An empirical feature-based learning algorithm producing sparse approximations

Xin Guo, Ding Xuan Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)


A learning algorithm for regression is studied. It is a modified kernel projection machine (Blanchard et al., 2004 [2]) in the form of a least square regularization scheme withℓ1-regularizer in a data dependent hypothesis space based on empirical features (constructed by a reproducing kernel and the learning data). The algorithm has three advantages. First, it does not involve any optimization process. Second, it produces sparse representations with respect to empirical features under a mild condition, without assuming sparsity in terms of any basis or system. Third, the output function converges to the regression function in the reproducing kernel Hilbert space at a satisfactory rate. Our error analysis does not require any sparsity assumption about the underlying regression function.
Original languageEnglish
Pages (from-to)389-400
Number of pages12
JournalApplied and Computational Harmonic Analysis
Issue number3
Publication statusPublished - 1 May 2012
Externally publishedYes


  • ℓ 1 -regularizer
  • Empirical features
  • Learning theory
  • Reproducing kernel Hilbert space
  • Sparsity

ASJC Scopus subject areas

  • Applied Mathematics


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