Semi-inner-products in Banach Spaces with Applications to Regularized Learning, Sampling, and Sparse Approximation

Abstract

The goal of this project is to fully develop Banach space methods for kernel-based machine learning that extend the Hilbert space framework of regularized learning. We proposed to study Reproducing Kernel Banach Spaces (RKBS) by the semi-inner-product, develop the theory of vector-valued RKBS with applications of RKBS to manifold learning, study frames and Riesz bases for sequence spaces, and construct RKBS with the l1-norm known to enforce sparse solutions. We will also explore classification algorithms that are mathematically rigorous while rooted in human cognitive principles for categorization. Our execution plan include three specific topics (Aims) 1. Apply RKBS theory to Orlicz space, to perform convergence analysis, and to study Shannon sampling schemes; 2. Work out vector-valued RKBS, and study s.i.p with l1 norm; 3. Develop frames and Riesz bases for Banach spaces, and extend analysis and synthesis operators.

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Document Details

Document Type
Technical Report
Publication Date
Mar 13, 2016
Accession Number
AD1011125

Entities

People

  • Jun Zhang

Organizations

  • University of Michigan

Tags

Communities of Interest

  • Autonomy
  • Human Systems

DTIC Thesaurus Topics

  • Abstracts
  • Agreements
  • Algorithms
  • Banach Space
  • Cognitive Radio
  • Communication Systems
  • Compressed Sensing
  • Department Of Defense
  • Engineering
  • Geometry
  • Hilbert Space
  • Kernel Functions
  • Machine Learning
  • Mathematics
  • Students
  • Topology
  • Wireless Communications

Fields of Study

  • Computer science

Readers

  • Linear Algebra
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Space