Robust spherical principal curves

•Propose a new robust principal curve for data sets that deviate from the normality (Gaussian) assumption.•Investigate a theoretical property of the robust principal curve, termed ‘stationarity,’ which implies that the proposed method is canonical in the spherical domain.•Demonstrate the promising empirical performance of the proposed method through numerical experiments such as simulation study and real data analysis. 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.