An estimation method for switching points of multimode spatiotemporal data based on SFSTAR

Various traditional methods, including statistical and spatial map-based approaches, are employed to model spatiotemporal data. However, the lack of explicit descriptions of spatial and temporal dependencies leads to unnecessarily intensive and uninterpretable relationships among the variables. To address this problem, space–time autoregressive moving average (STARMA)-type models that can depict temporal and spatial dependencies in a parametric manner are adopted in this study. However, such models may not be applicable to unlabeled multimode spatiotemporal data. In this study, we propose a switching flexible space–time autoregressive (SFSTAR) model to describe multimode spatiotemporal data. Considering the coupling between the parameter estimation of each mode and determination of the switching points, an estimation method is proposed to identify the mode switching points to partition the multimode data into different segments. First, the proposed estimation method identifies the number of segments by locating the transition regions that enclose the switching points based on the spatiotemporal feature extraction proposed herein. Second, with the estimated number of segments that is actually the number modes and the constraints on the locations of the switching points given by the transition regions, the proposed method jointly estimates the switching points and the SFSTAR model parameters in each mode through Bayesian optimization. The effectiveness of the proposed method is evaluated using a numerical example and a fiber optic temperature measurement dataset.