Accession Number:

AD1011125

Title:

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

Descriptive Note:

Technical Report,01 May 2012,31 Dec 2015

Corporate Author:

University of Michigan - Ann Arbor Ann Arbor United States

Personal Author(s):

• Zhang,Jun

Report Date:

2016-03-13

Pagination or Media Count:

9.0

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.

Descriptors:

• banach space
• kernel functions
• machine learning
• hilbert space
• algorithms

Subject Categories:

• Cybernetics
• Numerical Mathematics
• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE