## 3 Implementation and Results
### Fusion Results  
Following the explained procedure, we discovered six IC linked triplets (Figure 7). The identified brain regions of each identified fALFF IC are summarized in Supplementary Table S1. Within each of the six triplets, three ICs that corresponded to three modalities (dMRI, sMRI and fMRI) were linked, representing a multimodal brain network with three nodes (WM, structural GM, and functional GM).  
We found that the structure-structure associations were generally stronger than the structure-function associations (dMRI-sMRI: \(|\rho|=0.48\pm 0.26\); dMRI-fMRI: \(|\rho|=0.32\pm 0.11\); sMRI-fMRI: \(|\rho|=0.33\pm 0.13\); see Table 1). We also examined group differences (HC vs. SZ) for each IC on its corresponding subject covariation and found that more ICs showed significant group differences in sMRI than the other two modalities (5 in sMRI; 2 in dMRI; 1 in fMRI; \(p<0.05\); two-sample \(t\)-test; see Figure 7). Interestingly, for all these ICs in both the dMRI and the sMRI data that showed significant group differences, the SZ group showed less activation, suggesting both a reduced volume of the GM and reduced integrity of the WM in patients with SZ. For the ICs in fMRI that showed significant group differences, the SZ group had higher activation, perhaps suggesting less neural efficiency in patients with SZ.  
Figure 4: Spatial maps of 10 retained ICs from the FA dataset. These results reflect the IC results of SZ and HC groups combined. The brain maps are visualized at \(|Z|\geq 2\), with positive \(Z\) values in red color and negative \(Z\) values in blue.  
We also note that one IC can be found in more than one triplet, meaning that one IC from one modality is associated with many ICs from other modalities. For instance, the IC (corticospinal tract and superior longitudinal fasciculus (CST-SLF)) from dMRI is not only associated with the uncus and inferior temporal gyrus (Uncus-ITG) from sMRI  
Figure 5: Spatial maps of 27 retained ICs from the GM dataset. These results reflect the IC results of SZ and HC groups combined. The brain maps are visualized at \(|Z|\geq 2\), with positive \(Z\) values in red color and negative \(Z\) values in blue.  
Figure 6: Spatial maps of 17 retained ICs from the fALFF dataset. These results reflect the IC results of SZ and HC groups combined. The brain maps are visualized at \(|Z|\geq 2\), with positive \(Z\) values in red color and negative \(Z\) values in blue.  
and superior frontal gyrus and middle frontal gyrus (SFG-MFG) from fMRI, but is also associated with the precuneus and paracentral lobule (Precuneus-PCL) from sMRI and superior temporal gyrus (STG) from fMRI, as shown in Figure 7 (green frame). Another shared IC between triplets is the postcentral gyrus and precentral gyrus (POG-PCG) from sMRI, which is not only associated with anterior thalamic radiation and the anterior corona radiata (ATR-ACR) from dMRI and thalamus from fMRI, but also associated with superior corona radiation and the corticospinal tract (SCR-CST) from dMRI and culmen from fMRI, as shown in Figure 7 (blue frame).  
Figure 7: Summary of the six IC linked triplets. The spatial maps of all ICs were converted to \(Z\)-scores and thresholded by \(|Z|\geq 2\). Each row shows the three associated ICs from dMRI, sMRI, and fMRI, respectively. The abbreviations of brain regions identified by ICs are shown above the spatial maps. If one IC shows a statistically significant activation between HCs and SZs (\(p<0.05\); \(t\)-test), the \(p\) value would be shown above the map, where the red color indicates higher activation in HCs than patients and the blue color indicates lower activation in HCs than patients. Note that the IC 7 (green frame) from dMRI is associated with two ICs from sMRI and two ICs from fMRI. IC 22 (blue frame) from sMRI is associated with two ICs from dMRI and two ICs from fMRI.