Two-Stage Principal Component Analyzes of Symbolic Data Using Patterned Covariance Structures

• Activity Number: 219
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Anuradha Roy*+ and Chengcheng Hao and Yuli Liang
• Companies: University of Texas at San Antonio and Stockholm University and Stockholm University
• Keywords: Two-stage principal component analysis ; symbolic data ; patterned covariance structures

Abstract

New approaches to derive the principal components of symbolic data are proposed. This is done in two stages: first getting eigenblocks and eigenmatrices of the variance-covariance matrix, and then analyzing these eigenblocks and the corresponding principal vectors together in some seemly sense to get the adjusted eigenvalues and the corresponding eigenvectors of the interval data. The proposed methods are very efficient in two-level and three-level symbolic data sets. Results illustrating the accuracy and appropriateness of the new methods over the existing methods are presented. We have clearly shown that our proposed method for principal component analysis (PCA) of three-level symbolic data generalizes the commonly used PCA for multivariate data.