CN115644893A - Method for classifying electroencephalogram channel communities by means of regional electroencephalogram modeling and diagonal block model - Google Patents
Method for classifying electroencephalogram channel communities by means of regional electroencephalogram modeling and diagonal block model Download PDFInfo
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Abstract
The invention discloses a method for classifying brain electrical channel communities of a partitioned brain electrical modeling and diagonal block model, belonging to the field of bioelectricity signal processing and clustering, and comprising the following steps of: s1, data generation: establishing a multi-channel coupled neuron group electroencephalogram model, and generating multi-channel electroencephalogram data by using the multi-channel coupled neuron group electroencephalogram model; s2, judging the clustering number: selecting clustering hyper-parameters based on the multi-channel coupling neuron group electroencephalogram model generated by the contour coefficient pair; s3, searching a community structure: and carrying out community structure classification on the generated electroencephalogram data channels by using a block hybrid model method. The method can reflect the relation between the electroencephalogram signals of different brain areas by searching the community structure among the electroencephalogram channels.
Description
Technical Field
The invention relates to the field of bioelectrical signal processing and clustering, in particular to a method for carrying out partitioned electroencephalogram modeling and diagonal block model electroencephalogram channel community classification.
Background
With the development of computational neuroscience, the modeling of the electroencephalogram signal becomes a new way for people to research the generation of the electroencephalogram signal and an information processing mechanism after researching brain tissue segments.
At present, brain nerve models are mainly divided into two types, the first type models neurons on a microscopic level, and the modeling of the neurons is beneficial to human understanding of the most basic working principle of the brain, but the brain is composed of hundreds of millions of different types of nerve cells, and the brain function is also the result of cooperative work of a plurality of neuron groups, so that the study on the microscopic level is far from sufficient. The second type of model is called a lumped parameter model, such as a neuron population model (NMM), which constructs electroencephalogram signals from the perspective of "tissue structure" of the nervous system, and represents the average behavior of the entire cell population in the neural network using lumped state variables. The coupled NMM can reflect the mutual connection among neuron groups, and the current multi-channel electroencephalogram modeling can simulate the influence of the coupling on the electroencephalogram signals, but cannot indicate the electroencephalogram of the region.
Aiming at the problem, a multi-channel electroencephalogram modeling is required to be provided, electroencephalogram signals of different brain areas can be reflected, and the method has important significance for researching the relation between the electroencephalogram signals of all areas in the fields of medicine, biology and the like.
Disclosure of Invention
The invention provides a method for carrying out partitioned electroencephalogram modeling and diagonal block model electroencephalogram channel community classification, which can reflect the relationship between electroencephalogram signals of different brain areas by searching community structures among electroencephalogram channels.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a partition electroencephalogram modeling and diagonal block model electroencephalogram channel community classification method comprises the following steps:
s1, data generation: establishing a multichannel coupled neuron group electroencephalogram model, and generating multichannel electroencephalogram data by using the multichannel coupled neuron group electroencephalogram model;
s2, judging the clustering number: selecting clustering hyper-parameters based on the multi-channel coupling neuron group electroencephalogram model generated by the contour coefficient pair;
s3, searching a community structure: and carrying out community structure classification on the generated electroencephalogram data channels by using a block hybrid model method.
The technical scheme of the invention is further improved as follows: s1 specifically comprises the following steps:
s1.1 modeling of a basic neuron model: converting presynaptic information into postsynaptic information;
s1.2, establishing a multi-dynamic neuron model according to the basic neuron model in the S1.1;
s1.3, establishing a multichannel coupled neuron group electroencephalogram model according to the multi-dynamic neuron model in S1.2.
The technical scheme of the invention is further improved as follows: in S1.1, the pre-synaptic information comprises the average pulse density of the action potential, and the post-synaptic information comprises the excitation or inhibition point position of a post-synaptic membrane; setting a single-channel basic neuron model, wherein the information after the salient of other non-pyramidal cells respectively comprises the following unit impact responses:
wherein h is e To excite the postsynaptic membrane voltage, h i Is an inhibitory postsynaptic membrane voltage; u is a unit impulse response; h e And H i Excitatory and inhibitory mean cell gains, respectively, for modulating the maximum value of the postsynaptic voltage; tau. e And τ i The sum of the excitatory and inhibitory mean time constants, respectively;
linear function h e (t) and h i (t) is described by a first order differential equation of the form:
wherein G represents excitatory average cell gain H e Inhibitory mean cell gain H i G represents the sum of the excitation mean time constant e Sum of inhibitory mean time constants τ i (ii) a x (t) and z (t) are the input and output signals of the subgroup, respectively;
converting the average membrane voltage into the average density of the action point position, namely the average ignition rate, through a static nonlinear function, and taking the average density as the input of a linear transformation function; the static nonlinear function is expressed as:
wherein S (v) is the average density of the action points and is a nonlinear function, v is the average membrane voltage, 2e 0 At maximum ignition rate, v 0 Is related to the ignition rate e 0 R represents the degree of curvature of the sigmoid function, and v is the presynaptic average membrane potential;
the basic neural cell population model is represented by the following differential equation:
wherein y is 0 (t)、y 1 (t) and y 2 (t) excitatory output of pyramidal cells, excitatory output of non-pyramidal cells and inhibitory output of non-pyramidal cells in the single-channel basic neuron population model, respectively, and the excitation input p (t) of Gaussian distribution is all external inputs from an indefinite region and a subcortical region; constant C 1 、C 2 、C 3 And C 4 The average number of synaptic links seen for the population of pyramidal cells and the population of interneurons;
simulated brain wave (EEG) signals are the sum of excitatory and inhibitory post-synaptic potentials:
y(t)＝y 1 (t)-y 2 (t)。
the technical scheme of the invention is further improved as follows: s1.2, by adjusting the excitatory and inhibitory parameters H in the transfer function H e,i And τ e,i Adjusting dynamic balance between excitatory and inhibitory cell populations, wherein the single-channel model can generate various electroencephalogram signals, and the electroencephalogram signals generated through parameter adjustment comprise delta, theta, alpha, beta and gamma waves; each cell subgroup is composed of five nerve oscillators of delta, theta, alpha, beta and gamma waves, the weight of each wave is changed according to the weight of each wave in each brain area, and the weight is set as W = { a, b, c, d, e }. Epsilon [0,1 =]Wherein a + b + c + d + e =1.
The technical scheme of the invention is further improved as follows: in S1.3, the average pulse density of the cone cell action potential is delayed correspondingly and is used as excitatory input of other areas to form coupling between different areas of a brain, the multi-dynamic neuron model in S1.2 is expanded into a multi-channel coupling nerve model, and the coupling brain wave signals of j channels to k channels are as follows:
wherein q is kj Representing the coupling coefficient of a j channel to a k channel, wherein RM (x) = x-mean (x) is a mean value removing function, an S function is a nonlinear function, tau is delay time, i =1,2, \ 8230, and N represents that N subgroups with different dynamic characteristics are connected in parallel;
the multichannel coupled neuron group electroencephalogram model is expressed by a differential equation as follows:
wherein j =1,2, \ 8230;, M, denotes the generation of M channels of electroencephalogram signals; i =1,2, \ 8230, N still indicating the presence of N subgroups in parallel with different dynamics.
After the corresponding solution is obtained, the multichannel electroencephalogram signals are obtained according to the electroencephalogram signal formula simulated in S1.1:
wherein j =1,2, \ 8230;, M, denotes the generation of M channels of electroencephalogram signals; i =1,2, \ 8230;, N still indicates the presence of N subgroups of different dynamics in parallel, y 1 Represents the output potential of an excitatory cell, y 2 The output potential of the inhibitory cells is represented, and y represents the finally output electroencephalogram signal.
The technical scheme of the invention is further improved as follows: s2 specifically comprises the following steps:
s2.1, calculating a contour coefficient;
regarding the multi-channel electroencephalogram data generated in the S1, clustering each channel as a vector for different clustering numbers, calculating the contour coefficients of the channels, and setting the contour coefficient of the ith channel as S (i):
wherein a (i) is the intra-cluster dissimilarity, which represents the average value of the dissimilarity from the i vector to other points in the same cluster, and represents the degree of aggregation, b (i) represents the inter-cluster dissimilarity, which represents the minimum value of the dissimilarity from the i vector to other clusters, and represents the degree of separation;
s2.2, calculating a nearest cluster;
the average distance from the ith channel to all samples in the kth cluster is used as a measure of the distance from the point to the cluster, and then the distance from X is selected i The closest cluster is taken as the closest cluster; let the nearest cluster be C:
wherein, X i Is the ith channel, p is a cluster C k The sample of (1);
s2.3, selecting a clustering number;
and (3) calculating the contour coefficients of all samples, then calculating the average value to obtain the average contour coefficient, and selecting the cluster number with the best contour coefficient average effect as the number of the community structures in the S3.
The technical scheme of the invention is further improved as follows: the number of clusters is 4.
The technical scheme of the invention is further improved as follows: s3 specifically comprises the following steps:
s3.1, generating a similarity matrix: for a given set of N data samples { x) in C-dimension 1 ,x 2 ,...,x N Therein of
Constructing a similarity matrix W by using a Gaussian kernel;
s3.2, visualizing community relation: and (4) searching the maximum value of the similarity matrix W obtained in the S3.1 according to the row direction, judging a clustering result, and displaying a similarity matrix with indexes sorted according to the clustering result.
The technical scheme of the invention is further improved as follows: in S3.1, assume that the data can be divided into K clusters, giving each sample x n Indicator z for allocating K element clusters nk And form a K-order vector, expressed as:
when x is n Z belonging to the kth element cluster nk =1, otherwise z nk =0, so z n An absolute distribution is followed:
z n ～Categorical(π) (3.1)
where π is a k-element vector, indicating that the probability assigned to each cluster obeys a Dirichlet distribution:
π～Dirichlet(λ) (3.2)
wherein pi is a sample of Dirichlet distribution, and lambda is a concentration parameter of the Dirichlet distribution;
if x i And x j Belong to the same cluster k, then z ik z jk =1 and w ij Belongs to the kth diagonal block, then set z ik z jk For the indicator in the diagonal block(s),
an indicator of an off-diagonal block region;
all elements in the similarity matrix W satisfy 0 < W ij 1, so W is modeled using a beta distribution, which is a distribution defined over the interval (0, 1) parameterized by two positive shape parameters α and β; it is assumed that the similarity matrix W can be divided into k clusters, W ij The probability density of (a) is:
wherein, theta k ＝(α k ,β k ) Represents W ij Parameter of Bate distribution in diagonal Block, Θ 0 ＝(α 0 ,β 0 ) Represents W ij Parameters of the Bate distribution in the off-diagonal blocks; ζ and η are the hyperparameters of Θ:
according to the formula (3.4), theta is calculated k K, calculating Θ according to formula (3.5) 0 (ii) a Pi is calculated according to the formula (3.2), and z is calculated according to the formula (3.1) n N = 1.. N, W is calculated according to the formula (3.3) ij I =1,.. N, j =1,.. N, W may only compute the upper triangular matrix since W is a symmetric matrix;the similarity matrix W is obtained as described above.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. according to the invention, delta waves usually appear in the frontal part and only occur in the cortex, theta waves are scattered in the frontal area, the central area and the temporal area, the apical area is also a small amount, alpha waves are the main expression of the time point activity when the cerebral cortex is in a waking and relaxing state, the beta wave central area and the frontal area are most obvious, the gamma wave frontal area and the central area are most, 5 electroencephalogram rhythm signals of delta, theta, alpha, beta and gamma generated by using a Jansen neuron model are endowed with different weights in different cortical areas, and the effect of distinguishing the electroencephalogram signals of different areas of the cerebral cortex is achieved.
2. According to the method, the BMM algorithm for classifying the electroencephalogram data is applied to classification of the electroencephalogram channels for the first time, and the electroencephalogram channels which are in one-time motor imagery are found to have stronger correlation, so that the result of obviously reflecting the similarity of each channel in a community is achieved.
Drawings
FIG. 1 is a flow chart of a method for partitioned electroencephalogram modeling and diagonal block model electroencephalogram channel community classification in the present invention;
FIG. 2 is a block diagram of a single channel neuron population model in the present invention;
FIG. 3 is a block diagram of a multi-dynamical neuron population model in the present invention;
FIG. 4 is 14 channels of electroencephalogram data generated in the present invention;
FIG. 5 is a diagram illustrating the size of a clustering hyperparameter selected by 64-channel electroencephalogram data on a generated electroencephalogram model by using a contour coefficient SC in the present invention;
FIG. 6 shows the result of using BMM algorithm to find the community structure for 64 brain electrical channels in the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and examples:
the relevance of each brain region and each channel has important significance in the medical field and the biological field, so that the search of a community structure among electroencephalogram channels becomes one of important research directions in the electroencephalogram field, and the electroencephalogram channels need to be divided into several groups. Clustering is a task of discovering structures and interesting patterns in data, and similarity matrix-based methods have been highly successful in different applications. However, in a generative model with the similarity matrix as input, the work for clustering is limited. In the clustering problem, it is necessary to ensure that samples within the same cluster are similar, while samples from different clusters are less similar. Thus, given a similarity matrix, if the indices of the similarity matrix are ordered according to the cluster index, the elements in the diagonal block usually have larger values because these elements measure the similarity between samples in the same cluster; while elements in non-diagonal blocks typically have smaller values because these measure the similarity between samples from different clusters. In view of this, a probability clustering Model based on a similarity matrix, which is called a Block Mixture Model (BMM) needs to be proposed. It is a generative model that finds clusters by finding block diagonal structures in a similarity matrix. As a bayesian approach, BMM takes into account model uncertainty, allowing us to provide information in front of the model and prevent overfitting. Before the process, the BMM method only classifies the electroencephalogram data, and is used for classifying the electroencephalogram channels, so that the community structure can be more obviously represented.
As shown in FIG. 1, a method for classifying a block-by-block electroencephalogram modeling and diagonal block model electroencephalogram channel community comprises the following steps:
s1, data generation: establishing a multi-channel coupled neuron group electroencephalogram model, and generating multi-channel electroencephalogram data by using the multi-channel coupled neuron group electroencephalogram model; the method specifically comprises the following steps:
s1.1 modeling of a basic neuron model: converting presynaptic information into postsynaptic information; the pre-synaptic information comprises an average pulse density of an action potential, and the post-synaptic information comprises a post-synaptic membrane excitation or inhibition site; setting a single-channel basic neuron model, wherein the information after the salient of other non-pyramidal cells is as follows for unit impulse response:
wherein h is e For excitatory postsynaptic membrane voltage, h i Is an inhibitory postsynaptic membrane voltage; u is a unit impulse response; h e And H i Excitatory and inhibitory mean cell gains, respectively, for modulating the maximum value of the postsynaptic voltage; tau is e And τ i The sum of the excitatory and inhibitory average time constants, respectively;
linear function h e (t) and h i (t) can be described by a first order differential equation of the form:
wherein G represents excitatory average cell gain H e Inhibitory mean cell gain H i G represents the sum of the excitation mean time constant e Sum of inhibitory mean time constants τ i (ii) a x (t) and z (t) are the input and output signals of the subgroup, respectively;
converting the average membrane voltage into the average density of the action point position, namely the average ignition rate through a static nonlinear function, and taking the average density as the input of a linear transformation function; the static nonlinear function is expressed as:
wherein S (v) is the average density of the action points and is a nonlinear function, v is the average membrane voltage, 2e 0 To maximum ignition rate, v 0 Is related to the ignition rate e 0 R represents the degree of curvature of the sigmoid function, and v is the presynaptic average membrane potential;
in summary, according to fig. 2, the basic neural cell population model is represented by the following differential equation:
wherein y is 0 (t)、y 1 (t) and y 2 (t) excitatory output of pyramidal cells, excitatory output of non-pyramidal cells and inhibitory output of non-pyramidal cells in the single-channel basic neuron population model, respectively, and the excitation input p (t) of Gaussian distribution is all external inputs from an indefinite region and a subcortical region; constant C 1 、C 2 、C 3 And C 4 The average number of synaptic links seen for the population of pyramidal cells and the population of interneurons;
simulated brain wave (EEG) signals are the sum of excitatory and inhibitory post-synaptic potentials:
y(t)＝y 1 (t)-y 2 (t)
s1.2, establishing a multi-dynamic neuron model according to the basic neuron model in the S1.1;
by adjusting the excitatory and inhibitory parameters H in the transfer function H e,i And τ e,i Adjusting dynamic balance between excitable and suppressive cell populations, wherein the single-channel model can generate various electroencephalogram signals, and delta, theta, alpha, beta and gamma waves which are common in the electroencephalogram signals are generated through parameter adjustment; each cell subgroup is composed of five nerve oscillators of delta, theta, alpha, beta and gamma waves, the weight of each wave is changed according to the weight of each wave in each brain area, and the weight is set as W = { a, b, c, d, e }. Epsilon [0,1 =]Wherein a + b + c + d + e =1.
S1.3, establishing a multichannel coupled neuron group electroencephalogram model according to the multi-dynamic neuron model in S1.2;
from neurophysiological studies it has been demonstrated that brain function is formed by strong coupling between regions at greater distances and that the cortex is excitable to the output of distant targets, introducing new delay time parameters, taking into account the delay in coupling between distant brain regions.
In summary, the multi-dynamic neuron model in S1.2 is expanded to a multi-channel coupled neural model by delaying the average pulse density of the pyramidal cell action potential by a corresponding amount to serve as excitatory inputs to other regions of the brain, as shown in fig. 3;
the j-channel to k-channel coupled brain wave signals are:
wherein q is kj Representing the coupling coefficient of a j channel to a k channel, RM (x) = x-mean (x) is a mean value removing function, S function is a nonlinear function, tau is delay time, i =1,2, \ 8230, N represents that N subgroups with different dynamic characteristics in parallel connection exist;
the multichannel coupled neuron group electroencephalogram model is expressed by a differential equation as follows:
wherein j =1,2, \ 8230;, M, denotes the generation of M channels of electroencephalogram signals; i =1,2, \ 8230, N still indicating the presence of N subgroups in parallel with different dynamics.
After the corresponding solution is obtained, the multichannel electroencephalogram signals are obtained according to the electroencephalogram signal formula simulated in S1.1:
wherein j =1,2, \ 8230;, M, denotes the generation of M channels of electroencephalogram signals; i =1,2, \ 8230;, N still indicates the presence of N subgroups of different dynamics in parallel, y 1 Represents the output potential of an excitatory cell, y 2 The output potential of the inhibitory cells is represented, and y represents the finally output electroencephalogram signal.
The generated 14-channel brain electrical signals are shown in fig. 4.
S2, judging the clustering number: selecting clustering hyper-parameters based on the multi-channel coupling neuron group electroencephalogram model generated by the contour coefficient pair; the method specifically comprises the following steps:
s2.1, calculating a contour coefficient;
regarding the multi-channel electroencephalogram data generated in the S1, regarding each channel as a vector, clustering different clustering numbers, calculating the contour coefficient of each channel, and setting the contour coefficient of the ith channel as S (i):
wherein a (i) is the intra-cluster dissimilarity, which represents the average value of the dissimilarity from the i vector to other points in the same cluster, and represents the degree of aggregation, b (i) represents the inter-cluster dissimilarity, which represents the minimum value of the dissimilarity from the i vector to other clusters, and represents the degree of separation;
s2.2, calculating a nearest cluster;
the average distance from the ith channel to all samples in the kth cluster is used as a measure of the distance from the point to the cluster, and then the distance from X is selected i The closest cluster is taken as the closest cluster; let the nearest cluster be C:
wherein X i Is the ith channel, p is a cluster C k The sample of (1);
s2.3, selecting a clustering number;
calculating the contour coefficients of all samples, then calculating the average value to obtain an average contour coefficient, wherein the closer the intra-cluster sample distance is, the farther the inter-cluster sample distance is, the larger the average contour coefficient is, and selecting the clustering number with the best contour coefficient average effect as the number of the community structures in S3; the average profile coefficient of each channel is shown in fig. 5, and it can be obtained from fig. 5, and when the clustering number is 4, the effect of integrating the average profile coefficients of each channel is the best.
S3, searching a community structure: carrying out community structure classification on the generated electroencephalogram data channels by using a block hybrid model method; the method specifically comprises the following steps:
s3.1, generating a similarity matrix: for a given set of N data samples { x) in C-dimension 1 ,x 2 ,...,x N Therein of
Constructing a similarity matrix W by using a Gaussian kernel;
assume that the data can be divided into K clusters, given each sample x n Indicator z for allocating K element clusters nk And form a K-order vector, expressed as:
when x is n Z belonging to the kth element cluster nk =1, otherwise z nk =0, therefore z n One absolute distribution is followed:
z n ～Categorical(π) (3.1)
where π is a k-element vector, indicating that the probability assigned to each cluster obeys a Dirichlet distribution:
π～Dirichlet(λ) (3.2)
wherein pi is a sample of Dirichlet distribution, and lambda is a concentration parameter of the Dirichlet distribution;
if x i And x j Belong to the same cluster k, then z ik z jk =1 and w ij Belongs to the kth diagonal block, then set z ik z jk For the indicator in the diagonal block(s),
an indicator of an off-diagonal block region;
all elements in the similarity matrix W satisfy 0 < W ij 1, so W is modeled using a beta distribution, which is a distribution defined over the interval (0, 1) parameterized by two positive shape parameters α and β; the beta distribution was chosen because it is a simple equation describing a random variable between 0 and 1(ii) distribution of activity; it is assumed that the similarity matrix W can be divided into k clusters, W ij The probability density of (a) is:
wherein, theta k ＝(α k ,β k ) Close to 1, denotes W ij Parameter of Bate distribution in diagonal Block, Θ 0 ＝(α 0 ,β 0 ) Close to 0, denotes W ij Parameters of the Bate distribution in the off-diagonal blocks; ζ and η are the hyperparameters of Θ:
according to the formula (3.4), theta is calculated k K, calculating Θ according to formula (3.5) 0 (ii) a Pi is calculated according to the formula (3.2), and z is calculated according to the formula (3.1) n N = 1.. N, W is calculated according to the formula (3.3) ij I =1,.. N, j =1,.. N, W may only compute the upper triangular matrix since W is a symmetric matrix; obtaining a similarity matrix W according to the above;
s3.2, visualization of community relations: and (4) searching the maximum value of the similarity matrix W obtained in the S3.1 according to the row direction, judging a clustering result, and displaying a similarity matrix with indexes sorted according to the clustering result.
The 64-channel electroencephalogram signals generated by the S1 are artificially set into four communities, wherein the coupling strength of 16 adjacent channels is strong, the community structure obtained by applying the BMM algorithm to the channels generates the four communities as shown in FIG. 6, the similarity of the channels in diagonal blocks is high, and the similarity of elements in non-diagonal blocks is low.
In conclusion, the invention can reflect the relation between the electroencephalogram signals of different brain areas by searching the community structure among the electroencephalogram channels.
Claims (9)
1. A partition electroencephalogram modeling and diagonal block model electroencephalogram channel community classification method is characterized by comprising the following steps: the method comprises the following steps:
s1, data generation: establishing a multichannel coupled neuron group electroencephalogram model, and generating multichannel electroencephalogram data by using the multichannel coupled neuron group electroencephalogram model;
s2, judging the clustering number: selecting a clustering hyper-parameter based on the multi-channel coupling neuron group electroencephalogram model generated by the contour coefficient pair;
s3, searching a community structure: and carrying out community structure classification on the generated electroencephalogram data channels by using a block hybrid model method.
2. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 1, characterized in that: s1 specifically comprises the following steps:
s1.1 modeling of a basic neuron model: converting presynaptic information into postsynaptic information;
s1.2, establishing a multi-dynamic neuron model according to the basic neuron model in the S1.1;
s1.3, establishing a multichannel coupled neuron group electroencephalogram model according to the multi-dynamic neuron model in S1.2.
3. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 2, characterized in that: in S1.1, the pre-synaptic information comprises the average pulse density of the action potential, and the post-synaptic information comprises the excitation or inhibition point position of a post-synaptic membrane; setting a single-channel basic neuron model, wherein the information after the salient of other non-pyramidal cells respectively comprises the following unit impact responses:
wherein h is e For excitatory postsynaptic membrane voltage, h i Is an inhibitory postsynaptic membrane voltage; u is a unit impulse response; h e And H i Excitatory and inhibitory mean cell gains, respectively, for regulating the maximum value of the postsynaptic voltage; tau is e And τ i The sum of the excitatory and inhibitory average time constants, respectively;
linear function h e (t) and h i (t) is described by a first order differential equation of the form:
wherein G represents the excitatory mean cell gain H e Inhibitory mean cell gain H i G represents the sum of the excitation mean time constant e Sum of inhibitory mean time constants τ i (ii) a x (t) and z (t) are the input and output signals of the subgroup, respectively;
converting the average membrane voltage into the average density of the action point position, namely the average ignition rate through a static nonlinear function, and taking the average density as the input of a linear transformation function; the static nonlinear function is expressed as:
wherein S (v) is the average density of the action points and is a nonlinear function, v is the average membrane voltage, 2e 0 At maximum ignition rate, v 0 Relative to the ignition rate e 0 R represents the degree of curvature of the sigmoid function, and v is the presynaptic average membrane potential;
the basic neural cell population model is represented by the following differential equation:
wherein y is 0 (t)、y 1 (t) and y 2 (t) excitatory output of pyramidal cells, excitatory output of non-pyramidal cells and inhibitory output of non-pyramidal cells in the single-channel basic neuron population model, respectively, and the excitation input p (t) of Gaussian distribution is all external inputs from an indefinite region and a subcortical region; constant C 1 、C 2 、C 3 And C 4 The average number of synaptic links seen for the population of pyramidal cells and the population of interneurons;
simulated brain wave (EEG) signals are the sum of excitatory and inhibitory post-synaptic potentials:
y(t)＝y 1 (t)-y 2 (t)。
4. the method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 2, characterized in that: s1.2, by adjusting the excitatory and inhibitory parameters H in the transfer function H e,i And τ e,i Adjusting dynamic balance between excitable and suppressive cell populations, wherein the single-channel model can generate various electroencephalogram signals, and the electroencephalogram signals generated through parameter adjustment comprise delta, theta, alpha, beta and gamma waves; each cell subgroup is composed of five nerve oscillators of delta, theta, alpha, beta and gamma waves, the weight of each wave is changed according to the weight of each wave in each brain area, and the weight is set as W = { a, b, c, d, e }. Epsilon [0,1 =]Wherein a + b + c + d + e =1.
5. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 2, characterized in that: in S1.3, the average pulse density of the cone cell action potential is correspondingly delayed to be used as excitatory input of other areas to form coupling among different areas of the brain, the multi-dynamic neuron model in S1.2 is expanded into a multi-channel coupling neural model, and the coupling brain wave signals of j channels to k channels are as follows:
wherein q is kj Representing the coupling coefficient of a j channel to a k channel, RM (x) = x-mean (x) is a mean value removing function, S function is a nonlinear function, tau is delay time, i =1,2, \ 8230, N represents that N subgroups with different dynamic characteristics in parallel connection exist;
the multichannel coupled neuron group electroencephalogram model is expressed by a differential equation as follows:
wherein j =1,2, \8230;, M, represents the generation of electroencephalogram signals of M channels; i =1,2, \ 8230, N still indicating the presence of N subgroups of different dynamics in parallel;
after solving the corresponding solution, obtaining the multichannel electroencephalogram signals according to the electroencephalogram signal formula simulated in S1.1:
wherein j =1,2, \8230;, M, represents the generation of electroencephalogram signals of M channels; i =1,2, \8230, N still indicating the presence of N subgroups of different dynamics connected in parallel, y 1 Indicates the output potential of the excitatory cell, y 2 The output potential of the inhibitory cells is represented, and y represents the finally output electroencephalogram signal.
6. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 1, characterized in that: s2 specifically comprises the following steps:
s2.1, calculating a contour coefficient;
regarding the multi-channel electroencephalogram data generated in the S1, clustering each channel as a vector for different clustering numbers, calculating the contour coefficients of the channels, and setting the contour coefficient of the ith channel as S (i):
wherein a (i) is the intra-cluster dissimilarity, which represents the average value of the dissimilarity from the i vector to other points in the same cluster, and represents the degree of aggregation, b (i) represents the inter-cluster dissimilarity, which represents the minimum value of the dissimilarity from the i vector to other clusters, and represents the degree of separation;
s2.2, calculating a nearest cluster;
the average distance from the ith channel to all samples in the kth cluster is used as a measure of the distance from the point to the cluster, and then the distance from X is selected i The closest cluster is taken as the closest cluster; let the nearest cluster be C:
wherein, X i Is the ith channel, p is a cluster C k The sample of (1);
s2.3, selecting a clustering number;
and (3) calculating the contour coefficients of all samples, then calculating the average value to obtain the average contour coefficient, and selecting the cluster number with the best contour coefficient average effect as the number of the community structures in the S3.
7. The method of claim 6, wherein the method comprises the steps of: the number of clusters is 4.
8. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 1, characterized in that: s3 specifically comprises the following steps:
s3.1, generating a similarity matrix: for a given set of N data samples { x ] in C dimensions 1 ,x 2 ,...,x N Therein of
Constructing a similarity matrix W by using a Gaussian kernel;
s3.2, visualization of community relations: and (4) searching the maximum value of the similarity matrix W obtained in the S3.1 according to the row direction, judging a clustering result, and displaying a similarity matrix with indexes sorted according to the clustering result.
9. The method for partition brain electrical modeling and diagonal block model brain electrical channel community classification as claimed in claim 8, characterized in that: in S3.1, assume that the data can be divided into K clusters, given each sample x n Indicator z for allocating K element clusters nk And form a K-order vector, expressed as:
when x is n Z belonging to the kth element cluster nk =1, otherwise z nk =0, so z n An absolute distribution is followed:
z n ～Categorical(π) (3.1)
where π is a k-element vector, indicating that the probability assigned to each cluster obeys a Dirichlet distribution:
π～Dirichlet(λ) (3.2)
wherein pi is a sample of Dirichlet distribution, and lambda is a concentration parameter of the Dirichlet distribution;
if x i And x j Belong to the same cluster k, then z ik z jk =1 and w ij Belongs to the kth diagonal block, then set z ik z jk Is an indicator in the diagonal block that,
an indicator of an off-diagonal block region;
all elements in the similarity matrix W satisfy 0 < W ij 1, so W is modeled using a beta distribution, which is a distribution defined over the interval (0, 1) consisting of two orthogramsParameterizing shape parameters alpha and beta; it is assumed that the similarity matrix W can be divided into k clusters, W ij The probability density of (a) is:
wherein, theta k ＝(α k ,β k ) Represents W ij Parameters of Bate distribution in diagonal blocks, [ theta ] 0 ＝(α 0 ,β 0 ) Represents W ij Parameters of the Bate distribution in the off-diagonal blocks; ζ and η are the hyperparameters of Θ:
according to the formula (3.4), theta is calculated k K, calculating Θ according to formula (3.5) 0 (ii) a Pi is calculated according to the formula (3.2), and z is calculated according to the formula (3.1) n N = 1.. N, W is calculated according to the formula (3.3) ij I =1, say, N, j =1, say, N, W may only compute the upper triangular matrix since W is a symmetric matrix; the similarity matrix W is obtained as described above.
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