A full-node detection method for brain functional network based on random matrix analysis

Abstract

The present invention relates to a method for detecting all nodes of a brain functional network based on random matrix analysis, comprising: collecting electroencephalogram signals, constructing functional brain networks of different motor tasks, and obtaining a brain network data set, wherein the brain network data set is classified into categories with different motor tasks as labels; performing a difference analysis on the functional brain networks of the different motor tasks based on random theory, obtaining a functional brain network that meets a difference threshold, and screening the motor tasks; obtaining the functional brain network and node features of the screened motor tasks and inputting them into an R-GCN model to obtain a motor task prediction result. The present invention uses random matrix theory to analyze the eigenvalue statistical characteristics of a brain network based on electroencephalogram signals to achieve the accuracy of the result quantification theoretical prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of brain-computer interface research, and in particular to a method for detecting all nodes of a brain function network based on random matrix analysis. Background Art

[0002] In the EEG-based brain-computer interface system, the core technology is to realize the decoding of movement intention in EEG signals. To this end, researchers understand the specific movement types in movement intention from different perspectives and propose a variety of detection models based on machine learning theories. At present, these models can achieve high recognition accuracy in certain specific movement types, but the intention classification implemented at this stage is mainly focused on some simple movements. More detailed movements cannot be detected. Therefore, the existing technology lacks a characteristic expression of movement intention in a complete set of types, that is, it lacks a method to achieve refined movement intention detection. Summary of the invention

[0003] The purpose of the present invention is to provide a method for detecting all nodes of a brain functional network based on random matrix analysis, which uses random matrix theory to analyze the eigenvalue statistical characteristics of a brain network based on EEG signals to achieve the accuracy of theoretical prediction of quantitative results.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for detecting all nodes of a brain functional network based on random matrix analysis, comprising:

[0006] Collecting electroencephalogram signals, constructing functional brain networks for different motor tasks, and obtaining brain network data sets, wherein the brain network data sets are classified according to different motor tasks as labels;

[0007] Performing a difference analysis on the functional brain networks of the different motor tasks based on random theory, obtaining the functional brain networks that meet the difference threshold, and screening the motor tasks;

[0008] The functional brain network and node features of the screened motor task are obtained and input into the R-GCN model to obtain the motor task prediction results.

[0009] Optionally, constructing the functional brain networks of different motor tasks includes: processing the functional brain networks of the different motor tasks using a sliding time window.

[0010] Optionally, performing differential analysis on the functional brain networks of the different motor tasks based on stochastic theory includes:

[0011] Based on the brain network dataset, obtaining a Hermitian matrix;

[0012] Based on the Hermitian matrix, obtaining eigenvalues;

[0013] Based on the random theory, the eigenvalues ​​of the covariance matrix are counted, and according to Wigner's semicircle law, a test function is obtained;

[0014] Based on the test function, a difference analysis is performed on the functional brain networks of the different motor tasks.

[0015] Optionally, based on the test function, performing difference analysis on the functional brain networks of the different motor tasks includes:

[0016] Will Expand and obtain the expanded eigenvalues, where is the expanded eigenvalue, G(·) is the numerical curve fitting estimation function, λ i is the Hermitian matrix eigenvalue;

[0017] The unfolded eigenvalues ​​are used to calculate the nearest neighbor distance distribution and quantity variance, and to perform differential analysis on the functional brain networks of the different motor tasks.

[0018] Optionally, the test function is:

[0019]

[0020] Among them, f X (φ) is the Wigner semicircular distribution function, λ j are the sample covariance matrix eigenvalues, and N is the number of eigenvalues.

[0021] Optionally, the R-GCN model is:

[0022]

[0023] in, represents the regularized connectivity matrix operator that encodes the graph structure, is the node feature, is a random matrix, σ is the activation function, and Φ is the output result.

[0024] The beneficial effects of the present invention are as follows: the present invention constructs a brain network data set under multiple tasks through data fitting, and the use of a sliding time window is conducive to moderate expansion when the data set size is limited; random matrix theory has a more essential characterization of the complex network perspective of the brain system; it is not limited to a specific form of movement, and explores the identification and classification of movement tasks under a complete set; it can locate cognitive networks under different tasks through multi-node identification, and explore the functional network representation of the essence of different movement tasks. The present invention provides a new method for realizing multi-task brain-computer interface system recognition through the recognition of EEG movement intentions and the characterization of task networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0026] Figure 1 A flowchart of a method for detecting all nodes of a brain function network based on random matrix analysis according to an embodiment of the present invention;

[0027] Figure 2 A schematic diagram of a method for detecting all nodes of a brain function network based on random matrix analysis according to an embodiment of the present invention;

[0028] Figure 3 This is a detection example between the actual data and the theoretical value of the embodiment of the present invention. DETAILED DESCRIPTION

[0029] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0030] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0031] Random matrix theory is a spectral statistical method based on complex systems, which describes the randomness and determinism of the same system. For the complex network system of the brain, random matrix theory can evaluate and predict the significant differences that may exist under refined movement intentions from the perspective of the whole and the part.

[0032] The present invention discloses a characterization detection method based on EEG motor intention recognition, which detects the nodes activated in the cognitive network, extracts the aggregated network between the functional networks constructed by different methods, and realizes the brain network-specific representation of refined motor intention. Since the number of nodes in the functional network is directly related to the number of electrodes of the EEG cap, it is mainly aimed at the cognitive network detection method with multiple nodes of Q=64 electrodes or more.

[0033] Specifically include:

[0034] Collect EEG signals, construct functional brain networks for different motor tasks, and obtain brain network datasets, where the brain network datasets are divided into categories based on different motor tasks.

[0035] Furthermore, constructing the functional brain networks of different motor tasks includes: processing the functional brain networks of the different motor tasks using a sliding time window.

[0036] Furthermore, based on the existing various functional brain network construction methods, the functional networks (connection matrices) under different tasks are obtained. The brain network construction methods are similarity measurement methods, such as Pearson's correlation coefficient (PCC), coherence (COH), imaginary part of coherence (iCOH), phase locking value (PLV) and phase lag index (PLI), etc. for undirected networks, and Granger causality (GC), partial directed coherence (PDC), directed transfer function (DTF) and mutual information (MIF), etc. for directed networks. Combined with the construction requirements of time-varying networks, the concept of sliding time windows is introduced to characterize the brain network state at the 50ms level. Through simple data fusion, a large-scale brain network dataset from a mesoscopic perspective is constructed, and the data is classified according to different motor tasks as labels;

[0037] Performing a difference analysis on the functional brain networks of the different motor tasks based on random theory, obtaining the functional brain networks that meet the difference threshold, and screening the motor tasks;

[0038] Furthermore, the difference analysis of the functional brain networks of different motor tasks based on random theory includes: obtaining the Hermitian matrix based on the brain network data set; obtaining the eigenvalue based on the Hermitian matrix; performing statistics on the eigenvalues ​​of the covariance matrix based on random theory, and obtaining the test function according to Wigner's semicircle law;

[0039] Based on the test function, the functional brain networks of different motor tasks were differentially analyzed.

[0040] Based on random matrix theory, the gap between the experimental data set and the theoretical prediction value is analyzed and quantified, and the typical statistical characteristics of the brain network data set based on big data are described. The impact of the intention of a specific motor task on the "quasi-random system" of the brain and the statistical differences between different tasks are explained, providing a basis for the specific implementation of the multi-task classification model. Among them, the experimental data set can be any data set with motor intention collected by EEG, as long as there is a category label, and the theoretical prediction is the result of the random matrix theory analysis of the random system.

[0041] The functional brain network and node features of the screened motor task are obtained and input into the R-GCN model to obtain the motor task prediction results.

[0042] Furthermore, based on the graph convolutional neural network model, node features and graph structure matrix, i.e., connection matrix, are used as model inputs to achieve the classification purpose of multiple tasks in intent recognition. Among them, node features use the eigenvalue vector of the connection matrix, and the graph structure matrix is ​​initially defined as a random matrix.

[0043] like Figure 1-2 As shown in the figure, a method for detecting all nodes of a brain function network based on random matrix analysis is disclosed, which specifically includes: combining cognitive psychology experiments, using EEG data related to specific motor tasks collected by multi-channel EEG equipment, and the data is regarded as data containing specific conscious behaviors after preprocessing such as electrode positioning, filtering, and segmentation, and is expressed as X=(x1, x2,…, x L )∈R N×L , where N is the number of electrodes and L is the time sampling point. Combining the random matrix theory, the random variable (x1, x2, ..., x L )∈R N That is, the basic elements of EEG data. Define the N×N dimension Hermitian matrix H, λ1,λ2,…,λ N is the eigenvalue of H. If the eigenvalue λ i is a real number, the one-dimensional empirical spectral distribution function is defined as:

[0044]

[0045] When N→∞, H is completely random. In the real world, N is finite, and F H is a finite distribution. The random matrix model is usually based on the sample covariance matrix A N =N -1 XX H Perform data modeling, X H is the transpose of the EEG data matrix, I is the unit matrix, combined with the actual scene of EEG data, the correlation matrix can be used to construct a dynamically changing brain network based on the basic definition of covariance, using the amplitude, phase, imaginary part of real numbers or polynomial regression in signal transformation. These methods are widely used in the study of brain cognitive principles. For example:

[0046] iCOH:

[0047]

[0048] Among them, im[*] is the imaginary part of the real number, x, y are the EEG time series of different electrodes, S xy (f) is the cross power spectral density between x and y, S xx (f) and S yy (f) are the power spectral densities of x and y, respectively.

[0049] PLV:

[0050]

[0051] Where t is the instantaneous time, ω is the selected frequency band, K is the total number of time points in a single trial, ΔΦ k is the phase difference between x and y, and j is the sign of the imaginary number.

[0052] PDC:

[0053] The multivariate autoregressive (MAR) process is defined as

[0054]

[0055] Among them, ε i (k) is an independent Gaussian white noise with variance matrix Σ, x M (k) is the prediction of x by the past sample values ​​of x and y at the Mth element of the x electrode, x M (kr) is the autoregressive coefficient of the Mth element of the x electrode at the kth order. Yr is the coefficient matrix of the autoregressive model of the y electrode data, and r is the data point.

[0056] The power spectral density matrix is ​​defined as

[0057] S(f)=H(f)∑H H (f), (5)

[0058] in,(·) H is the Hermitian conjugate transpose, H is the transfer function matrix, defined as H(f) = Y -1 (f) = [IY(f)] -1 , Y(f) is the coefficient of Fourier transform, yes Therefore, the PDC from signal y to x is defined as:

[0059]

[0060] Laguerre unitary sets are more suitable for analyzing real-world data and satisfy the central So define Yes A N The eigenvalues ​​of the random matrix theory can be used to count the eigenvalues ​​of the covariance matrix of all samples. According to Wigner's semicircle law, it can be assumed that the test function φ(·) of the linear eigenvalue statistics of the random matrix is ​​defined as:

[0061]

[0062] And N -1 f X (φ) can converge to:

[0063]

[0064] Among them, ρ(λ) is the probability distribution function of the eigenvalue. Different test functions are designed to obtain different indicators to compare the gap between actual observations and theoretical values. The specific method is to To expand, is the expanded eigenvalue, and G(·) is the numerical curve fitting estimation function. Using the expanded eigenvalue, the nearest-neighbor spacing distribution (NNSD) and number variance (NV) are tested. Specifically, NNSD is calculated by s i =λ i+1 -λ i (λ i ≤λ i+1 ) is calculated, which only reflects the short-distance correlation between eigenvalues. If s satisfies P(s) = exp(-s), it conforms to the Poisson distribution; if s satisfies P(s) = π / 2sexp(-πs 2 / 4), it is approximately a Gaussian orthogonal distribution. NV characterizes the long-range correlation between eigenvalues ​​and is defined as Σ 2 (L)=<({λ i<L}-L) 2 >, L is the expected number of spectra in the interval [λ,λ+L], {λ i <L} indicates the number of eigenvalues ​​less than L. 2 (L) satisfies Σ 2 (L)=L, then it conforms to the Poisson distribution; if Σ 2 (L) satisfies Σ 2 (L)≈2 / π 2 (log(2πL)+1.5772-π 2 / 8), it is approximately a Gaussian orthogonal population. Figure 3 It is the result of the sample data tested by NNSD, which has a large gap with the theoretical value. Poisson distribution shows that the prediction result is close to a random system, which means that the experimental data does not have a basis for classification. Gaussian distribution shows that the prediction result is not random. As the predicted data, the task state is expected to be close to Gaussian distribution. Based on Gaussian distribution, statistical tests are performed between different tasks, and p<0.05 can indicate the significance between different tasks.

[0065] According to the theory of complex networks, the brain network is a complex network between deterministic networks and random networks with small-world network properties. Therefore, it is assumed that the overall distribution of eigenvalues ​​of different correlation algorithms is also between normal distribution and Poisson distribution, and there is no significant difference between different methods. Based on this assumption, a cognitive function network detection of all nodes in the EEG connection matrix is ​​constructed. This embodiment uses a graph convolutional neural network (GCN) as the basic detection model, assuming a random GCN model, defined as:

[0066]

[0067] in, represents the regularized connectivity matrix operator that encodes the graph structure, is the node feature, is a random matrix, W ij is an independent and identically distributed matrix N(0,1), σ is the activation function, Φ is the output, n is the number of samples, p is the feature dimension, and d is the dimension of the random matrix. In particular, the spectral property of the Gram matrix is ​​defined as:

[0068]

[0069] Node Characteristics: Definition where λ1,...,λ n is an independent node feature vector, that is, the eigenvalue vector in the matrix H. Each sample is a category label {C1,...C Q}, from the analysis of random matrix theory, the distribution of eigenvalues ​​is a distribution between determinism and randomness. Assuming that the node feature λ n Obey the Gaussian mixture model, let λ i ∈C a When in z i ~N(0,I p / p).

[0070] Graph structure: Assume that the connection matrix A is a random variable that follows an independent Bernoulli distribution, and the parameter is defined as π ij =q 2 C ab ∈(0,1), where λ i ∈C a and λ j ∈C b , q∈(0,1) is the probability of a connection between two nodes, C ab It is in category C a and C b The probability of a connection between nodes. In addition, for all i, A ii = 1. The initial graph structure is positioned as a random matrix.

[0071] R-GCN model: The node features and graph structure in the EEG signal are input into the GCN model as the input layer, and the basic functional connection of the output layer is calculated by the hidden layer. Since this embodiment mainly involves EEG signals, the methods of constructing the graph structure are all based on the similarity principle. The hidden layer can use common methods such as random multi-layer perceptron and spectral clustering to complete the information transmission and update of node features. When there is noise in the similar graph structure, the introduction of node core can suppress random noise. Figure 1 The basic model structure of R-GCN is included.

[0072] The implementation process of the proposed method is explained using the classification of left and right feet in lower limb movement imagination as an example:

[0073] (1) Based on the motor imagery paradigm, the EEG signals of the subjects were collected. The specific task was to complete the unilateral lower limb movement of the actual movement according to the instructions of the picture, that is, to gently lift the toes with the heel as the reference, without obvious pauses during the process of lifting the foot, and the movement was smooth. This movement only needed to be completed once in a single trial. Then, the motor imagery was performed, and the subjects imagined the actions in the movement execution module. The subjects were required to imagine the action of lifting the toes as the first person, and avoid only imagining the image of lifting the foot, that is, the subjects were required to have the intention of lifting the foot. In this way, a data set containing the intention of imagining the movement of the left and right feet was obtained.

[0074] (2) Based on the RMT, the lateralization of the brain network of lower limb motor imagery was evaluated. First, the nine functional connectivity methods of PCC, COH, iCOH, PLV, PLI, GC, PDC, DTF and MIF were used to construct the brain functional network. Then, a network population was defined. The null hypothesis was that there was no significant difference in the functional network of each group. The characteristic values ​​of the brain functional network were statistically tested including NNSD and NV. On the one hand, it showed the difference between the lower limb motor imagery task and the random system, and on the other hand, it proved the existence of left and right foot lateralization in the lower limb motor imagery task.

[0075] (3) Random matrix-based graph convolutional neural network (R-GCN) classification, node features are defined as feature vector sets of the functional network matrix, and the architecture graph structure based on the R-GCN model can be initialized as a random matrix, that is, the relationship between samples is random. The model structure used in this embodiment mainly adopts a single-layer GCN, and the training and testing models adopt a 10-fold split method. Each fold of data will use a 10-fold cross-validation to evaluate the model.

[0076] Finally, this embodiment conducted preliminary experiments in the experimental data set of left and right foot classification of lower limb motor imagery, explored the global and local characteristics of the functional network of the lower limb motor imagery task through random matrix theory, verified the non-randomness of the left and right foot data based on the resting state data, established the significance between the left and right foot task state data, and further used the R-GCN deep learning model to improve the classification accuracy to more than 90%, achieving high-precision recognition in the brain-computer interface system.

[0077] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for detecting all nodes of a brain functional network based on random matrix analysis, characterized in that: include: Collecting electroencephalogram signals, constructing functional brain networks for different motor tasks, and obtaining brain network data sets, wherein the brain network data sets are classified according to different motor tasks as labels; Performing a difference analysis on the functional brain networks of the different motor tasks based on random theory, obtaining the functional brain networks that meet the difference threshold, and screening the motor tasks; Obtaining the functional brain network and node features of the screened motion task and inputting them into the R-GCN model to obtain the motion task prediction result, wherein the node features are defined as a feature vector set of the functional network matrix, and the architecture graph structure based on the R-GCN model is initialized to a random matrix, and the R-GCN model is a graph convolutional neural network based on a random matrix; The difference analysis of the functional brain networks of the different motor tasks based on stochastic theory includes: Based on the brain network dataset, obtaining a Hermitian matrix; Based on the Hermitian matrix, obtaining eigenvalues; Based on the random theory, the eigenvalues ​​of the covariance matrix are counted, and according to Wigner's semicircle law, a test function is obtained; Based on the test function, performing difference analysis on the functional brain networks of the different motor tasks; Based on the test function, performing difference analysis on the functional brain networks of the different motor tasks includes: Will Expand and obtain the expanded eigenvalues, where is the expanded eigenvalue, G(·) is the numerical curve fitting estimation function, λ i is the Hermitian matrix eigenvalue; The unfolded eigenvalues ​​are used to calculate the nearest neighbor distance distribution and quantity variance, and to perform differential analysis on the functional brain networks of the different motor tasks.

2. The method for detecting all nodes of a brain function network based on random matrix analysis according to claim 1, characterized in that: After constructing the functional brain networks of different motor tasks, the method includes: processing the functional brain networks of the different motor tasks by using a sliding time window.

3. The method for detecting all nodes of a brain function network based on random matrix analysis according to claim 1, characterized in that: The test function is: Among them, f X (φ) is the Wigner semicircular distribution function, λ j are the sample covariance matrix eigenvalues, and N is the number of eigenvalues.

4. The method for detecting all nodes of a brain function network based on random matrix analysis according to claim 1, characterized in that: The R-GCN model is: in, represents the regularized connectivity matrix operator that encodes the graph structure, is the node feature, is a random matrix, σ is the activation function, and Φ is the model output.

Images