TY - JOUR
T1 - Symbolic covariance principal component analysis and visualization for interval-valued data
AU - Le-Rademacher, Jennifer
AU - Billard, Lynne
N1 - Funding Information:
The authors thank the Editor, the Associate Editor, and the referees for their helpful comments. Partial support to both authors from the National Science Foundation (NSF) grants is gratefully acknowledged.
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
KW - Convex hull
KW - Linear transformation
KW - Polytopes
KW - Symbolic data analysis
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U2 - 10.1080/10618600.2012.679895
DO - 10.1080/10618600.2012.679895
M3 - Article
AN - SCOPUS:84862569554
SN - 1061-8600
VL - 21
SP - 413
EP - 432
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
IS - 2
ER -