Deep sparse graph functional connectivity analysis in AD patients using fMRI data

Functional magnetic resonance imaging (fMRI) is a non-invasive method that helps to analyze brain function based on BOLD signal fluctuations. Functional Connectivity (FC) catches the transient relationship between various brain regions usually measured by correlation analysis. The elements of the correlation matrix are between -1 to 1. Some of them are very small values usually related to weak and spurious correlations due to noises and artifacts. They can not be concluded as real strong correlations between brain regions and their existence could make a misconception and leads to fake results. It is crucial to make a conclusion based on reliable and informative correlations. In order to eliminate weak correlations, thresholding is a common method. In this routine, by adjusting a threshold the values below the threshold turn to zero and the rest remains. In this paper, in addition to thresholding, two other methods including spectral sparsification based on Effective Resistance (ER) and autoencoders are investigated for sparsing the correlation matrices. Autoencoders are based on deep learning neural networks and ER considers the network as a resistive circuit. The fMRI data of the study correspond to Alzheimer's patients and control subjects. Graph global measures are calculated and a non-parametric permutation test is reported. Results show that the autoencoder and spectral sparsification achieved more distinctive brain graphs between healthy and AD subjects. Also, more graph global features were significantly different from these two methods due to better elimination of weak correlations and preserve more informative ones. Regardless of the sparsification method features including average strength, clustering, local efficiency, modularity, and transitivity are significantly different (P-value=0.05). On the other hand, the measures radius, diameter, and eccentricity showed no significant differences in none of the methods. In addition, according to three different methods, the brain regions show fragile and solid FCs are determined.