A new Robust Principal Component Analysis algorithm based on Linear Programming

Principal Component Analysis (PCA) is a standard tool in modern data analysis. It is a simple method for extracting relevant low-dimensional information from high-dimensional datasets, with many applications including neuroscience, image reconstruction, computer graphics, signal processing, dimensionality reductions, quality control and outlier detection. Classical PCA methods use the L2-norm (Euclidean distance) but this makes them vulnerable to noise and outliers and L1-norm PCA is an attractive alternative because it is more robust, and it is indicated for most real world datasets. Several such methods exist, and we present a new L1-norm PCA method based on backward iterated linear programming. We show that it outperforms existing methods, especially in the presence of extreme outliers.