Diffusion maps for changing data

DOI10.1016/j.acha.2013.03.001zbMath1302.62122arXiv1209.0245OpenAlexW3103521248MaRDI QIDQ2252180

Matthew J. Hirn, Ronald R. Coifman

Publication date: 16 July 2014

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

Full work available at URL: https://arxiv.org/abs/1209.0245

zbMATH Keywords

kernel methoddimensionality reductionspectral graph theorymanifold learninggraph Laplaciandynamic graphsdiffusion distance

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Nonparametric hypothesis testing (62G10) Linear inference, regression (62J99) Computing methodologies for image processing (68U10) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Related Items (19)

Local kernels and the geometric structure of data ⋮ Spatial-spectral operator theoretic methods for hyperspectral image classification ⋮ Time coupled diffusion maps ⋮ Multi-view kernel consensus for data analysis ⋮ The pre-image problem for Laplacian Eigenmaps utilizing L ₁ regularization with applications to data fusion ⋮ The stability of the first Neumann Laplacian eigenfunction under domain deformations and applications ⋮ Ensemble forecasts in reproducing kernel Hilbert space family ⋮ Data Based Construction of Kernels for Classification ⋮ Manifold learning for parameter reduction ⋮ A unified framework for harmonic analysis of functions on directed graphs and changing data ⋮ Introducing User-Prescribed Constraints in Markov Chains for Nonlinear Dimensionality Reduction ⋮ Determining baseline profile by diffusion maps ⋮ Diffusion maps-aided neural networks for the solution of parametrized PDEs ⋮ Diffusion maps tailored to arbitrary non-degenerate Itô processes ⋮ Diffusion representation for asymmetric kernels ⋮ Diffusion nets ⋮ Partitions of networks that are robust to vertex permutation dynamics ⋮ Recovering Hidden Components in Multimodal Data with Composite Diffusion Operators ⋮ Sparse control of alignment models in high dimension

Cites Work

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• Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets
• Mercer’s Theorem, Feature Maps, and Smoothing
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• Theory of Reproducing Kernels

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