On Koopman mode decomposition and tensor component analysis

Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into low modes that capture the most relevant features and/or dynamics. Despite their similar goal, methods largely used by different scientific communities formulated in distinct mathematical languages. We examine together show that, under a certain (reasonable) condition on data, theoretical given is \textit{same} decomposition. This provides "bridge" with which should be able to more effectively communicate. When this not met, still an \textit{a priori} computable error, providing alternative non-convex optimization requires. Our work new possibilities for algorithmic analysis, perspective success builds upon growing body showing dynamical systems, operator theory particular, can useful problems have historically made use theory.