As we are in the end trying to maximize the covariance between Y 1a (i) and Y 2b (i) and to minimize their respective variance, we might obtain components that are well correlated among each other, but that are not explaining well Y 1 and Y 2. Constraints must be introduced so that the solution for a (i) and b (i) is unique. Canonical Correlation Analysis aims at obtaining two vectors a (i) and b (i) such that Let Y 1 and Y 2 be two tables, with respectively p and q variables. This method is symmetrical, contrary to RDA, and is not oriented towards prediction. Principles of Canonical Correlation Analysis Origins and aim of Canonical Correlation AnalysisĬanonical Correlation Analysis (CCorA, sometimes CCA, but we prefer to use CCA for Canonical Correspondence Analysis) is one of the many statistical methods that allow studying the relationship between two sets of variables.It studies the correlation between two sets of variables and extract from these tables a set of canonical variables that are as much as possible correlated with both tables and orthogonal to each other.ĭiscovered by Hotelling (1936) this method is used a lot in ecology but is has been supplanted by RDA ( Redundancy Analysis) and by CCA (Canonical Correspondence Analysis).
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