Research On Bayesian Factorization Analysis For Multi-dimensional EEG

Since 2013,the United States,the European Union and China have put forward the “brain plan”.The research on brain science and brain disease has become a strategic commanding point for world powers to compete,which focus on advancing the exploration of brain working mechanism and pathology based on big data.Brain wave is the key for the coordinated operation of brain regions.Electroencephalogram(EEG),non-invasively collected by scalp electrodes,is the most advantageous technology in encephalopathy research and clinical diagnosis,which directly reflects the electrica l activity of the brain and can explore the neural activity process with different levels.In signal processing,EEG is traditionally regarded as low-dimensio na l independent time series.EEG reflects the complex neurological state of activity in the brain,which presents strong data correlation and multiple data attributions.Compared with traditional time series,multi-dimensional EEG is more informative and more natural in expressing brain science issues.In addition,it is necessary to obtain the potential(hidden)low-dimensional features in multi-dimensional EEG to summar ize the large scale of complex neuron activities and understand the activity patterns of different neural states in the brain.Tensor decomposition and factorization analysis is the most advantageous method to obtain multi-dimensional EEG characteristics in the brain science.The key technical indicators of factorization solution are mainly reflected in accuracy and efficiency,which are corresponding to two major technical chal enge s : factor distribution estimation and accurate feature discovery:(1)Factor distribution estimation.With the complex data structure of EEG,the initial low-dimensional factors are strongly related to the performance of the factorization analysis methods,where improper initial characteristic leads to ineffic ie nt process of the factorization analysis method,or even fall into the local optimum,and cannot effectively represent the source signal characteristics,but the selection of initia l low-dimensional factors is extremely difficult.The current methods in initializing the features of multi-dimensional EEG mainly depended on the information by multip le experiments or lack sufficient confidence level,therefore the reliability and applicability of the methods is not enough.Thus,it is crucial to develop the method of factor distribution estimation of EEG for estimating the distribution region of lowdimensional characteristic factors and provide guidance for the selection of initia l characteristic factors.(2)Accurate feature discovery.With the high dimension of EEG,strong correlation between the data,and the characteristic of being easily disturbed by the noise,it's hard to accurately extract low-dimensional essential features of multidimensional EEG.The current methods in extracting the features of multi-dimensio na l EEG were mainly applied at the specific dimensions of data,and theoretically hard to factorized EEG with arbitrary dimension.What's more,feature extraction heavily relied on empirical analysis and the ability was not adequate for understanding the correlation between different dimensions of EEG,making it difficult to guarantee the universa lit y of the method.Thus,it is of great significance to study the method of accurate feature extraction of multi-dimensional EEG for adaptively eliminating the interference of noise,extracting the maximum information features and ultimately distinguishing the activity patterns of different neural states in the brain.In view of the two technical chal enges,this paper proposes Bayesian factoriza t io n analysis method for multi-dimensional EEG,which includes:(1)Factor distribution estimation of EEG data based on variational Bayesian inference(VBI).For the difficulty of selecting initial factors,firstly,build the mult ilinear probabilistic decomposition model and apply the theory of variational Bayesian inference to adaptively deduce the multi-linear model.Finally,estimate the distribut io n area of factors with the strategy of space contraction,and provide guidance for the selection of initial factors.EEG signals are used to verify the validity and reliability of the algorithm.The experimental results show that under different experime nt a l scenarios,the VBI algorithm can deduce the distribution area of factors with high reliability,and effectively improve the convergence speed and accuracy of the current factorization method for EEG,with the maximum increase 0.0022 of accuracy and the maximum improvement 12 times of convergence speed.(2)Accurate feature discovery of multi-dimensional EEG based on Bayesian tensor factorization(BTF).For the difficulty of extracting accurate essential features of multi-dimensional EEG,firstly,build the PARAFAC tensor decomposition model with unit constraint of factors and explore the estimation of multi-way factors and noise without the empirical analysis;Secondly,use the Bayesian inference to extract the most informative features of EEG,and achieve the adaptive learning of factors.The valid it y and reliability of the method are validated by epileptic EEG(CHB-MIT)and sleep EEG(Physio Bank).The experimental results show that the BTF algorithm can eliminate the interference of the noise adaptively and extract the most informative features of mult idimensional EEG efficiently.Meanwhile,the detection and classification model of the brain state based on BTF have good ability of learning and generalization,and the seizure detection and sleep stage classification could be achieved with averaged accuracy up to 99.5% and 90.8% respectively.In this paper,the VBI algorithm can efficiently estimate distribut ion area of factors of EEG data,and the BTF algorithm can accurately extract characteristic factors of multi-dimensional EEG,which effectively ensure the applicability and reliability of factorization analysis for multi-dimensional EEG.