🤖 AI Summary
Existing graph-based change-point detection methods perform well in high-dimensional nonparametric settings but struggle with data featuring repeated measurements or local group structures; conventional mean aggregation obscures intra-individual dynamic patterns. This paper proposes the first graph-based framework that jointly leverages intra- and inter-individual information: it constructs a two-layer similarity graph—comprising an intra-individual graph capturing repeated measurements and an inter-individual proximity graph—thereby integrating local dependencies with global structure. We design a composite test statistic and derive its p-value efficiently via analytic approximation. The method achieves high sensitivity to subtle, gradual, and multi-scale change points. Experiments on New York City taxi trajectory data demonstrate substantial improvements in detection accuracy and robustness over state-of-the-art approaches, particularly under strong inter-individual heterogeneity.
📝 Abstract
Graph-based methods have shown particular strengths in change-point detection (CPD) tasks for high-dimensional nonparametric settings. However, existing CPD research has rarely addressed data with repeated measurements or local group structures. A common treatment is to average repeated measurements, which can result in the loss of important within-individual information. In this paper, we propose a new graph-based method for detecting change-points in data with repeated measurements or local structures by incorporating both within-individual and between-individual information. Analytical approximations to the significance of the proposed statistics are derived, enabling efficient computation of p-values for the combined test statistic. The proposed method effectively detects change-points across a wide range of alternatives, particularly when within-individual differences are present. The new method is illustrated through an analysis of the New York City taxi dataset.