On Koopman Mode Decomposition and Tensor Component Analysis
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Koopman mode decomposition and tensor component analysis are two tools that decompose high dimensional data sets into low dimensional modes that capture relevant features and/or dynamics. Despite their similar goal, the two methods are largely used by distinct scientific communities. For the first time, examine the two together and show that, under a certain (reasonable) condition on the data, the theoretical decomposition given by tensor component analysis is the same as that given by Koopman mode decomposition. 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.
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