Canonical Correlation：典型相关分析.doc

Canonical Correlation Overview A canonical correlation is the correlation of two canonical (latent) variables, one representing a set of independent variables, the other a set of dependent variables. Each set may be considered a latent variable based on measured indicator variables in its set. The canonical correlation is optimized such that the linear correlation between the two latent variables is maximized. Whereas multiple regression is used for many-to-one relationships, canonical correlation is used for many-to-many relationships. There may be more than one such linear correlation relating the two sets of variables, with each such correlation representing a different dimension by which the independent set of variables is related to the dependent set. The purpose of canonical correlation is to explain the relation of the two sets of variables, not to model the individual variables. For each canonical variate we can also assess how strongly it is related to measured variables in its own set, or the set for the other canonical variate. Wilkss lambda is commonly used to test the significance of canonical correlation. Analogous with ordinary correlation, canonical correlation squared is the percent of variance in the dependent set explained by the independent set of variables along a given dimension (there may be more than one). In addition to asking how strong the relationship is between two latent variables, canonical correlation is useful in determining how many dimensions are needed to account for that relationship. Canonical correlation finds the linear combination of variables that produces the largest correlation with the second set of variables. This linear combination, or root, is extracted and the process is repeated for the residual data, with the constraint that the second linear combination of variables must not correlate with the first one. The process is repeated until a successive linear combination is no longer significant. Canonical correlation