Multi-Modal Tensor Factorization: Tucker Decomposition Applied to Medical Imaging Datasets

Tucker decomposition extends the singular valuedecomposition (SVD) to higher-order tensors by representing atensor as a smaller core tensor together with orthogonal factormatrices. This provides a way to reduce dimensionality andmakes it possible to analyze large medical tensors, such as 3Dvoxelized images, in a more efficient manner. In this study, we firstdemonstrate Tucker decomposition on a small 3 × 3 × 3 tensorand then apply mode-wise SVD to real 3D medical datasets:VesselMNIST3D (intracranial vessels) and OrganMNIST3D (livertumors). For vessel tensors, the singular values decay rapidlyacross modes, indicating low-rank, tubular structures. In contrast,liver tumor tensors show a slower decay with higher rank,reflecting more complex morphology. These results suggest thatTucker decomposition and mode-wise SVD are effective tools foridentifying and comparing structural features in 3D medical data.