In complex biological and engineering systems, structure, function, and dynamics tend to be highly coupled. Such interactions can be naturally captured via tensor based state space dynamical system representations. In this context, we extend the notion of Dynamic Mode Decomposition (DMD) and its variants to directly act on tensor time series data, and develop numerical procedures to compute DMD tensor modes/eigenvalues based on recent advances in computational tensor algebra. Compared to classical DMD methodology which requires vectorization of the tensor time series, the proposed DMD extension preserves the tensor structure inherent in the data, and could lead to more compact yet accurate representation of the time series evolution. We illustrate such benefits of the proposed approach on some real world datasets.
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