Spatially adaptive sparse grids for high-dimensional data-driven problems

Dirk Pflger, Benjamin Peherstorfer, Hans Joachim Bungartz

Research output: Contribution to journalArticle

Abstract

Sparse grids allow one to employ grid-based discretization methods in data-driven problems. We present an extension of the classical sparse grid approach that allows us to tackle high-dimensional problems by spatially adaptive refinement, modified ansatz functions, and efficient regularization techniques. The competitiveness of this method is shown for typical benchmark problems with up to 166 dimensions for classification in data mining, pointing out properties of sparse grids in this context. To gain insight into the adaptive refinement and to examine the scope for further improvements, the approximation of non-smooth indicator functions with adaptive sparse grids has been studied as a model problem. As an example for an improved adaptive grid refinement, we present results for an edge-detection strategy.

Original languageEnglish (US)
Pages (from-to)508-522
Number of pages15
JournalJournal of Complexity
Volume26
Issue number5
DOIs
StatePublished - Oct 2010

Keywords

  • Classification
  • High-dimensional approximation
  • Non-smooth functions
  • Regularization
  • Spatially adaptive sparse grids

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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