Canonical Correlation Analysis of Principal Component Scores for Multiple-set Random Vectors

Canonical correlation analysis (CCA) is often used to analyze correlations between the variables of two random vectors. As an extension of CCA, multiple-set canonical correlation analysis (MCCA) was proposed to analyze correlations between multiple-set random vectors. However, sometimes interpreting MCCA results may not be as straightforward as interpreting CCA results. Principal CCA (PCCA), which uses CCA between two sets of principal component (PC) scores, was proposed to address these difficulties in CCA. We propose multiple-set PCCA (MPCCA) by applying the idea to multiple-set of PC scores. PCs are ranked in descending order according to the amount of information they contain. Therefore, it is enough to use only a few PC scores from the top instead of using all PC scores. Decreasing the number of PC makes it easy to interpret the result. We confirmed the effectiveness of MPCCA using simulation studies and a practical example.