fMRI functional connectivity analysis via kernel graph in Alzheimer's disease

Functional magnetic resonance imaging (fMRI) is an imaging tool that is used to analyze the brain's functions. Brain functional connectivity analysis based on fMRI signals often calculated correlations among time series in different areas of the brain. For FC analysis most prior research works generate the brain graphs based on linear correlations, however, the nonlinear behavior of the brain can lower the accuracy of such graphs. Usually, the Pearson correlation coefficient is used which has limitations in revealing nonlinear relationships. One of the proper methods for nonlinear analysis is the Kernel trick. This method maps the data into a high dimensional space and calculates the linear relations in a new space that is equivalent to the nonlinear relation in primary space. Also, it does not need to know the nonlinear dependency in the initial space. In this study, after constructing weighted undirected graphs of fMRI data based on AAL atlas, different kernels have been applied to calculate the kernelized correlation in normal and Alzheimer's subjects. The determination of parameters has been done by two statistical methods. To compare the performance of Kernel correlation analysis, the global features of graphs are computed. Also, the non-parametric permutation test shows that kernelized correlation demonstrates a more significant statistical difference between groups in comparison to the simple linear correlation. In different kernel analysis, the best performance was for the third-degree polynomial kernel. The features strength, characteristic path length, local efficiency, transitivity, modularity, and small-worldness were significantly different forPvalue 0.01. Besides, comparison to random graphs and further analysis in the Occipital lobe confirmed the results.