Scalable Robust Sparse Principal Component Analysis

arXiv:2402.16712v1 Announce Type: new
Abstract: In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the problem is NP-hard, we introduce a linear relaxation-based approach. Additionally, we present a novel fitting procedure, utilizing simple ratios and sorting techniques. The proposed algorithm demonstrates a worst-case time complexity of $O(n^2 m \log n)$ and, in certain instances, …

abstract analysis arxiv criterion cs.lg error framework linear math.oc norm np-hard optimization representation robust scalable stat.ml terms type work