This article proposes a procedure for describing the relationship between high-dimensional data sets, such as multimodal brain images and genetic data. We propose a supervised technique to incorporate the clinical outcome to determine a score, which is a linear combination of variables with hieratical structures to multimodalities. This approach is expected to obtain interpretable and predictive scores. The proposed method was applied to a study of Alzheimer's disease (AD). We propose a diagnostic method for AD that involves using whole-brain magnetic resonance imaging (MRI) and positron emission tomography (PET), and we select effective brain regions for the diagnostic probability and investigate the genome-wide association with the regions using single nucleotide polymorphisms (SNPs). The two-step dimension reduction method, which we previously introduced, was considered applicable to such a study and allows us to partially incorporate the proposed method. We show that the proposed method offers classification functions with feasibility and reasonable prediction accuracy based on the receiver operating characteristic (ROC) analysis and reasonable regions of the brain and genomes. Our simulation study based on the synthetic structured data set showed that the proposed method outperformed the original method and provided the characteristic for the supervised feature.