CN111096743A - A task-state EEG signal analysis method based on algebraic topology - Google Patents

Abstract

The invention discloses a task state electroencephalogram signal analysis method based on algebraic topology, and belongs to the specific application of a complex network analysis technology in the field of neural signal processing. The method comprises the following steps: the electroencephalogram signals are used as data sources, the distance relation of electrodes in different spatial positions is constructed by calculating the coherence among the electrodes, a simplex brain function network is dynamically constructed by adopting an algebraic topology method, the neural characteristics of the electroencephalogram signals in the task state are represented, the properties of the brain function network are further analyzed by calculating Betti numbers and Eulerian numbers, and the quantitative research of the tested brain function mode in the task state is realized. The invention has good performance on task state electroencephalogram signal analysis, provides a new method for measuring the neural response under the task state, and explores new rules and evidences for brain-like calculation, thereby inspiring artificial intelligence framework, specific algorithm design and the like and promoting the development of new generation artificial intelligence.

Description

A task-state EEG signal analysis method based on algebraic topology

technical field

The invention relates to a complex network analysis technology in the field of neural signal processing, in particular to a task state EEG signal analysis method based on algebraic topology.

Background technique

The new generation of artificial intelligence is an intelligent system formed by combining theories, technologies and methods based on big data and brain-like intelligence mechanisms inspired by brain science. With the development of brain imaging technology and the enhancement of neural data acquisition capabilities, it is critical to find new ways to analyze brain function data. The brain is a complex giant system composed of 14 billion to 16 billion neurons. The analysis of a single neuron can only explain the local information of the brain. Scientists have gradually realized that the behavior of the brain is determined by the interaction between various regions of the brain. determined, resulting in functional network-based brain research. However, the use of networks is based on an important simplifying assumption: the most important unit in the brain is composed of two nodes (neurons or brain regions) connected by an edge, a fundamental assumption that inherently limits graphs that can be used to model types of neural structure and function. Moreover, compared with local geometric analysis, traditional network topology analysis is difficult to carry out quantitative research due to the loss of a large amount of detailed information. Therefore, it is necessary to find more powerful mathematical tools to analyze neural signals. Due to the common nature of cognitive basic units (such as chunks, perceptual objects, temporal gestalt, etc.) at different cognitive levels—identity invariance and wholeness—can be defined as a large-scale topology invariant property on tolerance space , therefore, the algebraic topological method (homology), which combines the advantages of geometric analysis and topological analysis, can overcome the limitation of graph generalization and lay the mathematical foundation of "large-scale first" perceptual organization, thus providing a great advantage in modeling and measuring neural phenomena. new possibilities and great research potential.

Algebraic topology is a powerful mathematical tool for the analysis of complex networks through simple geometric structures - simplex, Betti numbers, also known as beta numbers. Simplex is the basic unit of simplicial complex, which can be regarded as the generalization of a triangle or tetrahedron to their higher-dimensional counterparts, and it is very robust to changes in network dynamics, so that it can be analyzed by analyzing the network dynamics. Persistent homology features, such as Betti numbers, Euler characteristic numbers, etc., extract the essentially invariant topological features of complex discrete point sets without considering the specific changes in their spatial distribution.

To sum up, in order to analyze the brain function mode of the subjects under a specific task, the present invention adopts the algebraic topology method to analyze the EEG signal under the task state, and constructs a simplex-based brain function network to characterize the neural network of the task state EEG signal. and further analyze the nature of the brain functional network through the Betti number and Euler characteristic number, so as to realize the quantitative research on the brain function mechanism under the task state, and explore the cognitive activity law of the brain under the task state, so as to provide a new generation of artificial intelligence. Intelligence research provides a cognitive foundation, inspires artificial intelligence frameworks and specific algorithm design, etc., and promotes the development of a new generation of artificial intelligence.

SUMMARY OF THE INVENTION

The invention provides a task-state EEG signal analysis method based on algebraic topology. The algebraic topology method with the advantages of both geometric analysis and topological analysis is used to analyze the neural activity of the brain in the task state, and to explore the cognitive activity of the brain in the task state. It provides new laws and evidence for brain-like computing and promotes the development of a new generation of artificial intelligence.

The present invention is achieved through the following technical solutions:

A task state EEG signal analysis method based on algebraic topology, comprising the following steps:

其中，N为数据长度，M为采集EEG信号的电极数目，滤波后的EEG信号X中每一行即为每一电极的信号；(1) Filter the collected EEG signal to obtain the filtered EEG signal, and the filtered EEG signal is

Among them, N is the data length, M is the number of electrodes for collecting EEG signals, and each row in the filtered EEG signal X is the signal of each electrode;

(2) H(X) is obtained by performing Hilbert transform on the signal of each electrode in the filtered EEG signal X obtained in step (1);

(3) Calculate the instantaneous phase of each electrode using H(X) obtained in step (2)

其中，

j为虚数单位，φ^p(n)表示电极p中的第n个瞬时相位，φ^q(n)表示电极q中的第n个瞬时相位，PLV(p,q)为C_M×M中的一个元素；(4) Calculate the coherence matrix between electrodes using the instantaneous phase φ obtained in step (2)

in,

j is an imaginary unit, φ ^p (n) represents the n-th instantaneous phase in electrode p, φ ^q (n) represents the n-th instantaneous phase in electrode q, and PLV(p,q) is C _M×M in an element;

(5) Set the C _{M × M} diagonal elements in step (4) to zero to obtain a new

得到连接矩阵

根据连接矩阵

构建出无向图G＝(V,E)，其中，V是顶点集，E是边集，每一条边通过连接矩阵

所确定；(6) Take the absolute value of each element C _pq in the new C _M×M in step (5) to obtain |C _pq |, and |C _pq |

get the connection matrix

According to the connection matrix

Construct an undirected graph G=(V, E), where V is the vertex set, E is the edge set, and each edge passes through the connection matrix

determined;

其中，σ是在E中的单纯形，；(7) Construct the simplicial complex of the undirected graph G

where σ is a simplex in E,;

(8) Calculate the k-order Betti number Cl _k (ε) of R(G) in step (7);

计算欧拉示性数S。(9) Using the k-order Betti number Cl _k (ε) in step (8), according to

Calculate the Euler characteristic S.

In step (1), 5-40 Hz band-pass filtering is performed on the collected EEG signal.

X ₁₁ , X _1N , X _M1 , and X _MN represent data points of the EEG signal;

EEG signal is brain wave signal;

In step (4), PLV(p, q) is the coherence coefficient between electrodes p and q.

The simple complex R(G), Betti number and Euler characteristic number S obtained by the present invention can be used to analyze the cognitive mechanism of the brain under the task state, provide new rules and evidence for brain-like computing, and promote a new generation of artificial intelligence development of.

Task-state EEG signal analysis method based on algebraic topology The task-state EEG signal is analyzed by algebraic topology method, and simplex is used as the basic unit of EEG network, which breaks through the types of neural structures and functions that can be used for modeling. .

The task-state EEG signal analysis method based on algebraic topology defines the distance relationship in algebraic topological analysis by calculating the coherence between electrodes, thereby realizing the network construction between electrodes in different spatial positions.

Compared with the existing task state EEG signal analysis method, the present invention has the following beneficial effects:

The present invention takes into account the interaction between various regions of the brain when the task is completed, and uses a complex network to analyze the brain function. Compared with the traditional network topology analysis, the most important unit in the brain is two nodes connected by an edge (neural Elements or brain regions), the present invention breaks through the types of neural structures and functions that limit maps can be used to model. In addition, the present invention adopts the algebraic topology method to make up for the loss of detailed information in the traditional network topology analysis, thereby enabling quantitative research on task-state brain function. It has been verified that the present invention performs well in task state EEG signal analysis, and provides a new method for measuring neural responses in task state. Provide new design methods and ideas to promote the development of a new generation of artificial intelligence.

Description of drawings

Fig. 1 is the flow chart of algebraic topological feature calculation and modeling of EEG signal;

Figure 2 is a graph showing the change of network connectivity with ε;

Fig. 3 is the dynamic modeling and result (imaginary motion) diagram of algebraic topological feature of EEG signal in one trial;

Figure 4 is a graph of the variation of Euler's characteristic number within a trial.

Detailed ways

Below in conjunction with accompanying drawing 1 and examples, the embodiment of the present invention is described in detail with the specific flow, the efficiency of the present invention will be more obvious:

In order to verify the universality of the present invention, international public data is used as an example. Specifically, the data of group 2a of the 4th Brain-Computer Interface Competition is selected, that is, the EEG data during imaginary motor tasks.

其中，N为数据长度，M为采集EEG信号的电极数目；(1) Perform 5-40Hz bandpass filtering on the EEG signal data, preferably the EEG signal obtained at 6-14Hz is

Among them, N is the data length, and M is the number of electrodes for collecting EEG signals;

(2) Hilbert transform is performed on the signal of each electrode to obtain H(X);

(3) Calculate the instantaneous phase of each electrode

其中，

PLV(p,q)为电极p和q之间的相干系数。(4) Calculate the coherence matrix between electrodes

in,

PLV(p,q) is the coherence coefficient between electrodes p and q.

(5) Set the diagonal elements of C _{M × M} to zero to obtain a new

转换C_M×M得到连接矩阵

其中，C_pq是为电极p和q之间的相干系数，

为

中的元素，当

大于阈值ε时，导联被联通，其他时候不连通，从而根据连接矩阵构建出无向图G＝(V,E)，其中，V是顶点集，E是边集，每一条边通过连接矩阵

所确定。根据图2可以看到，当阈值发生变化时，相应的网络连通性也会发生变化。图2给出了ε从0到0.3变化时的EEG信号的代数拓扑特征动态建模结果，当ε越小时，连接矩阵

就会越稠密，因此脑功能网络连接的节点越多，所构成的单纯复形的维度也会越高，而当ε越大时，连接矩阵

就会越稀疏，表现为网络的连通性越差，所构成的单纯复形维度越低。(6) According to

Transform C _M×M to get the connection matrix

where C _pq is the coherence coefficient between electrodes p and q,

for

elements in , when

When it is greater than the threshold ε, the leads are connected, and other times are not connected, so an undirected graph G=(V, E) is constructed according to the connection matrix, where V is the vertex set, E is the edge set, and each edge passes through the connection matrix.

determined. As can be seen from Figure 2, when the threshold changes, the corresponding network connectivity also changes. Figure 2 shows the dynamic modeling results of algebraic topological features of EEG signals when ε varies from 0 to 0.3. When ε is smaller, the connection matrix

will be denser, so the more nodes connected to the brain function network, the higher the dimension of the simple complex formed will be, and when the ε is larger, the connection matrix

The sparser the network, the worse the connectivity of the network, and the lower the dimension of the simple complex formed.

其中，σ是在E中的单纯形，如图3所示。图3为一个试次内EEG信号的代数拓扑特征动态建模及结果，可以看到，被试在进行左手想象运动时，对侧(即右侧)的脑功能连接较强，而在被试进行右手想象运动时，对侧(即左侧)的脑功能连接较强，这符合神经学中被试进行想象运动时的一般规律，说明本发明的方法能够通过脑电信号成功揭示任务态大脑状态的一般规律。(7) Construct the simplicial complex of the graph G

where σ is the simplex in E, as shown in Figure 3. Figure 3 shows the dynamic modeling and results of the algebraic topological features of the EEG signal in one trial. It can be seen that when the subjects performed left-hand imaginary movements, the brain functional connections on the opposite side (ie, the right side) were stronger, while in the subjects When performing the right-hand imaginary movement, the brain function connection of the opposite side (ie the left side) is stronger, which is in line with the general law of the subjects in neurology when performing the imaginary movement, indicating that the method of the present invention can successfully reveal the task-state brain through EEG signals. General laws of state.

(8) Calculate the k-order Betti number Cl _k (ε).

计算欧拉示性数，图4为一个试次内欧拉示性数的变化，可以看到，随着时间的推移，欧拉示性数曲线出现了断点，即可以通过欧拉示性数表达网络的相变特征。(9) According to

Calculate the Euler characteristic number. Figure 4 shows the change of the Euler characteristic number within a trial. It can be seen that as time goes by, the Euler characteristic number curve has a breakpoint, that is, the Euler characteristic number can be passed. Express the phase transition characteristics of the network.

The example illustrates that through the present invention, it can be found that under the state of imaginative motor task, the functional connection of the contralateral area of the subject's imaginary motor is enhanced, and there will be a phase change over time, and this law can be used to design specific artificial intelligence. algorithm. For example, in the neural network framework, the connection between the input layer and the intermediate layer can be changed to the opposite side connection, and the training process of the neural network can be added with the characteristics of phase change over time, so as to design a new artificial neural network.

Examples illustrate that the present invention can quantitatively analyze the EEG signals in the task state, dynamically establish the neural activity state in the subject's task, and discover the cognitive activity law of the brain in the task state, thereby providing a cognitive foundation for the new generation of artificial intelligence research. .

The above examples are used to explain the present invention rather than limit the present invention. Any modifications and changes made to the present invention within the scope of protection of the spirit and claims of the present invention all fall into the protection scope of the present invention.

Claims (5)

1. A task state electroencephalogram signal analysis method based on algebraic topology is characterized by comprising the following steps:

(1) filtering the acquired EEG signal to obtain a filtered EEG signal of

Wherein, N is the data length, M is the number of electrodes for collecting EEG signals, and each row in the filtered EEG signals X is the signal of each electrode;

(2) performing Hilbert transform on the signal of each electrode in the filtered EEG signal X obtained in the step (1) to obtain H (X);

(3) calculating the instantaneous phase of each electrode by using H (X) obtained in the step (2)

(4) Calculating a coherence matrix between the electrodes by using the instantaneous phase phi obtained in the step (2)

Wherein,

j is an imaginary unit, phi^p(n) denotes the nth instantaneous phase in the electrode p, phi^q(n) denotes the nth instantaneous phase in the electrode q, PLV (p, q) being C_M×MOne element of (1);

(5) c in the step (4)_M×MThe diagonal elements are set to zero to obtain new

(6) Mixing the new C in the step (5)_M×MEach element C in (1)_pqTaking absolute value to obtain | C_pq|，|C_pqI conversion to

Epsilon is more than or equal to 0 and less than or equal to 1 to obtain a connection matrix

According to the connection matrix

Constructing an undirected graph G ═ (V, E), wherein V is a vertex set, E is an edge set, and each edge passes through a connection matrix

Determining;

(7) constructing a simple complex of undirected graph G

Where σ is the simplex in E;

(8) calculating the Betti number Cl of the k-order of R (G) in the step (7)_k(ε)；

(9) Adopting the k-order Betti number Cl in the step (8)_k(. epsilon.) according to

The euler index number S is calculated.

2. The algebraic topology-based task-state electroencephalogram signal analysis method of claim 1, wherein in step (1), the acquired EEG signal is subjected to 5-40Hz band-pass filtering.

3. The algebraic topology-based task-state electroencephalogram signal analysis method of claim 1, wherein in step (1), X is₁₁、X_1N、X_M1、X_MNData points representing an EEG signal.

4. The algebraic topology-based task-state electroencephalogram signal analysis method of claim 1, wherein in step (1), the EEG signal is a brain wave signal.

5. The algebraic topology-based task-state electroencephalographic signal analysis method of claim 1, wherein in step (4), PLV (p, q) is a coherence coefficient between electrodes p and q.

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