Tensor Dynamic Mode Decomposition
This work addresses the problem of analyzing complex, high-dimensional systems like images and videos for researchers in data-driven dynamics, though it appears incremental as an extension of existing DMD methods.
The authors tackled the limitation of conventional dynamic mode decomposition (DMD) in handling multidimensional data by proposing tensor dynamic mode decomposition (TDMD), which extends DMD to third-order tensors using the T-product framework, resulting in more efficient computation and better preservation of spatiotemporal structures compared to standard methods.
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which might be inefficient or inadequate for modeling inherently multidimensional data including images, videos, and higher-order networks. In this letter, we propose tensor dynamic mode decomposition (TDMD), a novel extension of DMD to third-order tensors based on the recently developed T-product framework. By incorporating tensor factorization techniques, TDMD achieves more efficient computation and better preservation of spatial and temporal structures in multiway data for tasks such as state reconstruction and dynamic component separation, compared to standard DMD with data flattening. We demonstrate the effectiveness of TDMD on both synthetic and real-world datasets.