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An improved multi-objective optimization-based CICA method with data-driver temporal reference for group fMRI data analysis

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Abstract

Group independent component analysis (GICA) has been successfully applied to study multi-subject functional magnetic resonance imaging (fMRI) data, and the group independent component (GIC) represents the commonality of all subjects in the group. However, some studies show that the performance of GICA can be improved by incorporating a priori information, which is not always considered when looking for GICs in existing GICA methods. In this paper, we propose an improved multi-objective optimization-based constrained independent component analysis (CICA) method to take advantage of the temporal a priori information extracted from all subjects in the group by incorporating it into the computational process of GICA for group fMRI data analysis. The experimental results of simulated and real data show that the activated regions and the time course detected by the improved CICA method are more accurate in some sense. Moreover, the GIC computed by the improved CICA method has a higher correlation with the corresponding independent component of each subject in the group, which means that the improved CICA method with the temporal a priori information extracted from the group can better reflect the commonality of the subjects. These results demonstrate that the improved CICA method has its own advantages in fMRI data analysis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants No. 31470954, No. 61271446), the Research Foundation from Shanghai Science and Technology Project (Grant No. 14590501700), the Innovation Program of Shanghai Municipal Education Commission (Grant No.15ZZ079), the Programs for Graduate Special Endowment Fund for Innovative Developing (Grant No. 2015ycx081), and Excellent Doctoral Dissertation Cultivation (Grant No. 2015bxlp005) of Shanghai Maritime University.

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Correspondence to Weiming Zeng.

Appendices

Appendix 1

In this section, we provide a detailed description of extracting spatial a priori information from group data [33]. Similar to extracting temporal a priori information from group data as described in this paper, we first need to implement ICA at the single-subject level. Now assuming that we have obtained the ICs, S i (i = 1, 2, …, K), of each subject in the group using formula (6), then these ICs will be used to extract the spatial a priori information by principal component analysis (PCA). For simplicity, we consider the situation in which each subject in the group has one IC of interest corresponding to the group IC (GIC). The correspondence of the ICs across different subjects corresponding to the GIC can be measured using the absolute value of the spatial correlation [36].

We denote the location set of voxels in the mask of subject i as VLS i i = 1, 2, …, K), and \( {\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}}\left(\ i=1,2,\dots, K\right) \) denotes the n i th IC of subject i corresponding to the GIC of interest. Then, we can calculate the location set of common activated voxels in all \( {\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}}\left(\ i=1,2,\dots, K\right) \) at the same threshold θ and denote it as CAVLS:

$$ \boldsymbol{CAVLS}=\left\{j| abs\left({\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}}\left(\boldsymbol{j}\right)\right)\ge \theta, j\in \boldsymbol{V}{\boldsymbol{LS}}_{\boldsymbol{i}},i=1,2,\dots, K\right\} $$
(s1)

Let \( {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}}\left(i=1,2,\dots, K\right) \) denote the common voxels from \( {\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}} \) with regard to the index CAVLS where \( {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}} \)is a column vector of size v × 1 and can be retrieved as

$$ {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}}=\left\{ abs\left({\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}}(j)\right)|j\in \boldsymbol{CAVLS}\right\},\left(i=1,2,\dots, K\right) $$
(s2)

Here, the absolute value in \( {\boldsymbol{s}}_{\boldsymbol{i}{\boldsymbol{n}}_{\boldsymbol{i}}} \) is used in formula (s1) and formula (s2) due to the network of interest possibly having negative activation in the IC. Although it may mean that \( {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}}\left(\ i=1,2,\dots, K\right) \) contains some noise, the spatial reference is extracted from all \( {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}}\left(\ i=1,2,\dots, K\right) \) by PCA, which has the ability to reduce the noise.

Now we use PCA to calculate the spatial reference signal from the K × v matrix R which consists of all\( {\boldsymbol{s}}_{{\boldsymbol{i}\boldsymbol{n}}_{\boldsymbol{i}}}^{\boldsymbol{c}}\left(i=1,2,\dots, K\right) \):

$$ \boldsymbol{R}={\left[{\boldsymbol{s}}_{1{\boldsymbol{n}}_1}^{\boldsymbol{c}},{\boldsymbol{s}}_{2{\boldsymbol{n}}_2}^{\boldsymbol{c}},\dots, {\boldsymbol{s}}_{{\boldsymbol{K}\boldsymbol{n}}_{\boldsymbol{K}}}^{\boldsymbol{c}}\right]}^{\prime } $$
(s3)

Then, the eigenvalue λ k  (k = 1, 2, …, K) such that λ 1 ≥ λ 2 ≥  ⋯  ≥ λ K  ≥ 0, and the corresponding eigenvectors e k  (k = 1, 2, …, K) of the covariance matrix C = E[RR ] can be calculated, where e k  is a column vector of size K × 1. Finally, we selected the first principal component as the spatial reference r:

$$ \boldsymbol{r}={\boldsymbol{e}}_1^{\prime}\boldsymbol{R} $$
(s4)

where r is a row vector of size 1 × v and the corresponding contribution of r can be calculated by \( {c}_r={\lambda}_1/\sum_{k=1}^K{\lambda}_k \). In particular, if all subjects in the group have the same mask, then the spatial a priori information can be obtained directly through formulas (s3) and (s4).

Appendix 2

Table 1 The evaluation results of the nine situations of the improved CICA method obtained by formula (14) on the 20 datasets in the simulated-data experiment

aThe bold numbers indicated the "index" values of the best situation obtained by formula (14) in each simulated dataset.

Table 2 The evaluation results of the nine situations of the improved CICA method obtained by formula (14) in the real-data experiment

bThe bold number indicated the "index" value of the best situation obtained by formula (14) in the real-data experiment.

Table 3 The average of AUCs and CCs of the nine situations of the proposed improved CICA method on the 20 datasets in the simulated-data experiment

cThe bold numbers indicated the average of AUCs and CCs of the best situation in each simulated dataset.

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Shi, Y., Zeng, W., Tang, X. et al. An improved multi-objective optimization-based CICA method with data-driver temporal reference for group fMRI data analysis. Med Biol Eng Comput 56, 683–694 (2018). https://doi.org/10.1007/s11517-017-1716-9

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