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. Multivariate analysis is a statistical method that considers several variables simultaneously. Compared with univariate analysis, which focus on the influence of one variable only, multivariate analysis takes into account not only the effect of each variable but also interaction between variables. Thus, multivariate analysis gets popular as researchers face to more complex data. A number of statistical methods concerning multivariate analysis have been developed and widely used. For instance, principle component analysis (PCA), first proposed by Pearson 1 is a method that compresses the data in the high dimensional space into the low dimensional space by identifying dimensions in which the variability of the data are explained the most. Factor analysis extracts underlying, but unobservable random quantities by assuming variables are expressed with those random quantities 2. One of the popular multivariate analysis is canonical correlation analysis (CCA). CCA, proposed by Hotelling 3 , explores association between two multivariate groups. CCA finds linear combinations of each group that maximize a Pearson correlation coefficient between them. In this way, CCA can also 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 4-7 , etc. Despite of its strength, CCA has some limitations. CCA is restricted to linear relationship only so that the result of CCA can be misleading if two variables are linked with a non-linear relation. This limitation is inherited from the characteristics of the Pearson correlation. For example, if two random variables X and Y are relat...

People experience the same event but do not feel the same way. Such individual differences in emotion response are believed to be far greater than those in any other mental functions. Thus, to understand what makes people individuals, it is important to identify the systematic structures of individual differences in emotion response and elucidate how such structures relate to what aspects of psychological characteristics. Reflecting this importance, many studies have attempted to relate emotions to psychological characteristics such as personality traits, psychosocial states, and pathological symptoms across individuals. However, systematic and global structures that govern the across-individual covariation between the domain of emotion responses and that of psychological characteristics have been rarely explored previously, which limits our understanding of the relationship between individual differences in emotion response and psychological characteristics. To overcome this limitation, we acquired high-dimensional data sets in both emotion-response (8 measures) and psychological-characteristic (68 measures) domains from the same pool of individuals (86 undergraduate or graduate students) and carried out the canonical correlation analysis in conjunction with the principal component analysis on those data sets. For each participant, the emotion-response measures were quantified by regressing affective-rating responses to visual narrative stimuli onto the across-participant average responses to those stimuli, while the psychological-characteristic measures were acquired from 19 different psychometric questionnaires grounded in personality, psychosocial-factor, and clinical-problem taxonomies. We found a single robust mode of population covariation, particularly between the ’accuracy’ and ’sensitivity’ measures of arousal responses in the emotion domain and many ‘psychosocial’ measures in the psychological-characteristics domain. This mode of covariation suggests that individuals characterized with positive social assets tend to show polarized arousal responses to life events.