EXPLICIT EXPRESSIONS OF PROJECTORS ON CANONICAL VARIABLES AND DISTANCES BETWEEN CENTROIDS OF GROUPS

抄録

Generalized expressions of canonical correlation analysis and partial canonical correlation analysis are introduced, in which the sum of the squared canonical and partial canonical correlation coefficients for each are given as the traces of the product of two orthogonal projectors and that of two oblique projectors respectively.
Following the result, some explicit expressions of projectors are obtained in connection with the product of two projectors defined in terms of canonical variables arising in canonical correlation analysis, partial canonical correlation analysis and part canonical correlation analysis, and the results are applied for showing that the Euclidian distance based on canonical variables turns out to be Mahalanobis' generalized distance with a slight modification.