### 1. Comparison of bases in reconstructing task activation maps

We first evaluated the effect of dimensions (i.e., number of bases) on model accuracy of reconstructing task activation maps (i.e., Pearson's correlation between reconstructed task activation maps and the actual activation maps). For each method (PCA, ICA, or Laplacian Eigenmaps), the individual bases were derived by running dual regression at a specific dimension each time for each subject. On HCP data, we compared the bases at dimensions 15, 25, 50, and 100; on UKB data, we compared 25, 100, and 200. The set of bases were then regressed against individual task activation maps to get reconstruction coefficients for each subject. To predict task activation maps of a new subject, we used the subject's own bases and the averaged reconstruction coefficients of 100 unseen subjects.

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@@ -28,7 +26,7 @@ All the above results are based on using residual bases to predict residual task

### 4. Prediction of amplitude of group-level activation maps

We also investigated whether amplitudes of group activation maps can be predicted by the amplitude of bases across subjects (UKB: 1529 subjects; HCP: 967 subjects). Amplitudes of group-level activation maps are the effect sizes (betas) of the group-level contrast maps in explaning the individual task activation maps, while the amplitude of bases are the standard derivations of the individual time courses calculated in dual regression. 80% of the subjects were taken as training data, and the rest 20% were used to evaluate the prediction. The process was repeated 1000 times for both UKB ([Figure 13](figs/ukb_amplitude_prediction.png)) and HCP ([Figure 14](figs/hcp_amplitude_prediction.png)) dataset.

### 5. Reconstruction coefficients across task domain

The reconstruction coefficients (i.e., betas of the residual bases in explaining residual task activations) are relatively consistent across task domain ([Figure 15](figs/ukb_betas.png): UKB data; [Figure 16](figs/hcp_betas.png)). This suggests that the reconstruction coefficient matrix is low-rank, and hopefully the prediction of a specific task can be further facilitated by using information from other task domains.