A0612
Title: Detecting change points in low-rank tensors via tucker decomposition and one-dimensional series analysis
Authors: Jiaqi Huang - Beijing Normal University (China) [presenting]
Ning Wang - Beijing Normal University (China)
Lixing Zhu - Beijing Normal University (China)
Abstract: The purpose is to address the challenge of detecting change points within tensor data characterized by a low-rank structure. It is proposed that these change points can manifest within the core tensors or their corresponding subspaces, as identified through Tucker decomposition. Initially, the approach targets change points associated with subspaces. A MOSUM-based criterion is introduced that captures the dimensionality of these subspaces, effectively simplifying the intricate, high-dimensional problem into a more manageable one-dimensional time series change point detection task. Subsequently, a change point detection algorithm is integrated with a dimensionality determination technique applied to the one-dimensional series, enabling the identification of all potential change points. Building upon this subspace analysis, change points are further pinpointed within core tensors using an adaptive ridge ratio statistic. The findings affirm the consistency of the estimated subspaces' foundational matrices derived from Tucker decomposition, as well as the consistency of the identified change points. Additionally, the methodology is extended to accommodate tensors featuring structural modes. Through numerical experiments, the robust performance of the method is demonstrated. A practical application is also included, using real-world data to illustrate the utility of the approach.
