Abstract
Multivariate analysis has been widely used and one of the popular multivariate analysis methods is canonical correlation analysis (CCA). CCA finds the linear combination in each group that maximizes the Pearson correlation. CCA has been extended to a kernel CCA for nonlinear relationships and generalized CCA that can consider more than two groups. We propose an extension of CCA that allows multi-group and nonlinear relationships in an additive fashion for a better interpretation, which we termed as Generalized Additive Kernel Canonical Correlation Analysis (GAKCCA). In addition to exploring multi-group relationship with nonlinear extension, GAKCCA can reveal contribution of variables in each group; which enables in-depth structural analysis. A simulation study shows that GAKCCA can distinguish a relationship between groups and whether they are correlated or not. We applied GAKCCA to real data on neurodevelopmental status, psychosocial factors, clinical problems as well as neurophysiological measures of individuals. As a result, it is shown that the neurophysiological domain has a statistically significant relationship with the neurodevelopmental domain and clinical domain, respectively, which was not revealed in the ordinary CCA.
Highlights
Multivariate analysis has been widely used and one of the popular multivariate analysis methods is canonical correlation analysis (CCA)
Generalized Additive Kernel Canonical Correlation Analysis (GAKCCA), we use a Gaussian kernel for each variable
The design matrix, scheme function, the number of resamples for the permutation test and the number of simulated data sets are same as the ones that we considered for GAKCCA
Summary
Multivariate analysis has been widely used and one of the popular multivariate analysis methods is canonical correlation analysis (CCA). We propose an extension of CCA that allows multi-group and nonlinear relationships in an additive fashion for a better interpretation, which we termed as Generalized Additive Kernel Canonical Correlation Analysis (GAKCCA). CCA finds linear combinations of each group that maximize a Pearson correlation coefficient between them In this way, CCA can serve as a dimension reduction method as each multi-dimensional variable is reduced to a linear combination. CCA can serve as a dimension reduction method as each multi-dimensional variable is reduced to a linear combination This advantage makes CCA widely used in many scientific fields that mostly deal with high dimensional data such as psychology, neuroscience, medical science and image recognition[4,5,6,7], etc. To find nonlinear relationship beyond linear one such as speech communication science, genetics and pattern recognition[9,10,11], etc
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