Abstract:
Principal Components Analysis (PCA) is a data analysis technique widely used in dimensionality reduction. It extracts a small number of orthonormal vectors that explain most of the variation in a dataset, which are called the Principal Components. Conventional PCA is sensitive to outliers because it is based on the
-norm, so to improve robustness several algorithms based on the
-norm have been introduced in the literature. We present a new algorithm for robust
-norm PCA that computes components iteratively in reverse, using a new heuristic based on Linear Programming. This solution is focused on finding the projection that minimizes the variance of the projected points. It has only one parameter to tune, making it simple to use. On common benchmarks it performs competitively compared to other methods. The data and software related to this paper are available at https://github.com/visentin-insight/L1-PCAhp.