Shift-Aware Sparse Kronecker Tensor Classification

Analyzing high-dimensional neuroimaging data for disease classification is challenged by spatial misalignment across subjects. We propose a cyclic-shift logistic sparse Kronecker product decomposition (SKPD) model, which embeds a shift-aware mechanism into a low-rank tensor regression framework. By generating adaptively aligned views of the input, the model improves robustness to anatomical variability while preserving interpretability through sparse spatial factorization. Theoretical analysis establishes asymptotic consistency under a restricted isometry condition adapted to logistic loss. Simulation studies demonstrate accurate signal recovery under noise and misalignment, with favorable trade-offs between resolution and efficiency. Applied to the Open Access Series of Imaging Studies (OASIS)-1 and Alzheimer's Disease Neuroimaging Initiative (ADNI)-1 MRI data, the model achieves strong classification performance for Alzheimer’s disease and identifies clinically relevant regions, such as the hippocampus and cerebellum. Together, these results highlight the method's promise as a scalable and interpretable tool for neuroimaging-based disease diagnosis. An open-source Python package implementing the method is publicly available.