Learning with Coherence Patterns in Multivariate Time-series Data via Dynamic Mode Decomposition

Understanding complex dynamics in the real world is a fundamental problem in various engineering and scientific fields. Dynamic mode decomposition (DMD) has attracted attention recently as a prominent way to obtain global modal descriptions of nonlinear dynamical processes from data without requiring explicit prior knowledge about the underlying systems. In this paper, we propose a novel learning method for multivariate time-series data involving complex dynamics using coherence patterns among attributes extracted by DMD. To this end, we develop kernels defined with Grassmann subspaces spanned by dynamic modes which are calculated by DMD and represent coherence patters among attributes with respect to the estimated modal dynamics. To incorporate information in labels attached to a set of time-series sequences, we employ a supervised embedding step in the DMD procedure. We illustrate and investigate the empirical performance of the proposed method using real-world data.