A core tensor sparsity enhancement method for solving Tucker-2 model of multi-subject fMRI data

• Published in: Biomedical signal processing and control Vol. 95; p. 106471
• Main Authors: Han, Yue, Lin, Qiu-Hua, Kuang, Li-Dan, Zhao, Bin-Hua, Gong, Xiao-Feng, Cong, Fengyu, Wang, Yu-Ping, Calhoun, Vince D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2024
• Subjects: Core tensor; Cross-subject relationship; Orthogonality constraint; Schizophrenia; Tucker-2 model; Cross-subject relationship; Schizophrenia; Tucker-2 model; Core tensor; Orthogonality constraint
• ISSN: 1746-8094; 1746-8108
• DOI: 10.1016/j.bspc.2024.106471

•Core tensor sparsity of a Tucker-2 model is enhanced in a particular Tucker-3 model.•Orthogonality constraint is imposed on the third mode matrix to remove cross-talks.•The proposed model is solved by ADMM and HQS using tensor flattening method.•The proposed method improves estimations of non-sparse spatial components.•Novel features of cross-subject relationship increase the classification accuracy. The Tucker-2 decomposition model can reveal the intrinsic relationship in three-way multi-subject fMRI data by fully utilizing tensor structural information and also provide spatial and temporal evidences at both individual and shared levels. However, the third mode factor matrix of Tucker-2 model is an identity matrix, resulting in insufficient sparseness of the core tensor. In this work, we propose a method to enhance core tensor sparsity within the Tucker-2 model. More precisely, the proposed method is a relaxed approach for the Tucker-2 model by separating a non-identity factor matrix in the third mode from the core tensor. An orthogonality constraint is imposed on the third mode factor matrix to eliminate cross-talks, in addition to low-rank constraints on other factor matrices and sparsity constraint on spatial maps. We represent the propose model by flattened tensors, and solve the model using alternating direction method of multipliers and half quadratic splitting. The third mode factor matrix is updated by the orthogonal Procrustes solution. We show results from simulated fMRI data, task-related fMRI data, and resting-state fMRI data including patients with schizophrenia and controls. These results highlight the improvement of the proposed method at both shared and individual levels, compared with the sparsity-low rank-constraint Tucker-2 model and the generalized Tucker-3 model. Moreover, we show that we can extract the cross-subject relationship (CSR) from the third mode matrix. The proposed method improves the estimations of non-sparse spatial sources. The novel CSR matrix bring 7% improvement of accuracy when classifying schizophrenia patients and healthy controls.