Canonical correlation analysis with linear constraints

Abstract We develop canonical correlation analysis by imposing linear constraints upon parameters corresponding to two sets of variables. The results of our method, which we call canolc , are shown in terms of projection operators both orthogonal and oblique. Further, calc (correspondence analysis with linear constraints) turns out to be a special case of canolc .

[1]  C. G. Khatri,et al.  A note on a manova model applied to problems in growth curve , 1966 .

[2]  H. Yanai,et al.  Some generalized forms of least squares g -inverse, minimum norm g -inverse, and Moore—Penrose inverse matrices , 1990 .

[3]  C. G. Khatri,et al.  A note on multiple and canonical correlation for a singular covariance matrix , 1976 .

[4]  C. Braak.  Canonical Correspondence Analysis: A New Eigenvector Technique for Multivariate Direct Gradient Analysis , 1986 .

[5]  EXPLICIT EXPRESSIONS OF PROJECTORS ON CANONICAL VARIABLES AND DISTANCES BETWEEN CENTROIDS OF GROUPS , 1981 .

[6]  H. Yanai,et al.  Canonical correlations associated with symmetric reflexive generalized inverses of the dispersion matrix , 1992 .

[7]  R. Clarke,et al.  Theory and Applications of Correspondence Analysis , 1985 .

[8]  Shin-ichi Mayekawa,et al.  Relationships among several methods of linearly constrained correspondence analysis , 1991 .

[9]  Y. Takane,et al.  Principal component analysis with external information on both subjects and variables , 1991 .

[10]  C. Khatri.  Some properties of BLUE in a linear model and canonical correlations associated with linear transformations , 1990 .

[11]  Ulf Böckenholt,et al.  Canonical analysis of contingency tables with linear constraints , 1990 .

[12]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[13]  C. Radhakrishna Rao,et al.  General definition and decomposition of projectors and some applications to statistical problems , 1979 .