Dynamics-Adapted Cone Kernels

DOI10.1137/140954544zbMath1370.37141arXiv1403.0361OpenAlexW2963557665WikidataQ125119762 ScholiaQ125119762MaRDI QIDQ5249799

Dimitrios Giannakis

Publication date: 12 May 2015

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0361

zbMATH Keywords

vector fieldkernel methoddelay coordinatesdiffusion operatormanifold embedding

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Time series analysis of dynamical systems (37M10)

Related Items

The diffusion geometry of fibre bundles: horizontal diffusion maps ⋮ Mitigating Model Error via a Multimodel Method and Application to Tropical Intraseasonal Oscillations ⋮ Spatiotemporal analysis using Riemannian composition of diffusion operators ⋮ Extraction and prediction of coherent patterns in incompressible flows through space-time koopman analysis ⋮ Data-driven Koopman operator approach for computational neuroscience ⋮ Reproducing kernel Hilbert space compactification of unitary evolution groups ⋮ Delay-coordinate maps and the spectra of Koopman operators ⋮ Data-driven spectral decomposition and forecasting of ergodic dynamical systems ⋮ Spatiotemporal pattern extraction by spectral analysis of vector-valued observables

Uses Software

• ARPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local kernels and the geometric structure of data
• Variable bandwidth diffusion kernels
• Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series
• Towards a theoretical foundation for Laplacian-based manifold methods
• Extracting qualitative dynamics from experimental data
• Embedology
• Spatiotemporal analysis of complex signals: Theory and applications
• Embedding Riemannian manifolds by their heat kernel
• Diffusion maps
• Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• From graph to manifold Laplacian: the convergence rate
• Time-Scale Separation from Diffusion-Mapped Delay Coordinates
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• An optimal algorithm for approximate nearest neighbor searching fixed dimensions
• Discrete Calculus
• The Geometry of Filtering
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• ARPACK Users' Guide
• Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
• Nonlinear Laplacian spectral analysis: capturing intermittent and low‐frequency spatiotemporal patterns in high‐dimensional data
• Preserving Symmetries in the Proper Orthogonal Decomposition
• Nonlinear Dimensionality Reduction
• Learning Theory
• Intermittency, metastability and coarse graining for coupled deterministic–stochastic lattice systems
• On Learning Vector-Valued Functions