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Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares
Author(s) -
Li-Dan Kuang,
Qiu-Hua Lin,
Xiao-Feng Gong,
Jianming Zhang,
Wenjun Li,
Feng Li,
Vince D. Calhoun
Publication year - 2022
Publication title -
ieee transactions on neural systems and rehabilitation engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.093
H-Index - 140
eISSN - 1558-0210
pISSN - 1534-4320
DOI - 10.1109/tnsre.2022.3198679
Subject(s) - bioengineering , computing and processing , robotics and control systems , signal processing and analysis , communication, networking and broadcast technologies
Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- ${R}$ and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- ${R}$ least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- ${R}$ least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- ${R}$ and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

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