Orientability and diffusion maps

DOI10.1016/j.acha.2010.10.001zbMath1218.68131arXiv1102.0075OpenAlexW1994911252WikidataQ42007375 ScholiaQ42007375MaRDI QIDQ544038

Hau-Tieng Wu, Amit Singer

Publication date: 14 June 2011

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0075

zbMATH Keywords

dimensionality reductionorientabilitydiffusion maps

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (17)

Approximate and discrete Euclidean vector bundles ⋮ Learning from patches by efficient spectral decomposition of a structured kernel ⋮ Vector diffusion maps and the connection Laplacian ⋮ Embedding Riemannian manifolds by the heat kernel of the connection Laplacian ⋮ Spectral Discovery of Jointly Smooth Features for Multimodal Data ⋮ The diffusion geometry of fibre bundles: horizontal diffusion maps ⋮ Multi-view kernel consensus for data analysis ⋮ Kernel-based methods for solving time-dependent advection-diffusion equations on manifolds ⋮ Geometric scattering on measure spaces ⋮ Hierarchical data organization, clustering and denoising via localized diffusion folders ⋮ Spectral convergence of the connection Laplacian from random samples ⋮ Patch-to-tensor embedding ⋮ Coarse-grained localized diffusion ⋮ The geometry of synchronization problems and learning group actions ⋮ TAP free energy, spin glasses and variational inference ⋮ Unnamed Item ⋮ Embeddings of Riemannian manifolds with finite eigenvector fields of connection Laplacian

Cites Work

• Angular synchronization by eigenvectors and semidefinite programming
• On the local behavior of spaces of natural images
• The nonlinear statistics of high-contrast patches in natural images
• Diffusion maps
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• From graph to manifold Laplacian: the convergence rate
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• Learning Theory
• Learning Theory

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