SVM LEARNING AND Lp APPROXIMATION BY GAUSSIANS ON RIEMANNIAN MANIFOLDS

DOI10.1142/S0219530509001384zbMath1175.68346OpenAlexW4233058794WikidataQ115245537 ScholiaQ115245537MaRDI QIDQ3395345

Ding-Xuan Zhou, Gui-Bo Ye

Publication date: 26 August 2009

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530509001384

zbMATH Keywords

approximationreproducing kernel Hilbert spacesmanifold learninggeneral loss functionGaussian kernelsmulti-kernel regularized classifier

Mathematics Subject Classification ID

General nonlinear regression (62J02) Learning and adaptive systems in artificial intelligence (68T05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (9)

Normal estimation on manifolds by gradient learning ⋮ ERM learning algorithm for multi-class classification ⋮ Integral operator approach to learning theory with unbounded sampling ⋮ Intrinsic Dimension Adaptive Partitioning for Kernel Methods ⋮ Optimal learning rates for least squares regularized regression with unbounded sampling ⋮ Convergence rate of kernel canonical correlation analysis ⋮ Concentration estimates for learning with \(\ell ^{1}\)-regularizer and data dependent hypothesis spaces ⋮ Concentration estimates for the moving least-square method in learning theory ⋮ Adaptive learning rates for support vector machines working on data with low intrinsic dimension

Cites Work

• Semi-supervised learning on Riemannian manifolds
• Model selection for regularized least-squares algorithm in learning theory
• Multi-kernel regularized classifiers
• Learning and approximation by Gaussians on Riemannian manifolds
• Sobolev spaces on Riemannian manifolds
• The covering number in learning theory
• Statistical behavior and consistency of classification methods based on convex risk minimization.
• Regularization networks and support vector machines
• Fully online classification by regularization
• Consistency of spectral clustering
• Learning theory estimates via integral operators and their approximations
• Learning Theory: From Regression to Classification
• Learning Theory
• Capacity of reproducing kernel spaces in learning theory
• Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results
• ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY
• SVM Soft Margin Classifiers: Linear Programming versus Quadratic Programming
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

This page was built for publication: SVM LEARNING AND L^p APPROXIMATION BY GAUSSIANS ON RIEMANNIAN MANIFOLDS