A ‘subdivision regression’ model for data analysis

Sigalit Hed, David Levin

Research output: Contribution to journalArticlepeer-review

Abstract

Subdivision schemes are multi-resolution methods used in computer-aided geometric design to generate smooth curves or surfaces. We propose two new models for data analysis and compression based on subdivision schemes:(a) The ‘subdivision regression’ model, which can be viewed as a special multi-resolution decomposition.(b) The ‘tree regression’ model, which allows the identification of certain patterns within the data. The paper focuses on analysis and mentions compression as a byproduct. We suggest applying certain criteria on the output of these models as features for data analysis. Differently from existing multi-resolution analysis methods, these new models and criteria provide data features related to the schemes (the filters) themselves, based on a decomposition of the data into different resolution levels, and they also allow analysing data of non-smooth functions and working with varying-resolution subdivision rules. Finally, applications of these methods for music analysis and other potential usages are mentioned.

Original languageEnglish
Pages (from-to)1683-1712
Number of pages30
JournalInternational Journal of Computer Mathematics
Volume91
Issue number8
DOIs
StatePublished - 1 Aug 2014

Keywords

  • multi-resolution analysis and approximation
  • patterns
  • subdivision schemes
  • symmetry
  • trees

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