Extraction of spatiotemporal patterns from measured data via adaptive Laplacian eigenfunctions

A method for spatiotemporal analysis of high-dimensional dynamic datasets is presented. The method combines the use of the Laplace-Beltrami operator with time-lagged embedding to represent spatial and temporal patterns from measured data. The proposed method has the potential to render a significantly improved spatiotemporal representation of complex datasets and greatly facilitates extracting dynamic patterns. Because the temporal structures of the time-dependent means are modeled, the new approach displays increased statistical power and precision of parameter estimation. As an illustrative example, transient stability data is used to examine the potential usefulness of the proposed approach to characterize spatiotemporal dynamics.