Nonparametric Multiple Change-Point Detection for Random Objects

Change-point analysis for non-Euclidean data has become increasingly important in modern applications, where observations often lie in complex metric spaces rather than vector spaces. We propose a distance profiles-based change-point estimation framework for sequences of objects taking values in general metric spaces, which combines distance profiles with a dynamic programming scheme to enable efficient multiple change-point detection. The proposed method is fully nonparametric, requires minimal tuning, and is applicable as long as pairwise distances between observations are available. We establish a non-asymptotic oracle inequality for our method under mild regularity conditions. Extensive simulation studies demonstrate favorable performance compared to existing approaches. We further illustrate the practical relevance of our method through applications to three representative non-Euclidean datasets, including compositional data, network-valued data, and financial correlation matrices.