Penalized Canonical Correlation Analysis for MEG Data

Abstract

Canonical correlation analysis is a statistical method used to examine linear relationships between two sets of variables measured on the same statistical units, by forming highly correlated linear combinations of the variables in each set. This method cannot be used in the context of high-dimensional data, where the number of variables in either variable set exceeds the sample size. In this setting, sparse canonical correlation analysis (SCCA) can be utilized to perform regularized canonical correlation for high-dimensional data, producing sparse solutions more feasible for interpretation. In this thesis SCCA was used to explore the associations between temperamental traits and interoception. Temperamental traits decribe a person’s dispositional responses to changes in their environment, while interoception refers to a person’s sensitivity to stimuli originating from inside their own body, such as heart beat. Both of these attributes have a neurobiological basis, and some temperamental traits, especially ones related to anxiety have been found to be linked to interoceptive sensitivity. A data set consisting of magnetoencephalography (MEG) measurements of neuronal activity recorded during an interoception task and temperament questionnaire answers from 28 subjects was analyzed using SCCA with and without penalization in high dimensional setting, and after dimension reduction achieved by principal component analysis (PCA). While a pattern of higher α-oscillation activity during an interoception task in the left parietal and right frontal lobe associated with lower scores on the Beck Anxiety Inventory and Fun seeking section of Behavioral Activation Scale, and higher α-activity in the left frontal lobe associated with higher scores on the same questionnaires was observed, no statistically significant canonical pairs were found based on permutation tests. SCCA was found to ease interpretation of the canonical coefficients of the questionnaire variables via sparse coefficients, but overly sparse coefficients for MEG variables can hinder interpretation, as the spatial resolution of MEG is not enough to discern small areas of neuronal activation. For this reason larger areas of brain activation are preferred and canonical coefficients gained through PCA can be more useful for interpretation.