Anisotropic diffusion on sub-manifolds with application to Earth structure classification

DOI10.1016/j.acha.2011.06.002zbMath1316.62067OpenAlexW1991167541MaRDI QIDQ412409

Ali Haddad, Dan Kushnir, Ronald R. Coifman

Publication date: 4 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.acha.2011.06.002

zbMATH Keywords

embeddinggraph Laplacianindependent components analysisanisotropic diffusion mapsNyström extension

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Factor analysis and principal components; correspondence analysis (62H25) Diffusion processes (60J60)

Related Items

Local kernels and the geometric structure of data ⋮ Reconstruction of a Riemannian Manifold from Noisy Intrinsic Distances ⋮ Diffusion-based kernel methods on Euclidean metric measure spaces ⋮ Local conformal autoencoder for standardized data coordinates ⋮ Multi-view kernel consensus for data analysis ⋮ Manifold learning for the emulation of spatial fields from computational models ⋮ The pre-image problem for Laplacian Eigenmaps utilizing L ₁ regularization with applications to data fusion ⋮ Variable bandwidth diffusion kernels ⋮ Bi-stochastic kernels via asymmetric affinity functions ⋮ Texture separation via a reference set ⋮ Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation ⋮ A Geometrical Method for Low-Dimensional Representations of Simulations ⋮ Intrinsic modeling of stochastic dynamical systems using empirical geometry

Uses Software

• FastICA

Cites Work

• Non-linear independent component analysis with diffusion maps
• Finite sample approximation results for principal component analysis: A matrix perturbation approach
• On the distribution of the largest eigenvalue in principal components analysis
• Diffusion maps
• Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions
• Spectral independent component analysis
• Theory of Reproducing Kernels
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