Abstract: Fisher Linear Discriminant Analysis（FLDA） is a classical method of feature extraction with supervised information, which maximizes the Fisher criterion to find the optimal projection matrix. In the criterion of standard FLDA, the involved metric is based on [L2] norm metric, which is usually lack of robustness and sensitive to outliers. In order to improve the robustness, this paper proposes a new model and algorithm for FLDA, which is based on [L1] norm metric. The experimental results show that, FLDA with [L1] norm outperforms that with [L2] norm in classification accuracy and robustness in many cases.

Key words: Fisher linear discriminant analysis, Fisher criterion, [L1] norm metric, robustness, feature extraction

摘要： Fisher线性判别分析（Fisher Linear Discriminant Analysis，FLDA）是一种典型的监督型特征提取方法，旨在最大化Fisher准则，寻求最优投影矩阵。在标准Fisher准则中，涉及到的度量为[L2]范数度量，此度量通常缺乏鲁棒性，对异常值点较敏感。为提高鲁棒性，引入了一种基于[L1]范数度量的FLDA及其优化求解算法。实验结果表明：在很多情形下，相比于传统的[L2]范数FLDA，[L1]范数FLDA具有更好的分类精度和鲁棒性。

关键词: Fisher线性判别分析, Fisher准则, [L1]范数度量, 鲁棒性, 特征提取