# Comparison of Functional Connectivity Analysis Methods in Alzheimer's Disease
## 3 Functional Connectivity Analysis Methods
### Data-Driven Methods
#### 3.2.2 Independent Components Analysis (ICA)  
ICA is a well-known technique for detecting FC using fMRI. ICA is ideally suited for resting-state fMRI studies since it requires no prior knowledge of the source signals' spatial or temporal patterns. As a result, there is growing interest in using the ICA method to discover FC in resting-state fMRI studies. ICA, similar to PCA, seeks a linear combination of components. The difference is that ICA would look for components that are as statistically independent as possible.  
In some studies, the DMN and its anti-correlated network, such as the executive control network (ECN) in MCI, were explored [34]. They discovered decreased connectivity in MCI in main DMN hubs such as the PCC and mPFC and the angular gyrus. They also measured decreased connectivity in the superior parietal lobule (SPL) and prefrontal cortex (PFC) in MCI, both hubs of those networks, in the ECN. The ICA studies of AD connectivity indicate unique reductions, particularly in the DMN, consistent with seed-based studies. The results in the ECN appear to be less consistent, which might be due to analytical decisions or the intensity of the subject's symptoms.  
Regions of the default mode network similar to the PCC, ventral, precuneus and dorsal medial prefrontal cortex display more significant activity during rest, indicating that this network reflects the human brain's baseline or default functioning [35]. The DMN has gained a great deal of attention in the rs-fMRI field [36; 37]. Several studies have examined alterations in DMN resting-state connectivity in neurocognitive and mental disorders such as AD [38]. For fMRI data F having n voxels and t time points, the ICA model can be expressed as:  
\[F=\sum_{i=1}^{n}A_{i}C_{i} \tag{8}\]  
Here, \(C_{i}\) is the ith IC component of the signal source, and \(A\) is the mixing matrix of the dimension of \(n\times t\)[39].  
In ICA, two widely used approaches are the Infomax and the Fixed-Point. Both approaches operate by reducing component mutual information \(C_{i}\). Fixed-Point utilized the negentropy concept, whereas Infomax used adaptive entropy maximization of a neural network with as many outputs as the number of ICs evaluated. In terms of spatial and temporal accuracy, Fixed-Point surpasses Infomax. In contrast, Infomax outperforms Fixed-Point in terms of global model estimation and noise reduction.  
ICA, similar to PCA, decomposes the original time sources into statically independent components and related IC maps that evaluate the correlation. ICA can be split into spatial ICA (ICA) and temporal ICA (tICA) depending on whether the data are decomposed into spatially-independent components and spatially-independent time course or temporarily-independent components and temporarily-independent time course. If the underlying signals are spatially linked but only temporarily, this may be preferable to sICA since sICA will almost certainly not give the proper activation pattern if the null spatial correlation is significantly broken, and vice versa for tICA.  
To visualize the independent component or ROI, we used ADNI datasets and performed decomposition. The decomposed ROIs in the resting state are plotted on DMN, and all of the independent components are shown in Figure 5.