Canonical correlation analysis (Hotelling, 1935, 1936) has been long used as a standard method in multivariate analysis. Whose merit is simply to catch the linear relations between p x 1 vector Y-set and q x 1 vector X-set. However, it could fail when there is no linear trend between them while the relation goes through nonlinear way. To overcome this drawback, here we develop a new canonical correlation method between Y-set and X-set, called moment canonical correlation. This method finds relationships between the two sets whether linearly or nonlinearly. It can recover nonlinear relations between the two sets if exists. It extends the usual canonical correlation analysis. Examples illustrating this new method are presented.
Nonlinear Canonical Correlation Method in Multivariate Analysis