Principal component histograms from interval-valued observations

J. Le-Rademacher, L. Billard

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The focus of this paper is to propose an approach to construct histogram values for the principal components of interval-valued observations. Le-Rademacher and Billard (J Comput Graph Stat 21:413-432, 2012) show that for a principal component analysis on interval-valued observations, the resulting observations in principal component space are polytopes formed by the convex hulls of linearly transformed vertices of the observed hyper-rectangles. In this paper, we propose an algorithm to translate these polytopes into histogram-valued data to provide numerical values for the principal components to be used as input in further analysis. Other existing methods of principal component analysis for interval-valued data construct the principal components, themselves, as intervals which implicitly assume that all values within an observation are uniformly distributed along the principal components axes. However, this assumption is only true in special cases where the variables in the dataset are mutually uncorrelated. Representation of the principal components as histogram values proposed herein more accurately reflects the variation in the internal structure of the observations in a principal component space. As a consequence, subsequent analyses using histogram-valued principal components as input result in improved accuracy.

Original languageEnglish (US)
Pages (from-to)2117-2138
Number of pages22
JournalComputational Statistics
Volume28
Issue number5
DOIs
StatePublished - Oct 1 2013

Keywords

  • Histogram-valued output data
  • Interval-valued input data
  • Linear transformation
  • Polytopes
  • Principal component analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

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