Before revision:  This realization provides possibilities for new  algorithmic approaches to both Koopman mode decomposition and tensor component analysis, new insight into what is being captured by the tensor component analysis modes, and a "bridge" with which the two communities can more effectively communicate .
After revision:  This realization provides possibilities for new algorithmic approaches to both Koopman mode decomposition and tensor component analysis, new insight into what is being captured by the tensor component analysis , and builds upon a growing body of work showing that dynamical systems, and Koopman operator theory in particular, can be useful for problems that have historically made use of optimization theory .