Multi-Modal Tensor Factorization: Tucker Decomposition Applied to Medical Imaging Datasets
Year: 2025
Type: article
Abstract: 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.
Authors: Sharma, Upashana, Rai, Sulochana, Regmi, Sudip, Singh, Britan, Mukherjee, Dr. Rupak
Institution: Sikkim University
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7087447033
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