Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares
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 usin...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2022-01-01
|
| Series: | IEEE Transactions on Neural Systems and Rehabilitation Engineering |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9856690/ |
| _version_ | 1797805115932934144 |
|---|---|
| author | Li-Dan Kuang Qiu-Hua Lin Xiao-Feng Gong Jianming Zhang Wenjun Li Feng Li Vince D. Calhoun |
| author_facet | Li-Dan Kuang Qiu-Hua Lin Xiao-Feng Gong Jianming Zhang Wenjun Li Feng Li Vince D. Calhoun |
| author_sort | Li-Dan Kuang |
| collection | DOAJ |
| description | 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares. |
| first_indexed | 2024-03-13T05:47:16Z |
| format | Article |
| id | doaj.art-d0b4ebcb48a74ca8a45281f451d2affe |
| institution | Directory Open Access Journal |
| issn | 1558-0210 |
| language | English |
| last_indexed | 2024-03-13T05:47:16Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Transactions on Neural Systems and Rehabilitation Engineering |
| spelling | doaj.art-d0b4ebcb48a74ca8a45281f451d2affe2023-06-13T20:09:09ZengIEEEIEEE Transactions on Neural Systems and Rehabilitation Engineering1558-02102022-01-01302630264010.1109/TNSRE.2022.31986799856690Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least SquaresLi-Dan Kuang0https://orcid.org/0000-0002-0704-8950Qiu-Hua Lin1https://orcid.org/0000-0003-0145-7136Xiao-Feng Gong2https://orcid.org/0000-0001-8360-8107Jianming Zhang3https://orcid.org/0000-0002-4278-0805Wenjun Li4https://orcid.org/0000-0001-6121-588XFeng Li5https://orcid.org/0000-0003-2718-9918Vince D. Calhoun6https://orcid.org/0000-0001-9058-0747School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, ChinaSchool of Information and Communication Engineering, Dalian University of Technology, Dalian, ChinaSchool of Information and Communication Engineering, Dalian University of Technology, Dalian, ChinaSchool of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, ChinaSchool of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, ChinaSchool of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, ChinaTri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Atlanta, GA, USAComplex-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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> 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-<inline-formula> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.https://ieeexplore.ieee.org/document/9856690/Canonical polyadic decomposition (CPD)complex-valued fMRI dataorthonormalityshift-invariancesource phase sparsity |
| spellingShingle | Li-Dan Kuang Qiu-Hua Lin Xiao-Feng Gong Jianming Zhang Wenjun Li Feng Li Vince D. Calhoun Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares IEEE Transactions on Neural Systems and Rehabilitation Engineering Canonical polyadic decomposition (CPD) complex-valued fMRI data orthonormality shift-invariance source phase sparsity |
| title | Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares |
| title_full | Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares |
| title_fullStr | Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares |
| title_full_unstemmed | Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares |
| title_short | Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-<italic>R</italic> and Rank-1 Least Squares |
| title_sort | constrained cpd of complex valued multi subject fmri data via alternating rank italic r italic and rank 1 least squares |
| topic | Canonical polyadic decomposition (CPD) complex-valued fMRI data orthonormality shift-invariance source phase sparsity |
| url | https://ieeexplore.ieee.org/document/9856690/ |
| work_keys_str_mv | AT lidankuang constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT qiuhualin constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT xiaofenggong constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT jianmingzhang constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT wenjunli constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT fengli constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares AT vincedcalhoun constrainedcpdofcomplexvaluedmultisubjectfmridataviaalternatingrankitalicritalicandrank1leastsquares |