Identifying the temporal distribution structure in multivariate data for time-series segmentation based on two-sample test
Justyna Witulska, Marta Hendler, Magdalena Kasprowicz, Marek Czosnyka, Ireneusz Jabłoński, Agnieszka Wyłomańska · Information Fusion · 2025
The research tackles the challenge of monitoring and managing a complex system by distinguishing consecutive states while observing multiple variables, especially in non-Gaussian environment. We introduce a novel methodology – MIDAST – aimed at fusion-based multivariate data segmentation and grounded in multivariate statistical tests, including the Kolmogorov–Smirnov test, a Maximum Mean Discrepancy-based test, and a kernel-based test. The performance of the method is evaluated through a comparative analysis against selected baseline techniques, specifically e-Divisive and Kernel Change Point Analysis methods, with a focus on segmentation accuracy. Additionally, the computational complexity of the proposed methodology is assessed. Computer simulation experiments, conducted across two distinct data models: (a) multivariate sub-Gaussian and (b) multivariate Student’s t distributions, has been performed to evaluate the efficiency of designed methodology. Various scenarios have been examined, with different change factors considered, such as strength of the correlation between components, number of degrees of freedom (for the Student’s t distribution), and the stability index (for the sub-Gaussian distribution). Finally, to depict a practical meaning of the proposed approach we successfully demonstrated invasiveness minimization of intracranial hypertension events detection by identifying the temporal distribution structure in multivariate data. MIDAST supplemented with a windowing mechanism enables screening temporal changes in one or many statistical parameters describing multivariate distribution of measured time series , uncovering single or multiple data change points marking the boundaries within which the homogeneous laws governing the evolution of the physical system and/or process apply.