Phase-related spatial feature extraction via dynamic complex-valued tucker decomposition in multi-subject fMRI data

Group analysis of multi-subject fMRI data is vital for decoding brain functions and detecting brain disorders. Tucker decomposition, a multidimensional factorization technique, efficiently extracts shared spatiotemporal components and core tensors from fMRI datasets, making it well-suited for dynamic analyses. However, existing dynamic Tucker decomposition-based approaches overlook complex-valued information and underutilize the structural richness of core tensors. To address these gaps, we propose a sliding-window-based complex-valued Tucker decomposition framework with one-time-point overlap to capture fine-grained features. Our method incorporates spatial sparsity constraints, solved via the alternating direction method of multipliers combined with gradient descent approach, and resolves spatiotemporal ambiguity through core tensor uncompressing strategy. Using the extracted complex-valued spatial components for all the time windows, we propose to extract spatial voxel (SV) features and spatial functional network connectivity (sFNC) features. More importantly, we leverage the complex-valued core tensor to extract dynamic phase eigenvalue (PEV) features. Using resting-state fMRI data from schizophrenia patients (SZs) and healthy controls (HCs), the proposed method obtains SV features that captures group- and individual-level discrimination via one/two-sample t-tests on spatial components. By using PEV features along with sFNC features, our approach achieves 92.5% classification accuracy for SZ vs. HC, a 14.7% improvement over real-valued Tucker decomposition. This work highlights the utility of complex-valued Tucker decomposition methods in enhancing fMRI-based disease diagnosis by leveraging full tensor structural information and dynamic neural signatures.