CN114587384A - Motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning - Google Patents

Motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning Download PDF

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CN114587384A
CN114587384A CN202111313783.5A CN202111313783A CN114587384A CN 114587384 A CN114587384 A CN 114587384A CN 202111313783 A CN202111313783 A CN 202111313783A CN 114587384 A CN114587384 A CN 114587384A
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祝磊
朱洁萍
胡奇峰
丁旺盼
何光发
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Abstract

The invention discloses a motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning, which comprises the following steps of: s1, sampling the motor imagery electroencephalogram signals and establishing a sample set; s2, preprocessing the data by using a filter bank common space mode to obtain a data sample original feature set, and simultaneously dividing the data sample original feature set into a training sample original feature set and a test sample original feature set; s3, further extracting data characteristics by using the proposed characteristic extraction method and reducing dimensions; and S4, classifying the extracted features by using a support vector machine. The method comprises the following steps of dividing original data into a clean part and a noise part by using a low-rank representation method, effectively removing noise and having strong robustness to the noise; the low-rank representation, discriminant projection and manifold learning methods are integrated into a unified model, so that the global structure information of the original sample is reserved, the local neighborhood relation of the original sample is also reserved, effective features are obtained to a greater extent, and the subsequent classification precision is improved.

Description

Motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning
Technical Field
The invention belongs to the technical field of classification and identification of motor imagery electroencephalogram signals, and particularly relates to a motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning.
Background
The brain-computer interface records and analyzes brain activities through the signal acquisition system, so that the connection between a computer and the brain is realized, and the brain-computer interface is mainly used for physical rehabilitation of patients and assistance of behavior activities at present. The key points of the application of the method lie in the feature selection and extraction of the electroencephalogram signals and the construction of classification models. Not all features extracted from the brain electrical signal are relevant to classification. Too many features not only increase the dimension of the feature matrix, but also result in low classification success rates. The electroencephalogram signal has the characteristics of nonlinearity, instability, weak signal and the like, the signal acquired by the electrode is not pure vectorized data but multi-channel matrix data, time sequence sampling of each electrode channel is collected, and the sampling data of each electrode channel synthesizes the whole electroencephalogram signal. Conventional feature extraction methods tend to ignore nonlinear features in the signal as well as spatial structure information. Therefore, how to perform noise reduction enhancement on the original electroencephalogram data sample and solve the problems of high computational complexity and low classification precision caused by high-dimensional data are very important. Manifold learning is an imitation of an information processing mechanism for recognizing, processing and memorizing external things by a human neural perception system, and is essentially a nonlinear dimension reduction method, namely a low-dimensional feature space is used for representing the intrinsic geometric distribution of high-dimensional nonlinear data, the information integrity of the data can be maintained in the low-dimensional data, key information can be extracted, and the inherent rule of the data can be found. The basic idea is to assume that an original sample is positioned on a manifold structure in a high-dimensional data space, maintain the neighborhood relationship among data unchanged, and map the high-dimensional data sample into a low-dimensional space through nonlinear transformation, thereby achieving the purpose of data dimension reduction or visualization. In recent years, manifold learning algorithms have obtained a great deal of research results, and show certain advantages in the research of electroencephalogram signals.
The traditional dimension reduction method only obtains the global structure information of the observation data. In the manifold learning method, the local neighborhood structure of the original sample is well preserved, and the global structure information of the observation sample is ignored. Manifold learning methods typically use euclidean distances to preserve local structural information, which distances are very sensitive to errors and noise in the observed data. Some scholars think that noiseless data has low-rank structural characteristics, and the method based on low-rank representation can explore the low-rank structure of the data, remove redundant information while keeping the global structure of the data, can effectively remove noise, and has strong robustness to the noise.
For example, a "motor imagery electroencephalogram signal feature extraction method" disclosed in chinese patent literature, the publication number thereof: CN113239778A, filing date thereof: in 2021, 5 months and 10 days, the method can balance the calculation complexity and the convergence rate, is convenient to realize in a single chip microcomputer, and can meet the requirement of acquiring electroencephalogram signals in real time. The method has the effects of high convergence rate, difficulty in changing the waveform shape and capability of effectively removing physiological artifacts and circuit noise, but has the problems of incapability of effectively removing noise, incomplete global structure information, incomplete effective feature extraction and low classification accuracy.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning, and solves the problems that noise cannot be effectively removed, global structure information is incomplete, effective feature extraction is incomplete and classification accuracy is low.
The invention discloses a technical scheme, in particular to a motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning, which comprises the following steps of:
s1, sampling the motor imagery electroencephalogram signals and establishing a sample set;
s2, preprocessing the data by using a filter bank common space mode to obtain a data sample original feature set, dividing the data sample original feature set into a training sample original feature set and a test sample original feature set, and setting maximum iteration times T and dimensionality d;
s3, further extracting data characteristics by using the proposed characteristic extraction method and reducing dimensions;
and S4, classifying the extracted features by using a support vector machine.
Preferably, the pretreatment method comprises the following steps: all electroencephalogram signals are divided into a plurality of sub-frequency bands by a Chebyshev II type filter bank covering 4-40Hz, and each 4Hz frequency band is divided into 9 sub-frequency bands.
Preferably, feature extraction is carried out on the 9 frequency band data obtained after processing by adopting OVR-CSP, and a group of frequency-space feature data sets are obtained.
Preferably, an alternating iterative algorithm is designed to solve the data characteristics after dimensionality reduction: fixing variable A to update Z and E, fixing Z to update A; where A is the required projection matrix, and Z and E are the low rank projection matrix and error matrix of the low rank representation.
Preferably, the method for updating Z and E is as follows: initializing A, and solving Z and E by utilizing an augmented Lagrange algorithm according to an LRR algorithm.
Figure BDA0003342852050000021
Solving the function with an LRR algorithm, treating XA as a data matrix for low rank decomposition;
optimization with ALM algorithm:
Figure BDA0003342852050000031
the following augmented Lagrangian function is minimized:
Figure BDA0003342852050000032
where μ > 0 is a penalty factor, | · |FIs the Frobenious norm, Y of the matrix1，Y2Is the lagrange multiplier. The variables Z, J, E can be minimized one by fixing the other variables and then updating the lagrange multipliers.
Solving and optimizing J by using a singular value threshold operator:
Figure BDA0003342852050000033
optimum Z*：
Z*＝(I+ATXTXA)-1[ATXT(XA-E)+J+(ATXTY1-Y2)/μ]
Solving for optimal E by matrix-complemented singular value threshold algorithm*：
Figure BDA0003342852050000034
Update multipliers and parameters as follows:
Y1＝Y1+μ(XA-XAZ-F)
Y2＝Y2+μ(Z-J)
μ＝min(ρμ，μmax)
where ρ is a parameter and ρ > 0.
Preferably, the method for obtaining A is as follows. Let XmRespectively constructing an inter-class weight matrix B and z intra-class weight matrices W, wherein element expressions of the inter-class weight matrix B and the z intra-class weight matrices W are respectively as follows:
Figure BDA0003342852050000041
wherein M isiIs a sample mean matrix of the i-th class samples,
Figure BDA0003342852050000042
nithe number of samples of the ith type; t is a parameter, and the weight can be modified by adjusting t; calculating the intra-class divergence matrices P according to the following formulawAnd an inter-class divergence matrix Pb:
Figure BDA0003342852050000043
Figure BDA0003342852050000044
Based on the constraint term XA XAZ + E, the objective function can be converted to:
Figure BDA0003342852050000045
simplified to the following formula:
Figure BDA0003342852050000046
and converting the generalized eigenvalue solution problem into a generalized eigenvalue solution problem, and sorting the solved eigenvalue matrix according to the magnitude of the eigenvalue to obtain a projection matrix A.
In the above-mentioned parameters, the value of α is set to 1, and the value of λ is set to 0.01.
Preferably, matrices A, Z and E are updated simultaneously until a specified maximum number of iterations T is reached.
Preferably, the method for extracting d-dimensional feature data comprises the following steps: and calculating to obtain a projected feature matrix Y according to Y-XA, drawing into a vector, and selecting the front d data as d-dimensional feature data after dimension reduction.
Preferably, the d-dimensional feature data is classified by an SVM classifier.
The invention has the beneficial effects that: capturing the global subspace structure of the original sample by using a low-rank representation method to obtain the lowest-rank representation of the original electroencephalogram data, dividing the original data into a clean part and a noise part, effectively removing noise, and having strong robustness to the noise; the low-rank representation, discriminant projection and manifold learning methods are integrated into a unified model, so that the global structure information of the original sample is retained, the local neighborhood relationship of the original sample is retained, effective features are obtained to a greater extent, and the subsequent classification accuracy is improved.
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FIG. 1 is a logic flow diagram of a motor imagery electroencephalogram feature extraction method combining low rank representation and manifold learning according to the present invention.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings. In addition, numerous specific details are set forth below in order to provide a better understanding of the present invention. It will be understood by those skilled in the art that the present invention may be practiced without some of these specific details. In some instances, methods, instrumentalities well known to those skilled in the art have not been described in detail in order to not unnecessarily obscure the present invention.
Example (b): to demonstrate the feasibility of the above method, the algorithm was examined below using the 2008 motor imagery data set Dataset 2 a. The Data set 2a consists of electroencephalographic Data of nine healthy subjects, and the Data is extracted as follows: at the beginning of the experiment, a cross will appear on the black screen, prompting the subject to be ready, and then an arrow in a certain direction will appear on the screen as a visual prompt for several seconds, at which time the subject is required to perform a specific motor imagery task according to the prompt. Until the visual cue disappears, a short break is made to wait for the next experiment to start. Each subject was instructed to perform four different motor imagery tasks, namely left hand, right hand, feet and tongue movements. At a sampling frequency of 250HZ, 22 channels of EEG signals and 3 channels of EOG signals were recorded. Training data and test data were taken from subjects on two days, respectively.
In this embodiment, the specific steps are as follows:
step 1: and (4) sampling the motor imagery electroencephalogram signals and establishing a sample set.
Step 2: preprocessing the data by using a filter bank common space mode to obtain a data sample primitive feature set
Figure BDA0003342852050000061
Wherein
Figure BDA0003342852050000062
Feature matrix X for each sampleiIs of size Nf×NgTotal sample ofN, corresponding matrix set of categories
Figure BDA0003342852050000063
nsThe number of samples in the s-th class, i.e., 1, 2. Simultaneous partitioning
Figure BDA0003342852050000064
Training sample raw feature sets and testing sample raw feature sets.
Firstly, a Chebyshev II type filter bank covering 4-40Hz is adopted to divide all electroencephalogram signals into a plurality of sub-frequency bands, each 4Hz frequency band is divided into 9 sub-frequency bands, and the 9 sub-frequency bands are respectively 4-8 Hz, 8-12 Hz, 12-16 Hz, 16-20 Hz, 20-24 Hz, 24-28 Hz, 28-32 Hz, 32-36 Hz and 36-40 Hz.
And then, performing feature extraction in a first stage on the 9 frequency band data obtained after processing by adopting a one-to-many common space pattern algorithm (OVR-CSP) to obtain a group of frequency-space feature data sets. OVR-CSP is a common method of extending CSP into multi-class classes, which takes one of the classes of patterns as one class and all of the remaining patterns as another class, thus forming a new two classes, thus computing the corresponding CSP for each class of patterns in turn. Combining the obtained z groups of characteristics, wherein z is the total number of classes, and finally obtaining a group with the size of Nf×NgIs given by a feature matrix X, where N isfFor the number of divided frequency bands, NgAnd p is a parameter of the selected number of eigenvectors when the projection matrix is calculated in the CSP algorithm. And p is an integer, the value range is set to be 1-4, and the maximum iteration number T and the dimension d are set.
And step 3: and further extracting data features by using the proposed feature extraction method, and reducing dimensions. The proposed LR2DDLPP feature extraction method has the following standard functions:
Figure BDA0003342852050000065
where a is the projection matrix and the projected features are Y ═ XA.
In the step 3, a plurality of variables are involved, the optimal solution of the variables cannot be obtained simultaneously, and the method is designed to solve through an alternating iterative algorithm. The variable A is fixed to update Z and E, and Z is fixed to update A. Where A is the required projection matrix and Z, E is the low rank projection matrix and error matrix of the low rank representation.
First, a is fixed to find Z and E. Initializing A, and solving Z and E by utilizing an augmented Lagrange algorithm according to an LRR algorithm. The objective function at this time is as follows:
Figure BDA0003342852050000066
it can be found to be a modified LRR problem, so the function is solved with the LRR algorithm, treating XA as a data matrix for low rank decomposition. The optimization problem can be solved by using an ALM algorithm.
The above formula is converted to the following formula:
Figure BDA0003342852050000071
the above problem can be solved with the ALM method, with the goal of minimizing the following augmented lagrangian function:
Figure BDA0003342852050000072
in the above formula, μ > 0 is a penalty factor, | |FIs the Frobenious norm, Y of the matrix1，Y2Is the lagrange multiplier. The variables Z, J, E can be minimized one by fixing the other variables and then updating the lagrange multipliers.
J is optimized by the following formula:
Figure BDA0003342852050000073
the above equation can be solved by a singular value threshold operator.
Optimum Z*Can be updated by:
Z*＝(I+ATXTXA)-1[ATXT(XA-E)+J+(ATXTY1-Y2)/μ]
optimum E*Can be updated by:
Figure BDA0003342852050000074
the above equation can be solved by a matrix-completed singular value threshold algorithm.
Update multipliers and parameters as follows:
Y1＝Y1+μ(XA-XAZ--)
Y2＝Y2+μ(Z-J)
μ＝min(ρμ，μmax)
where ρ is a parameter and ρ > 0.
Then, Z is fixed to determine ρ. When Z and E are fixed, let XmRespectively constructing an inter-class weight matrix B and z intra-class weight matrices W, wherein element expressions of the inter-class weight matrix B and the z intra-class weight matrices W are respectively as follows:
Figure BDA0003342852050000081
wherein M isiIs a sample mean matrix of the i-th class samples,
Figure BDA0003342852050000082
niis the number of samples of the ith type of sample. t is a parameter and the weight can be modified by adjusting t.
Then, the intra-class divergence matrix P is calculated according to the following formulawAnd an inter-class divergence matrix Pb:
Figure BDA0003342852050000083
Figure BDA0003342852050000084
Based on the constraint term XA XAZ + E, the objective function may be transformed into:
Figure BDA0003342852050000085
this can be further simplified to the following formula:
Figure BDA0003342852050000086
and converting the generalized eigenvalue solution problem into a generalized eigenvalue solution problem, and sorting the solved eigenvalue matrix according to the magnitude of the eigenvalue to obtain a projection matrix A.
In the above-mentioned parameters, the value of α is set to 1, and the value of λ is set to 0.01.
Then, matrices A, Z and E are updated simultaneously until a specified maximum number of iterations T is reached.
And then, calculating to obtain a projected feature matrix Y according to Y-XA, drawing into a vector, and selecting the first d data as d-dimensional feature data after dimension reduction.
And 4, step 4: and classifying the extracted features by using a support vector machine.
In this embodiment, the experiment only uses the electroencephalogram data of the left-hand and right-hand motor imagery in the training phase, which includes complete labeling information. The experimental procedure was set up as follows:
preprocessing the data set according to the step S2 to obtain an original sample feature data set, and then respectively carrying out the following three feature extraction methods as comparison experiments, wherein the three methods are respectively as follows: and finally, classifying d-dimensional feature data serving as the input of the SVM classifier by not performing feature extraction processing, performing 2DDLPP method feature extraction and the feature extraction of the method. The parameters d and p are both optimized. The results of the experiment are shown in table 1:
table 1 comparative experiment classification accuracy statistical table.
Figure BDA0003342852050000091
According to the comparison experiment result, the method shows the best classification precision in all comparison algorithms, the method provides a better method for extracting the characteristics of the motor imagery electroencephalogram signals, the global structure information is kept, meanwhile, the local neighborhood relation is kept, the robustness is better, and the acquisition of the distinguishing characteristics is greatly improved.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (9)

1. A motor imagery electroencephalogram signal feature extraction method combining low-rank representation and manifold learning is characterized by comprising the following steps:
s1, sampling the motor imagery electroencephalogram signals and establishing a sample set;
s2, preprocessing the data by using a filter bank common space mode to obtain a data sample original feature set, dividing the data sample original feature set into a training sample original feature set and a test sample original feature set, and setting maximum iteration times T and dimensionality d;
s3, further extracting data characteristics by using the proposed characteristic extraction method and reducing dimensions;
and S4, classifying the extracted features by using a support vector machine.
2. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning according to claim 1, wherein the preprocessing method comprises: all the electroencephalogram signals are divided into a plurality of sub-frequency bands, and the intervals of the sub-frequency bands are equal.
3. The method for extracting characteristics of motor imagery electroencephalogram signals combining low-rank representation and manifold learning according to claim 2, wherein a set of frequency-space characteristic data sets is obtained by performing characteristic extraction on a plurality of sub-band data.
4. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning according to claim 1 or 3, wherein an alternating iterative algorithm is designed to solve the data features after dimensionality reduction: fixing variable A to update Z and E, fixing Z to update A; wherein A is a projection matrix, Z is a low-rank projection matrix of the low-rank representation part, and E is an error matrix of the low-rank representation part.
5. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning according to claim 4, wherein the method for updating Z and E is as follows: initializing A, and solving Z and E by utilizing an augmented Lagrange algorithm according to an LRR algorithm.
Figure FDA0003342852040000011
Solving the function with an LRR algorithm, treating XA as a data matrix for low rank decomposition;
optimization with ALM algorithm:
Figure FDA0003342852040000012
the following augmented lagrange function is minimized:
Figure FDA0003342852040000021
where μ > 0 is a penalty factor, | · |FIs the Frobenious norm, Y of the matrix1，Y2Is the Lagrangian multiplier; updating Lagrange multipliers by respectively fixing other variables, and minimizing the variables Z, J and E one by one;
solving and optimizing J by using a singular value threshold operator:
Figure FDA0003342852040000022
optimum Z*：
Z*＝(I+ATXTXA)-1[ATXT(XA-E)+J+(ATXTY1-Y2)/μ]
Solving for optimal E by matrix-complemented singular value threshold algorithm*：
Figure FDA0003342852040000023
Update multipliers and parameters as follows:
Y1＝Y1+μ(XA-XAZ-E)
Y2＝Y2+μ(Z-J)
μ＝min(ρμ，μmax)
where ρ is a parameter and ρ > 0.
6. The method for extracting characteristics of motor imagery electroencephalogram signals combining low rank representation and manifold learning according to claim 5, wherein the method for solving A is as follows: let XmRespectively constructing an inter-class weight matrix B and z intra-class weight matrices W, wherein element expressions of the inter-class weight matrix B and the z intra-class weight matrices W are respectively as follows:
Figure FDA0003342852040000024
wherein M isiIs a sample mean matrix of the i-th class samples,
Figure FDA0003342852040000031
nithe number of samples of the ith type; t is a parameter, 1The weight can be modified by adjusting t; calculating the intra-class divergence matrices P according to the following formulawAnd an inter-class divergence matrix Pb:
Figure FDA0003342852040000032
Figure FDA0003342852040000033
Based on the constraint term XA XAZ + E, the objective function may be transformed into:
Figure FDA0003342852040000034
simplified to the following formula:
Figure FDA0003342852040000035
sorting the obtained feature matrix according to the magnitude of the feature value to obtain a projection matrix A; in the above-mentioned parameters, the value of α is set to 1, and the value of λ is set to 0.01.
7. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning of claim 6, wherein the matrices A, Z and E are updated simultaneously until a specified maximum number of iterations T is reached.
8. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning according to claim 7, wherein the method for extracting d-dimensional feature data comprises: and calculating to obtain a projected feature matrix Y according to Y-XA, drawing into a vector, and selecting the front d data as d-dimensional feature data after dimension reduction.
9. The method for extracting features of motor imagery electroencephalogram signals combining low rank representation and manifold learning of claim 8, wherein an SVM classifier is used for classifying the d-dimensional feature data.
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CN115019368A (en) * 2022-06-09 2022-09-06 南京审计大学 Face recognition feature extraction method in audit investigation based on 2DESDLPP
CN115019368B (en) * 2022-06-09 2023-09-12 南京审计大学 Face recognition feature extraction method in audit investigation

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