of small sample size and rank limit as existed in the conventional LDA. Experiment results of image recognition confirm the effectiveness of the proposed method.
Fisher 线性判别分析（LDA）是一种经典的子空间学习技术，用于提取模式识别问题的判别特征。Fisher 准则的公式基于 L2 范数，这使得 LDA 容易受到异常值的影响。在本文中，我们提出了一种新的方法，称为 LDA-L1，通过使用 L1 范数而不是 L2 范数最大化类间离散度与类内离散度的比值。LDA-L1 对异常值具有鲁棒性，并通过提出的迭代算法进行求解。该算法易于实现，理论上证明可以达到局部极大值。LDA-L1 不会像传统 LDA 那样受到小样本量和秩限制的问题的影响。图像识别的实验结果证实了所提出方法的有效性。
