Symbolic covariance principal component analysis and visualization for interval-valued data

Jennifer Le-Rademacher, Lynne Billard

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


This article proposes a new approach to principal component analysis (PCA) for interval-valued data. Unlike classical observations, which are represented by single points in p-dimensional space R p interval-valued observations are represented by hyperrectangles in R p, and as such, have an internal structure that does not exist in classical observations. As a consequence, statistical methods for classical data must be modified to account for the structure of the hyper-rectangles before they can be applied to intervalvalued data. This article extends the classical PCA method to interval-valued data by using the so-called symbolic covariance to determine the principal component (PC) space to reflect the total variation of interval-valued data. The article also provides a new approach to constructing the observations in a PC space for better visualization. This new representation of the observations reflects their true structure in the PC space. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)413-432
Number of pages20
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Jun 2012


  • Convex hull
  • Linear transformation
  • Polytopes
  • Symbolic data analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics


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