Kernel Granger Causality Based on Back Propagation Neural Network Fuzzy Inference System on fMRI Data

Granger causality (GC) is one of the most popular measures to investigate causality influence among brain regions and has been achieved significant results for exploring brain networks based on functional magnetic resonance imaging (fMRI). However, the predictors and order selection of conventional GC are based on linear models which result in such restrictions as poorly detection of nonlinearity and so on, in the application. This paper proposes a novel GC model called back propagation (BP) based kernel function Granger causality (BP_KFGC), in which symplectic geometry is used for embedding dimension and fuzzy inference system for predicting time series. The proposed method doesn't depend on the prediction of the vector auto-regression model, so that time series don't need to be wide-sense stationary as linear GC and kernel GC. In addition, it is a multivariate approach which is applicable to both linear and nonlinear systems and eliminates the effects of latent variables. The performance of the new method is evaluated and compared with linear GC, partial GC, neural network GC and kernel GC by simulated data with multiple adjustments to the nonlinearity. The results show that BP_KFGC outperforms the other four methods in detecting both linear and nonlinear causalities. Furthermore, we applied BP_KFGC to construct directed weight network (DWN) of Alzheimer's disease (AD) patients and health controls (HCs), and then nine graph-based features of DWN were used for classification by the classifier of support vector machine with radial basis kernel function. The accuracy of 95.89%, sensitivity of 93.31%, and specificity of 94.97% were achieved which may provide an auxiliary mean for the clinical diagnosis of AD.