Robust spherical principal curves

Abstract

Principal curves are a nonlinear generalization of principal components and go through the mean of data lying in Euclidean space. In this paper, we propose L1-type and Huber-type principal curves through the median of data to robustify the principal curves for a dataset that may contain outliers. We further investigate the stationarity of the proposed robust principal curves on S2. Results from numerical experiments on S2 and S4, including real data analysis, manifest promising empirical features of the proposed method.