Subspace Change-Point Detection: A New Model and Solution

Change-point detection has a long history of research in statistical signal processing and remains a fundamental problem in many real-world applications involving information extraction from streaming data. Exploiting low-dimensional structures (subspace in particular) of high-dimensional signals is another research topic of significance, as it improves not only efficiency in computation, storage, and communication, but also interpretability and understanding of data. In this paper, we formulate the problem of subspace change-point detection, where a stream of high-dimensional data points lie on a low-dimensional subspace that abruptly changes at a certain time instant. Then, we propose a cumulative-sum-based algorithm for the task of detection in this problem setup. From the algorithmic perspective, the proposed method is computationally efficient, as it proceeds in an online and recursive manner, and each iteration involves simple matrix computation; it is also practical and flexible, as it works under mild conditions on the distribution of data points after change point. From the theoretical perspective, we derive rigorous performance bounds of the proposed algorithm in terms of false alarm rate and detection delay. We also conduct extensive numerical experiments on both synthetic and real-world data to validate effectiveness of our algorithm and correctness of theoretical analysis.