Multi-scale geometric methods for data sets. II: Geometric multi-resolution analysis

DOI10.1016/j.acha.2011.08.001zbMath1242.42038arXiv1105.4924OpenAlexW2964012263MaRDI QIDQ413654

Guangliang Chen, William K. Allard, Mauro Maggioni

Publication date: 7 May 2012

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

Full work available at URL: https://arxiv.org/abs/1105.4924

zbMATH Keywords

multiresolution analysisframemulti-scale analysisdictionary learninggeometric waveletshigh-dimensional data set

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Learning and adaptive systems in artificial intelligence (68T05) Nontrigonometric harmonic analysis (42C99)

Related Items

Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data ⋮ Manifold Learning and Nonlinear Homogenization ⋮ A machine learning approach to optimal Tikhonov regularization I: Affine manifolds ⋮ Multiscale regression on unknown manifolds ⋮ Multiscale geometric methods for data sets. I: Multiscale SVD, noise and curvature. ⋮ Reprint of: A forward-backward greedy approach for sparse multiscale learning ⋮ Constraint matrix factorization for space variant PSFs field restoration ⋮ Deep nonparametric estimation of intrinsic data structures by chart autoencoders: generalization error and robustness ⋮ Hierarchical regularization networks for sparsification based learning on noisy datasets ⋮ Approximation of curve-based sleeve functions in high dimensions ⋮ Approximation of functions over manifolds: a moving least-squares approach ⋮ An analyst's traveling salesman theorem for sets of dimension larger than one ⋮ Extraction and prediction of coherent patterns in incompressible flows through space-time koopman analysis ⋮ Local Linear Regression on Manifolds and Its Geometric Interpretation ⋮ Learning sets with separating kernels ⋮ ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds ⋮ On recovery guarantees for one-bit compressed sensing on manifolds ⋮ The shape of data and probability measures ⋮ Metrics, quantization and registration in varifold spaces ⋮ Bayesian Multiscale Modeling of Closed Curves in Point Clouds ⋮ Solving inverse problems using data-driven models ⋮ Approximation of generalized ridge functions in high dimensions ⋮ A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks ⋮ Data-driven spectral decomposition and forecasting of ergodic dynamical systems ⋮ A forward-backward greedy approach for sparse multiscale learning ⋮ Unnamed Item

Uses Software

• PDCO

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
• Unnamed Item
• Fast high-dimensional approximation with sparse occupancy trees
• Asymptotic regularity of subdivisions of Euclidean domains by iterated PCA and iterated 2-means
• Rectifiable sets and the traveling salesman problem
• Random projections of smooth manifolds
• The traveling salesman problem and harmonic analysis
• Fast computation in adaptive tree approximation
• Multiscale geometric methods for data sets. I: Multiscale SVD, noise and curvature.
• Finding the homology of submanifolds with high confidence from random samples
• Diffusion maps
• Diffusion wavelets
• Diffusion wavelet packets
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• Curvature Measures
• A theory for multiresolution signal decomposition: the wavelet representation
• Image decomposition via the combination of sparse representations and a variational approach
• A Randomized Algorithm for Principal Component Analysis
• Ten Lectures on Wavelets
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
• Atomic Decomposition by Basis Pursuit
• A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
• Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
• Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods
• Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Uniform rectifiability and quasiminimizing sets of arbitrary codimension
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• Multiscale Representations for Manifold-Valued Data
• An introduction to frames and Riesz bases
• Intrinsic dimension estimation of data: An approach based on Grassberger-Procaccia's algorithm