Kuang Li-Dan, Lin Qiu-Hua, Gong Xiao-Feng, Cong Fengyu, Sui Jing, Calhoun Vince D
School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China.
School of Information and Communication Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China.
J Neurosci Methods. 2015 Dec 30;256:127-40. doi: 10.1016/j.jneumeth.2015.08.023. Epub 2015 Sep 4.
Canonical polyadic decomposition (CPD) may face a local optimal problem when analyzing multi-subject fMRI data with inter-subject variability. Beckmann and Smith proposed a tensor PICA approach that incorporated an independence constraint to the spatial modality by combining CPD with ICA, and alleviated the problem of inter-subject spatial map (SM) variability.
This study extends tensor PICA to incorporate additional inter-subject time course (TC) variability and to connect CPD and ICA in a new way. Assuming multiple subjects share common TCs but with different time delays, we accommodate subject-dependent TC delays into the CP model based on the idea of shift-invariant CP (SCP). We use ICA as an initialization step to provide the aggregating mixing matrix for shift-invariant CPD to estimate shared TCs with subject-dependent delays and intensities. We then estimate shared SMs using a least-squares fit post shift-invariant CPD.
Using simulated fMRI data as well as actual fMRI data we demonstrate that the proposed approach improves the estimates of the shared SMs and TCs, and the subject-dependent TC delays and intensities. The default mode component illustrates larger TC delays than the task-related component.
COMPARISON WITH EXISTING METHOD(S): The proposed approach shows improvements over tensor PICA in particular when TC delays are large, and also outperforms SCP with SM orthogonality constraint and SCP with ICA-based SM initialization.
TCs with subject-dependent delays conform to the true situation of multi-subject fMRI data. The proposed approach is suitable for decomposing multi-subject fMRI data with large inter-subject temporal and spatial variability.
在分析具有个体间变异性的多主体功能磁共振成像（fMRI）数据时，典范多向分解（CPD）可能会面临局部最优问题。贝克曼和史密斯提出了一种张量独立成分分析（PICA）方法，该方法通过将CPD与独立成分分析（ICA）相结合，在空间模态中纳入了独立性约束，缓解了个体间空间图谱（SM）变异性的问题。
本研究扩展了张量PICA，以纳入额外的个体间时间进程（TC）变异性，并以一种新的方式连接CPD和ICA。假设多个主体共享共同的时间进程，但具有不同的时间延迟，我们基于平移不变CP（SCP）的思想，将依赖于主体的时间延迟纳入CP模型。我们使用ICA作为初始化步骤，为平移不变CPD提供聚合混合矩阵，以估计具有依赖于主体的延迟和强度的共享时间进程。然后，我们使用平移不变CPD后的最小二乘拟合来估计共享的空间图谱。
使用模拟的fMRI数据以及实际的fMRI数据，我们证明了所提出的方法改进了共享空间图谱和时间进程的估计，以及依赖于主体的时间延迟和强度。默认模式成分显示出比任务相关成分更大的时间延迟。
所提出的方法尤其在时间延迟较大时，相对于张量PICA有改进，并且也优于具有SM正交性约束的SCP和基于ICA的SM初始化的SCP。
具有依赖于主体的延迟的时间进程符合多主体fMRI数据的真实情况。所提出的方法适用于分解具有大的个体间时间和空间变异性的多主体fMRI数据。
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