Employing tensor regression for analyzing the effect of alcohol on the brain

Abstract A tensor, also called a multidimensional array, is a generalization of a higher-order matrix and is used in many medical applications. In neuroimaging, tensor response regression is often employed to detect areas of the brain that are activated by specific predictors. Due to their large size, different decompositions are utilized when working with tensor-valued response. In this study, we compared the quality of the fit of several tensor decomposition approaches for analyzing the effect of alcohol abuse on different areas of the brain. This paper focuses on two of the main tensor decompositions: Tucker decomposition and penalized canonical polyadic (CP) decomposition. Our results show that the penalized CP regression provided the best performance, and Tucker PLS and 1D methods yielded similar results. All models outperformed the traditional ordinary least squares (OLS) approach.