Research On Complex Network Based On Renyi Entropy And Its Application In Mental Arithmeticrecognition

Mental arithmetic tasks can improve cognitive control and working memory,attention and concentration and can cause changes in electroencephalogram(EEG)signals,reflecting coordination and information transfer between different brain regions.In this thsis,we analyse brain signal changes based on EEG to investigate the effects of different mental arithmetic tasks on the brain.At the same time,the brain network of the mental arithmetic task is investigated using complex network theory to achieve the classification of EEG signals and the identification of mental arithmetic tasks.The main research components of this thsis are as follows.Firstly,to better investigate the effects of mental arithmetic tasks on the brain,this study designed five mental arithmetic tasks of different difficulty levels to compare the differences in brain signals between resting states and different loads of mental arithmetic work.The results of the behavioural analysis showed that as the difficulty of the mental arithmetic task increased and the working memory load increased,the reaction time gradually increased and the accuracy rate decreased.At the same time,this thsis uses phase-locked values as brain network connection edge weights to more accurately characterise the collaborative relationship of information flow between brain regions in the mental arithmetic state,addressing the problem of component interference in the frequency and amplitude of EEG signals.In this thsis,we found that the highest connection strength of brain region synchronization in different states was shown in the theta band and was higher in frontal regions in the mental arithmetic task.Secondly,an improved Renyi entropy algorithm(RFB)is proposed to study EEG networks under a mental arithmetic task to address the shortcomings of traditional network complexity assessment algorithms,introducing two important network properties-fractal dimensionality and mesoscopic centrality-to improve the measurement of network complexity.To evaluate the reliability and validity of the method,a series of complex networks consisting of a simple nearest-neighbour coupled network and six real-world networks were used.Finally,the new algorithm was used to assess the complexity of brain networks in both the mental arithmetic and resting states.The complexity of the brain networks in the resting and mental arithmetic states showed significant differences in the three structural entropy measures in the alpha band.The final evaluation accuracy of 88.42% was obtained in the support vector machine(SVM)after feature filtering.Finally,a Renyi entropy-based method(RSFB)is proposed to evaluate the importance of complex network nodes to reveal the importance of different brain regions during mental arithmetic,in response to the problem that traditional node importance assessment methods cannot measure network features comprehensively.The algorithm takes into account both local and global topological information of nodes,combines salton index and mesoscopic centrality,and fully considers the influence of nodes and neighbouring nodes.The algorithm was validated using monotonicity,the SIR model and the Kendall correlation coefficient as evaluation criteria and compared with other classical methods on six different real networks.The RSFB algorithm extracted and ranked important nodes from different brain regions and found significant differences in the importance of nodes in brain regions at different frequency bands.The highest classification accuracy of 90.21% could be achieved in the SVM classifier by using the node importance sequences of different working mental arithmetic states as the feature vectors for state classification.Overall,the RFB and RSFB methods proposed in the study are highly accurate and reliable in assessing brain network properties,and have been successfully applied to mental arithmetic task recognition.It helps to understand the functional characteristics of the brain at different frequency bands and the interactions between various brain regions,and provides more in-depth basic research and theoretical support for the development of neuroscience and brain-computer interface technologies.