tGLAD: A Sparse Graph Recovery Based Approach for Multivariate Time Series Segmentation

Segmentation of multivariate time series data is a valuable technique for identifying meaningful patterns or changes in the time series that can signal a shift in the system's behavior. We introduce a domain agnostic framework 'tGLAD' for multivariate time series segmentation using conditional independence (CI) graphs that capture the partial correlations. It draws a parallel between the CI graph nodes and the variables of the time series. Consider applying a graph recovery model uGLAD to a short interval of the time series, it will result in a CI graph that shows partial correlations among the variables. We extend this idea to the entire time series by utilizing a sliding window to create a batch of time intervals and then run a single uGLAD model in multitask learning mode to recover all the CI graphs simultaneously. As a result, we obtain a corresponding temporal CI graphs representation of the multivariate time series. We then designed a first-order and second-order based trajectory tracking algorithm to study the evolution of these graphs across distinct intervals. Finally, an 'Allocation' algorithm is designed to determine a suitable segmentation of the temporal graph sequence which corresponds to the original multivariate time series. tGLAD provides a competitive time complexity of O(N) for settings where number of variables D << N. We demonstrate successful empirical results on a Physical Activity Monitoring data. (Software: https://github.com/Harshs27/tGLAD).