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 for P value 0.01. Besides, comparison to random graphs and further analysis in the Occipital lobe confirmed the results.

中文翻译：

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通过核图在阿尔茨海默病中进行 fMRI 功能连接分析

功能磁共振成像 (fMRI) 是一种用于分析大脑功能的成像工具。基于 fMRI 信号的脑功能连接分析通常计算大脑不同区域时间序列之间的相关性。对于 FC 分析，大多数先前的研究工作基于线性相关性生成大脑图，但是，大脑的非线性行为会降低此类图的准确性。通常使用 Pearson 相关系数，它在揭示非线性关系方面存在局限性。非线性分析的正确方法之一是内核技巧。该方法将数据映射到高维空间，并在新空间中计算线性关系，等效于原始空间中的非线性关系。还，它不需要知道初始空间中的非线性依赖。在这项研究中，在基于 AAL 图谱构建 fMRI 数据的加权无向图后，已应用不同的内核来计算正常和阿尔茨海默氏症受试者的内核化相关性。参数的确定是通过两种统计方法完成的。为了比较核相关分析的性能，计算了图的全局特征。此外，非参数置换检验表明，与简单线性相关相比，核化相关在组之间具有更显着的统计差异。在不同的核分析中，三次多项式核的性能最好。特征强度、特征路径长度、局部效率、传递性、模块化、P 值 0.01 时，小世界性和小世界性有显着差异。此外，与随机图的比较和枕叶的进一步分析证实了结果。