Comparison and integration of subspaces from a biplot perspective

• Published in: Journal of statistical planning and inference Vol. 102; no. 2; pp. 411 - 423
• Main Authors: Martı́n-Rodrı́guez, Jesús, Galindo-Villardón, M a Purificación, Vicente-Villardón, José L.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.04.2002; New York,NY Elsevier Science; Amsterdam
• Subjects: Biplot method; Consensus subspace; Eigenvalue; Eigenvector; Exact sciences and technology; Mathematics; Multivariate analysis; Probability and statistics; Sciences and techniques of general use; Statistics; Eigenvalue; Biplot method; 62H99; Consensus subspace; Eigenvector; Multivariate analysis
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(01)00101-X

When one has information about a set of individuals on several variables, in different groups or contexts, and multivariate analysis is applied to each group the following questions arise: which groups show a similar response? how do the groups differ? how do the individuals differ in their responses in the different groups? These issues have led us to address a very interesting question in the practical context; the comparison and integration of the structures resulting from several multivariate analyses. Here we propose a method for the comparison and integration of the results arising from two Biplot analyses applied to the same variables in two different groups of individuals. By extension, we also develop the case of more than two Biplot analyses. Emphasis is placed on the underlying geometry and the interpretation of results, for which we offer indices that allow us to study the integrated structures and perform comparative analyses.