Publications and Preprints
Spatiotemporal Intrinsic Mode Decomposition (STIMD)
The analysis of spatiotemporal signals is of critical importance for characterizing emerging large-scale measurements in wide variety of scientific and engineering applications. Many methods have been developed to discover a low dimensional representation of these data. However, many widely used methods such as PCA do not incorporate the temporal structure of the data into the model. In this work we develop a new dimensionality reduction technique, known as the spatiotemporal intrinsic mode decomposition (STIMD) method, which factors spatiotemporal data into a product of spatial modes and temporal modes. Our method allows us to perform instantaneous time frequency analysis by computing a Hilbert transform of the data; in addition, it is possible to make future-state predictions of the spatiotemporal system. This work is currently under review. A preprint can be found here: https://arxiv.org/pdf/1806.08739.pdf.
Centering Improves the Dynamic Mode Decomposition
Originating in the fluids community, DMD has been used in a wide variety of fields with applications to neuroscience, climate science, and finance to name a few. Given spatiotemporal data, DMD decomposes the data into pairs of spatial temporal modes with the assumption that the dynamics are approximately linear, i.e. it is a regression to a best fit linear dynamical model. For many systems of interest, the dynamics we want to model are perturbations about equilibria, in which case subtracting the mean of the data is a natural preprocessing step. In this work, we prove that centering data improves the performance of DMD, and can be used to successfully extract dynamics about equilibria. This is a particularly important and surprising result, since previous work suggested that computing DMD on centered data may be restrictive and have undesirable consequences. The results are illustrated on the Lorenz attractor, in addition to applications to neural recordings and video surveillance. This work is currently under review. A preprint can be found here: https://arxiv.org/pdf/1906.05973.pdf