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 .
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 dimensional modes that capture the most relevant features and/or dynamics. Despite their similar goal, the two methods are largely used by different scientific communities and formulated in distinct mathematical languages. We 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 provides a "bridge" with which the two communities should be able to more effectively communicate. When this condition is not met, Koopman mode decomposition still provides a tensor decomposition with ana priori computable error, providing an alternative to the non-convex optimization that tensor component analysis requires. Our work provides new possibilities for algorithmic approaches to Koopman mode decomposition and tensor component analysis, provides a new perspective on the success of 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 .
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are two tools that decompose
(also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing
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distinct scientific communities . For the first time,
different scientific communities and formulated in distinct mathematical languages. We
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same
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realization provides possibilities for new
provides a "bridge" with which the two communities should be able to more effectively communicate. When this condition is not met, Koopman mode decomposition still provides a tensor decomposition with an
A
a priori
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computable error, providing an alternative to the non-convex optimization that tensor component analysis requires. Our work provides new possibilities for
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new insight into what is being captured by the
provides a new perspective on the success of
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modes, and a "bridge" with which the two communities can more effectively communicate
, 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