Principal component analysis (PCA) and Fisher's linear discriminant analysis (LDA) are widespread techniques in data analysis and pattern recognition. Recently, the L1-norm has been proposed as an alternative criterion to classical L2-norm in PCA, drawing considerable research interest on account of its increased robustness to outliers. The present work proves that, combined with a whitening preprocessing step, L1-PCA can perform LDA in an unsupervised manner, i.e., sparing the need for labelled data. Rigorous proof is given in the case of data drawn from a mixture of Gaussians. A number of numerical experiments on synthetic as well as real data confirm the theoretical findings.

中文翻译：

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LDA 通过 L1-PCA 的白化数据

主成分分析 (PCA) 和 Fisher 线性判别分析 (LDA) 是数据分析和模式识别中广泛使用的技术。最近，L1 范数已被提议作为 PCA 中经典 L2 范数的替代标准，由于其对异常值的鲁棒性增加，引起了相当大的研究兴趣。目前的工作证明，结合白化预处理步骤，L1-PCA 可以以无监督的方式执行 LDA，即不需要标记数据。在从高斯混合中提取的数据的情况下给出了严格的证明。对合成数据和真实数据进行的大量数值实验证实了理论发现。