Related papers: Spatiotemporal pattern extraction by spectral anal…

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…

We introduce a unified framework for learning the spatio-temporal dynamics of vector valued functions by combining operator valued reproducing kernel Hilbert spaces (OV-RKHS) with kernel based Koopman operator methods. The approach enables…

Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an…

We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…

The problem of data-driven identification of coherent observables of measure-preserving, ergodic dynamical systems is studied using kernel integral operator techniques. An approach is proposed whereby complex-valued observables with…

We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…

Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…

Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…

We develop a framework for dimension reduction, mode decomposition, and nonparametric forecasting of data generated by ergodic dynamical systems. This framework is based on a representation of the Koopman and Perron-Frobenius groups of…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional…

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector…

There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…

A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is developed. It is based on an approximation of the generator of…

We present a technique for spatiotemporal data analysis called nonlinear Laplacian spectral analysis (NLSA), which generalizes singular spectrum analysis (SSA) to take into account the nonlinear manifold structure of complex data sets. The…

Many scientific problems require identifying a small set of covariates that are associated with a target response and estimating their effects. Often, these effects are nonlinear and include interactions, so linear and additive methods can…

We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data…

We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…