On the discriminative properties of Principal Component Analysis based on L1-norm

Principal Component Analysis (PCA) is one the most widely-used techniques for the analysis of multivariate data. Unfortunately, PCA is extremely sensitive to the presence of large outliers in the data. To overcome this drawback, a robust variant of standard PCA, based on the L1-norm, has been proposed in recent years. This variant, called L1-PCA behaves like traditional PCA, while offering robustness against the presence of large outliers in the data. This paper shows that, combined with a whitening pre-processing, L1-PCA is also endowed with discriminative properties, allowing it to solve binary classification problems in an unsupervised way, thus sparing the need for training data.