Quantitative convergence analysis of kernel based large-margin unified machines

Jun FAN, Dao Hong Xiang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

High-dimensional binary classification has been intensively studied in the community of machine learning in the last few decades. Support vector machine (SVM), one of the most popular classifier, depends on only a portion of training samples called support vectors which leads to suboptimal performance in the setting of high dimension and low sample size (HDLSS). Large-margin unified machines (LUMs) are a family of margin-based classifiers proposed to solve the so-called "data piling" problem which is inherent in SVM under HDLSS settings. In this paper we study the binary classification algorithms associated with LUM loss functions in the framework of reproducing kernel Hilbert spaces. Quantitative convergence analysis has been carried out for these algorithms by means of a novel application of projection operators to overcome the technical difficulty. The rates are explicitly derived under priori conditions on approximation and capacity of the reproducing kernel Hilbert space.

Original languageEnglish
Pages (from-to)4069-4083
Number of pages15
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number8
DOIs
Publication statusPublished - Aug 2020

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Convergence rates
  • Kernel methods
  • LUMs
  • Projection operator
  • Regularization

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