Approximation with polynomial kernels and SVM classifiers

DOI10.1007/s10444-004-7206-2zbMath1095.68103OpenAlexW1996388931MaRDI QIDQ2498387

Ding-Xuan Zhou, Kurt Jetter

Publication date: 16 August 2006

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-004-7206-2

zbMATH Keywords

classification algorithmmisclassification errorsupport vector machinepolynomial kernelregularization schemeapproximation by Durrmeyer operators

Mathematics Subject Classification ID

Nonnumerical algorithms (68W05) Learning and adaptive systems in artificial intelligence (68T05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Best choices for regularization parameters in learning theory: on the bias-variance problem.
• The covering number in learning theory
• Support vector machines are universally consistent
• Statistical behavior and consistency of classification methods based on convex risk minimization.
• Optimal aggregation of classifiers in statistical learning.
• Support-vector networks
• Regularization networks and support vector machines
• Shannon sampling. II: Connections to learning theory
• On the mathematical foundations of learning
• 10.1162/153244302760185252
• Capacity of reproducing kernel spaces in learning theory
• ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY
• Structural risk minimization over data-dependent hierarchies
• 10.1162/153244302760200704
• Shannon sampling and function reconstruction from point values
• Learning Theory
• Convexity, Classification, and Risk Bounds
• Theory of Reproducing Kernels

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