Cyclic-Shift Sparse Kronecker Tensor Classifier for Signal-Region Detection in Neuroimaging

TL;DR

This paper introduces a cyclic-shift sparse Kronecker tensor classifier that improves robustness and interpretability in neuroimaging signal-region detection, achieving accurate disease classification and relevant brain region localization.

Contribution

It develops a novel cyclic-shift logistic SKPD model with theoretical guarantees, enhancing tensor analysis for neuroimaging data with improved robustness and interpretability.

Findings

Accurate detection of disease-relevant brain regions.

Robustness to misalignment across subjects.

Strong classification performance on neuroimaging datasets.

Abstract

This study proposes a cyclic-shift logistic sparse Kronecker product decomposition (SKPD) model for high-dimensional tensor data, enhancing the SKPD framework with a cyclic-shift mechanism for binary classification. The method enables interpretable and scalable analysis of brain MRI data, detecting disease-relevant regions through a structured low-rank factorization. By incorporating a second spatially shifted view of the data, the cyclic-shift logistic SKPD improves robustness to misalignment across subjects, a common challenge in neuroimaging. We provide asymptotic consistency guarantees under a restricted isometry condition adapted to logistic loss. Simulations confirm the model's ability to recover spatial signals under noise and identify optimal patch sizes for factor decomposition. Application to OASIS-1 and ADNI-1 datasets demonstrates that the model achieves strong classification accuracy and localizes estimated coefficients in clinically relevant brain regions, such as the hippocampus. A data-driven slice selection strategy further improves interpretability in 2D projections. The proposed framework offers a principled, interpretable, and computationally efficient tool for neuroimaging-based disease diagnosis, with potential extensions to multi-class settings and more complex transformations.