Research on Attentional EEG Based on Granger Causality of Polynomial Kernel

Attention is a neurocognitive process, which specifically describes a person's mental and physical ability to concentrate on certain things, covering a series of mental activities such as perception, analysis, logic, reasoning, and imagination. It's hard to concentrate for attention deficit patients with symptoms of impulsive and restless, which led to a decline in learning and work efficiency and even seriously affect our normal life. Therefore, it is necessary for us to study attentional Electroencephalogrphy (EEG), which has a certain guiding role in solving clinical attention-related diseases. In this paper, the Granger Causal algorithm based on polynomial kernel function is used to study the directionality of the interaction between the left-brain and right-brain EEG signals. The experimental results show that when m and p are fixed (m represents the embedding dimension, p represents the degree of the highest term of the polynomial kernel function), in the counting state, the Granger Causality Index from left brain to right brain is significantly larger than that from right brain to left brain. In the closed-eye state and idle state, the Granger Causality Index from left brain to right brain significantly smaller than in the opposite direction. It is further explained that in the counting state, the influence of the EEG signal of the left brain on the EEG signal of the right brain is greater than the influence of the right brain on the left brain. In the closed-eye state and idle state, the causal effect of the left brain on the right brain is less than that of the right brain on the left brain. In addition, we also compared the Granger Causality Index of the same individual in the three states. We found that the Granger Causality Index in the counting state is larger than the other two states, and it is the smallest in the closed-eye state.