A New Approach to Signal Processing of Spatiotemporal Data

@article{Slawinska2018ANA,
  title={A New Approach to Signal Processing of Spatiotemporal Data},
  author={Joanna Slawinska and Abbas Ourmazd and Dimitrios Giannakis},
  journal={2018 IEEE Statistical Signal Processing Workshop (SSP)},
  year={2018},
  pages={338-342}
}
We present a method combining ideas from the theory of operator-valued kernels with delay-coordinate embedding techniques in dynamical systems capable of identifying spatiotemporal patterns, without prior knowledge of the state space or the dynamical laws of the system generating the data. The approach is particularly powerful for systems in which characteristic patterns cannot be readily decomposed into temporal and spatial coordinates. Using simulated and observed sea-surface temperature data… 

Figures from this paper

Data-driven Koopman operator approach for computational neuroscience
TLDR
Applications of a Koopman operator approach for eigendecomposition of electrophysiological signals into orthogonal, coherent components and examine their associated spatiotemporal dynamics are presented.
Operator-theoretic framework for forecasting nonlinear time series with kernel analog techniques

References

SHOWING 1-10 OF 23 REFERENCES
Vector-Valued Spectral Analysis of Space-Time Data
TLDR
This work combines ideas from the theory of operator-valued kernels with delay-embedding techniques in dynamical systems to develop 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.
Spatiotemporal analysis of complex signals: Theory and applications
We present a space-time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal
Spatiotemporal Pattern Extraction by Spectral Analysis of Vector-Valued Observables
TLDR
Application of vector-valued spectral analysis to the Kuramoto–Sivashinsky model demonstrates significant performance gains in efficient and meaningful decomposition over eigendecomposition techniques utilizing scalar-valued kernels.
Spatiotemporal Feature Extraction with Data-Driven Koopman Operators
TLDR
This work presents a framework for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems by constructing feature maps using eigenfunctions of the Koopman group of unitary operators governing the dynamical evolution of observables and probability measures.
Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
TLDR
A technique for analyzing high-dimensional, complex time series that exploits the geometrical relationships between the observed data points to recover features characteristic of strongly nonlinear dynamics (such as intermittency and rare events), which are not accessible to classical singular spectrum analysis.
Data-driven spectral decomposition and forecasting of ergodic dynamical systems
  • D. Giannakis
  • Mathematics
    Applied and Computational Harmonic Analysis
  • 2019
Dynamic mode decomposition of numerical and experimental data
  • P. Schmid
  • Physics, Engineering
    Journal of Fluid Mechanics
  • 2010
The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information
Spectral analysis of nonlinear flows
We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an
Delay-Coordinate Maps and the Spectra of Koopman Operators
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting.
Diffusion maps
...
1
2
3
...