CN111096743A - Task state electroencephalogram signal analysis method based on algebraic topology - Google Patents

Task state electroencephalogram signal analysis method based on algebraic topology Download PDF

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CN111096743A
CN111096743A CN202010023638.2A CN202010023638A CN111096743A CN 111096743 A CN111096743 A CN 111096743A CN 202010023638 A CN202010023638 A CN 202010023638A CN 111096743 A CN111096743 A CN 111096743A
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刘畅
俞定国
马小雨
王娇娇
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Zhejiang University of Media and Communications
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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

Task state electroencephalogram signal analysis method based on algebraic topology
Technical Field
The invention relates to the field of neural signal processing of a complex network analysis technology, in particular to a task state electroencephalogram signal analysis method based on algebraic topology.
Background
The new generation artificial intelligence is an intelligent system formed by theories, technologies and methods which are established on the basis of big data and are inspired by brain science and integrated by brain-like intelligence mechanisms. With the development of brain imaging technology and the enhancement of neural data acquisition capabilities, it is crucial to find new methods for analyzing brain function data. The brain is a complex giant system consisting of 140-160 hundred million neurons, and the analysis of a single neuron can only explain local information of the brain, and scientists gradually realize that the behavior of the brain is determined by the interaction among all areas of the brain, thereby generating brain science research based on a functional network. However, the use of networks is based on an important simplifying assumption: the most important elements of the brain are made up of two nodes (neurons or brain regions) connected by an edge, a fundamental assumption that essentially limits the types of neural structures and functions that the graph can use to model. Moreover, compared to local geometric analysis, conventional network topology analysis is difficult to quantitatively study due to the loss of a large amount of detailed information. Therefore, a more powerful mathematical tool needs to be found for analyzing neural signals. Because the common essence, the same invariance and the integrity, of the cognitive basic units (such as chunks, perceptual objects, time format towers and the like) of different cognitive levels can be defined as the property of large-range topology invariance on a tolerance space, the algebraic topological method (coherence theory) with the advantages of geometric analysis and topological analysis can overcome the limitation of graphic generalization and lay the mathematical basis of large-range first perceptual organization, thereby providing new possibility in the aspects of modeling and measuring neural phenomena and having great research potential.
The algebraic topology is a powerful mathematical tool that analyzes complex networks by simple geometric structures, namely simplex, Betti number, also known as β number.
In summary, in order to analyze the brain function mode of a tested subject under a specific task, the brain function signals under the task state are analyzed by an algebraic topological method, the neural characteristics of the brain function networks under the task state are represented by constructing a simplex-based brain function network, and the properties of the brain function network are further analyzed by Betti numbers and Eulerian indicativity numbers, so that the quantitative research of the brain function mechanism under the task state is realized, the cognitive activity rule of the brain under the task state is explored, a cognitive basis is provided for the new generation of artificial intelligence research, an artificial intelligence framework, specific algorithm design and the like are inspired, and the development of new generation of artificial intelligence is promoted.
Disclosure of Invention
The invention provides a task state electroencephalogram signal analysis method based on algebraic topology, which analyzes brain nerve activity in a task state by an algebraic topology method with the advantages of geometric analysis and topological analysis, discovers a cognitive activity rule of a brain in the task state, provides a new rule and evidence for brain-like calculation and promotes the development of new-generation artificial intelligence.
The invention is realized by the following technical scheme:
a task state electroencephalogram signal analysis method based on algebraic topology comprises the following steps:
(1) filtering the acquired EEG signal to obtain a filtered EEG signal of
Figure BDA0002361682320000021
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)
Figure BDA0002361682320000022
(4) Calculating a coherence matrix between the electrodes by using the instantaneous phase phi obtained in the step (2)
Figure BDA0002361682320000023
Wherein,
Figure BDA0002361682320000024
j is an imaginary unit, phip(n) denotes the nth instantaneous phase in the electrode p, phiq(n) denotes the nth instantaneous phase in the electrode q, PLV (p, q) being CM×MOne element of (1);
(5) c in the step (4)M×MThe diagonal elements are set to zero to obtain new
Figure BDA0002361682320000031
(6) Mixing the new C in the step (5)M×MEach element C in (1)pqTaking absolute value to obtain | Cpq|，|CpqI conversion to
Figure BDA0002361682320000032
Obtaining a connection matrix
Figure BDA0002361682320000033
According to the connection matrix
Figure BDA0002361682320000034
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
Figure BDA0002361682320000035
Determining;
(7) constructing a simple complex of undirected graph G
Figure BDA0002361682320000036
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
Figure BDA0002361682320000037
The euler index number S is calculated.
In the step (1), 5-40Hz band-pass filtering is carried out on the collected EEG signals.
X11、X1N、XM1、XMNData points representing an EEG signal;
EEG signals are brain wave signals;
in step (4), PLV (p, q) is the coherence coefficient between electrodes p and q.
The simple complex R (G), Betti number and Euler suggestive number S obtained by the invention can be used for analyzing the brain cognitive mechanism in a task state, providing new rules and evidences for brain-like calculation and promoting the development of new-generation artificial intelligence.
The task state electroencephalogram signal analysis method based on the algebraic topology analyzes the task state electroencephalogram signal through the algebraic topology method, and the simplex is used as a basic unit of the electroencephalogram network, so that the types of neural structures and functions of a restriction map which can be used for modeling are broken through.
The task state electroencephalogram signal analysis method based on the algebraic topology defines the distance relation in the algebraic topology analysis by calculating the coherence among the electrodes, thereby realizing the network construction among the electrodes at different spatial positions.
Compared with the existing task state electroencephalogram signal analysis method, the task state electroencephalogram signal analysis method has the beneficial effects that:
the invention considers the interaction among all areas of the brain when the task is completed, adopts the complex network to analyze the brain function, and breaks through the type of the neural structure and function of the restriction map which can be used for modeling compared with the basic assumption that the most important unit in the brain in the traditional network topology analysis is composed of two nodes (neurons or brain areas) which are connected by one edge. In addition, the invention adopts an algebraic topology method to make up the problem of loss of detail information of the traditional network topology analysis, thereby being capable of carrying out quantitative research on task state brain function. The invention has good performance on task state electroencephalogram signal analysis, provides a new method for measuring the neural response under the task state, can explore the cognitive activity rule of the brain under the task state, provides a new design method and thought for brain-like calculation, and promotes the development of a new generation of artificial intelligence.
Drawings
FIG. 1 is a flow chart of algebraic topological feature computational modeling of an EEG signal;
FIG. 2 is a graph of network connectivity as a function of ε;
FIG. 3 is a graph of the algebraic topological feature dynamic modeling and results (imaginary kinematics) of an EEG signal within a trial run;
FIG. 4 is a graph showing the variation of the Eulerian index number within one trial.
Detailed Description
The effectiveness of the present invention will be more apparent from the following detailed description of the embodiments of the present invention with reference to the attached drawings 1 and examples:
in order to verify the universality of the invention, international public data is taken as an example, and specifically, the 2a group of data of the fourth brain-computer interface competition is selected, namely electroencephalogram data during imagining of an exercise task.
(1) The EEG signal data is subjected to 5-40Hz band-pass filtering, preferably EEG signals obtained at 6-14Hz are
Figure BDA0002361682320000041
Wherein N is the data length and M is the number of electrodes for collecting EEG signals;
(2) performing Hilbert transform on the signal of each electrode to obtain H (X);
(3) calculating the instantaneous phase of each electrode
Figure BDA0002361682320000042
(4) Calculating a coherence matrix between electrodes
Figure BDA0002361682320000051
Wherein,
Figure BDA0002361682320000052
PLV (p, q) is the coherence coefficient between electrodes p and q.
(5) C is to beM×MThe diagonal elements are set to zero to obtain new
Figure BDA0002361682320000053
(6) According to
Figure BDA0002361682320000054
Conversion CM×MObtaining a connection matrix
Figure BDA0002361682320000055
Wherein, CpqIs the coherence coefficient between electrodes p and q,
Figure BDA0002361682320000056
is composed of
Figure BDA0002361682320000057
The elements in (1) when
Figure BDA0002361682320000058
When the number of the leads is larger than the threshold value epsilon, the leads are connected, and the leads are not connected at other times, so that an undirected graph G (V, E) is constructed according to a connection matrix, wherein V is a vertex set, E is an edge set, and each edge passes through the connection matrix
Figure BDA0002361682320000059
And (4) determining. As can be seen from fig. 2, when the threshold value changes, the corresponding network connectivity also changes. FIG. 2 shows the results of the algebraic topological feature dynamic modeling of EEG signals with a change in ε from 0 to 0.3, the connection matrix being smaller as ε is smaller
Figure BDA00023616823200000510
The denser the nodes are, and thus the more nodes the brain function network is connected to, the higher the dimensionality of the formed simple complex, and when epsilon is larger, the connection matrix is
Figure BDA00023616823200000511
The more sparse the network becomes, the poorer the connectivity of the network becomes, and the lower the simple complex dimension is.
(7) Simple complex form of the construction graph G
Figure BDA00023616823200000512
Where σ is the simplex in E, as shown in FIG. 3. Fig. 3 is an algebraic topological feature dynamic modeling and result of an EEG signal in a trial, and it can be seen that the brain function connection of the contralateral side (i.e., right side) is strong when the left-handed imaginary movement is performed, and the brain function connection of the contralateral side (i.e., left side) is strong when the right-handed imaginary movement is performed, which conforms to the general rule of the neurological imaginary movement performed, and illustrates that the general rule of the task state brain state can be successfully revealed by the method of the present invention through the electroencephalogram signal.
(8) Calculating the k-order Betti number Clk(ε)。
(9) According to
Figure BDA00023616823200000513
Calculating the Eulerian index number, and fig. 4 shows the change of the Eulerian index number in one trial, it can be seen that, as time goes on, the Eulerian index number curve has break points, i.e. the phase change characteristics of the network can be expressed by the Eulerian index number.
By way of example, it has been found that in the motor task state, the functional link of the contralateral area of the tested motor is enhanced, and the phase change is generated in time, and the rule can be used for designing a specific algorithm in artificial intelligence. For example, in the neural network framework, the connection mode of the input layer to the middle layer can be changed into contralateral connection, and the training process of the neural network is added into the characteristic of phase change along with time, so that a new artificial neural network is designed.
The example shows that the method can perform quantitative analysis on the electroencephalogram signals of the task state, dynamically establish the neural activity state in the tested task, and explore the cognitive activity rule of the brain in the task state, thereby providing a cognitive basis for the new generation of artificial intelligence research.
The above examples are intended to illustrate the invention, but not to limit the invention, and any modifications and variations of the invention within the spirit and scope of the claims are intended to fall within the scope of the 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
Figure FDA0002361682310000011
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)
Figure FDA0002361682310000012
(4) Calculating a coherence matrix between the electrodes by using the instantaneous phase phi obtained in the step (2)
Figure FDA0002361682310000013
Wherein,
Figure FDA0002361682310000014
j is an imaginary unit, phip(n) denotes the nth instantaneous phase in the electrode p, phiq(n) denotes the nth instantaneous phase in the electrode q, PLV (p, q) being CM×MOne element of (1);
(5) c in the step (4)M×MThe diagonal elements are set to zero to obtain new
Figure FDA0002361682310000015
(6) Mixing the new C in the step (5)M×MEach element C in (1)pqTaking absolute value to obtain | Cpq|，|CpqI conversion to
Figure FDA0002361682310000016
Epsilon is more than or equal to 0 and less than or equal to 1 to obtain a connection matrix
Figure FDA0002361682310000017
According to the connection matrix
Figure FDA0002361682310000018
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
Figure FDA0002361682310000019
Determining;
(7) constructing a simple complex of undirected graph G
Figure FDA0002361682310000021
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
Figure FDA0002361682310000022
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、X1N、XM1、XMNData 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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