2018/05/07 by Dimitrios Giannakis, Joanna Sławińska, Giannakis, Dimitrios +5
Computer Science · Economics, Econometrics and Finance · Neuroscience · #Complex Systems and Time Series Analysis #Data Analysis #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.1805.09134
openalex publication_date 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding techniques in dynamical systems to develop of a method for objective identification of spatiotemporal coherent patterns, without prior knowledge of the state space and/or the dynamical laws of the system generating the data. A key aspect of this method is that it operates on a space of vector-valued observables using a kernel measure of similarity that takes into account both temporal and spatial degrees of freedom (in contrast, classical kernel techniques such as PCA utilize aggregate measures of similarity between 'snapshots'). As a result, spectral decomposition of data via our approach yields a significantly more efficient and physically meaningful representation of complex spatiotemporal signals than conventional methods based on scalar-valued kernels. We demonstrate this behavior with applications to an oscillator model and sea surface temperature data from a climate model.