CN104463206B - A kind of discrimination method of single trial motor imagery EEG signal - Google Patents
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Abstract
The invention discloses a kind of discrimination method of single trial motor imagery EEG signal, the discrimination method comprises the following steps：The first step：Set up single trial motor imagery EEG sample of signal；Second step：The covariance matrix for the single trial motor imagery EEG sample of signal set up to the first step is pre-processed；3rd step：Improve the object function of matrix L ogistic regression algorithms；4th step：By accelerating neighbouring gradient descent method to solve the object function after the improvement of the 3rd step, grader is obtained；5th step：The grader obtained using the 4th step is carried out the imagination right hand to five test sets in the first step or imagines the classification of pin, so as to realize single trial motor imagery EEG signal recognition.The discrimination method can improve identification precision to the non-stationary robust of EEG signal.
Description
Technical Field
The invention belongs to the field of brain-computer interfaces and pattern recognition, and particularly relates to a method for identifying a single motor imagery electroencephalogram signal.
Background
With the progress of Computer technology and the continuous and deep research on Brain function, people are trying to establish a new communication and control path independent of muscle and nerve activities for transmitting information and commands between the Brain and the external environment, namely Brain-Computer Interface (BCI). On the one hand, the brain-computer interface can help people with damaged neuromuscular pathways for brain communication and control with the external environment to perform rehabilitation training, or control prostheses, wheelchairs and the like. On the other hand, the system can become a man-machine interface, and the productivity and efficiency of tasks are improved.
The BCI is shown in a structural schematic diagram in fig. 1, an electroencephalogram acquisition device acquires electroencephalogram signals from cerebral cortex, training a classifier by using training set data through data preprocessing, and finally classifying test set data by using the trained classifier.
The inherent non-stationarity and limited spatial resolution and noise of electroencephalogram (EEG) signals make the identification of single motor imagery electroencephalogram signals a challenging problem in the field of brain-computer interfaces. Changes in EEG signal characteristics over a period of time can lead to a degradation of classification performance. This is generally because conventional feature extraction and classification methods do not take into account changes in the EEG signal. Although some methods have proposed reducing the sensitivity to signal non-stationarities, their feature extraction and classification are optimized differently from the objective function, and therefore the extracted features may not be optimal for the classifier.
The currently widely used Common Spatial Patterns (CSP) based methods have two major drawbacks: (1) the feature extraction algorithm CSP and a Linear Discriminant Analysis (LDA) classifier are different target functions optimized, so that the effective improvement of the classification effect is difficult to ensure. CSP is a decomposition method rather than a classification method because the variance difference between two classes of samples does not sufficiently distinguish between samples at the decision boundary. (2) The inherent non-stationarity of EEG signals can lead to a reduction in recognition accuracy. When the subject is performing a motor task, the EEG signal is disturbed by many factors, such as changes in attention, electrode loosening leading to impedance changes, blinking and eye movements, swallowing and tooth grinding, etc. These factors can introduce task-independent activity into the EEG signal. Also, the CSP method may rely on a small number of samples that dominate the sample covariance matrix, resulting in overfitting.
In order to overcome the above two disadvantages, Tomioka proposes a Matrix Logistic Regression (MLR) method, which integrates feature extraction and classifier training into a unified regularized convex empirical risk minimization problem, and directly uses a signal covariance matrix to establish a Logistic Regression classifier. In addition, the low-rank regularization factor of a forced weight matrix is utilized, and the judgment information is compressed into few components while the complexity is controlled. In the method, the feature extraction and classifier training optimization are the same objective function, and a theoretical global optimal point can be obtained. However, the MLR method is not robust to the non-stationary phenomenon of the EEG signal, which is unavoidable in practical applications, and the identification accuracy of the MLR method is seriously reduced.
Disclosure of Invention
The technical problem is as follows: the technical problem to be solved by the invention is as follows: the method for identifying the EEG signal by the single motor imagery can be used for robustness of non-stationarity of the EEG signal and improving identification precision.
The technical scheme is as follows: in order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for identifying a single motor imagery electroencephalogram signal comprises the following steps:
the first step is as follows: establishing a single motor imagery electroencephalogram signal sample: the experimental data are derived from data set IVa in BCI Competition III, and the experimental data comprise five experimental objects which are respectively marked as aa, al, av, aw and ay; the method comprises the following steps that 118 silver/silver chloride reference electrodes are connected with the scalp of an experimental object, the electrodes receive and record electroencephalogram signals of the experimental object, the electroencephalogram signals are subjected to band-pass filtering at 0.05-200 Hz and down-sampling to 100Hz, a quintet Butterworth band-pass filter is used for carrying out filtering at 7-30 Hz, and a time interval of 0.5-2.5 s after indication appears on a screen is used as a single imagination movement electroencephalogram signal sample; imagining a motor electroencephalogram signal sample comprises a right hand type and a foot type, wherein a label corresponding to the right hand type is +1, and a label corresponding to the foot type is-1; the right hand class and the foot class respectively carry out 140 times of experiments, and each experimental object carries out 280 times of experiments; the 1 st experiment to 168 th experiment performed by the subject aa is used as the training set of aa, and the 169 th experiment to 280 th experiment is used as the testing set of aa; the 1 st to 224 th experiments performed by the subject al are used as the training set of the al, and the 225 th to 280 th experiments are used as the testing set of the al; the test 1-84 times of the subject av as the training set of av, and the test 85-280 times of the subject av as the testing set of av; the experiment 1-56 times carried out by the experimental subject aw is used as a training set of aw, and the experiment 57-280 times is used as a testing set of aw; the experiment 1-28 times of the experiment performed by the experimental subject ay is used as the training set of ay, and the experiment 29-280 times of the experiment is used as the testing set of ay;
the second step is that: preprocessing the covariance matrix of the single motor imagery electroencephalogram signal sample established in the first step;
the third step: improving a target function of a matrix Logistic regression algorithm;
the fourth step: solving the improved objective function in the third step by an accelerated adjacent gradient descent method to obtain a classifier;
the fifth step: and (4) classifying the five test sets in the first step by using the classifier obtained in the fourth step to imagine the right hand or the feet, so as to realize the single motor imagery electroencephalogram signal identification.
Further, the second step comprises the following processes:
step 201) whitening treatment, as shown in formula (1), using the mean covariance matrix ∑ of the training set of each subject determined in the first steppCovariance matrix for each sample ∑iAnd (3) whitening treatment:
wherein,a covariance matrix representing the whitened samples;mean covariance matrix ∑ representing the training set for each subjectpTo the power of-1/2;n represents the total number of training samples per subject; i represents the serial number of the sample;
step 202) performing matrix logarithm transformation on the covariance matrix: mapping the convex cone of the covariance matrix subjected to whitening processing in the step 201) to a vector space of a symmetric matrix to obtain a covariance matrix subjected to matrix logarithm transformation:
wherein,representing a covariance matrix of each sample after matrix logarithm transformation;representation pair matrixAnd (6) carrying out logarithm calculation.
Further, in the third step, the improved objective function is as shown in formula (2):
wherein W is a weight matrix, Sym (C) is a symmetric matrix of CxC, b is a bias term, R is a real number set, n is the total number of training samples of each experimental object, e represents the base number of natural logarithm, yiLabel representing the ith training sample, XiIs the ith training sample; theta denotes the parameter set to be determined and is composed of W and b, theta: ═ (W, b), lambda1Is a regularization constant, λ, associated with a non-stationarity penalty factor2Is a regularization constant related to the trace norm of the weight matrix, s (w) is a non-stationarity penalty term,c represents 1 or 2, wherein 1 represents a right hand class, 2 represents a foot class, and ncDenotes the total number of samples in class c, NcRepresenting the number of blocks belonging to class c in each training set, wherein samples in the training sets are cut into blocks, and each block comprises u samples; symbol | | | purple*Representing and solving a trace norm;representation matrixTrace of Tr (W)T∑c) A representation matrix WT∑cWherein the superscript T denotes transpose,representing the mean covariance matrix of the k-th block belonging to class c, ∑cRepresents the mean covariance matrix of all samples belonging to class c.
Further, the establishing process of the non-stationarity penalty term comprises the following steps: firstly, dividing a training set of each experimental object into a plurality of blocks, wherein each block comprises u continuous samples of the same type, then calculating the average decision function value of each block according to the non-smoothness of each sample in the training setAnd the average mean square error of the average decision function values of all samples of each class is measured, so that a non-stationarity penalty term is obtained.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) the discrimination capability of the classifier and the robustness to the EEG signal non-stationary phenomenon can be optimized simultaneously, and the identification precision is high. According to the identification method, the non-stationarity penalty factor is added into the objective function, so that the whole method can simultaneously optimize the discrimination capability of the classifier and the robustness of the EEG signal non-stationarity phenomenon, and the identification precision is high.
(2) The feature extraction and classifier training optimization are the same objective function, and a global optimal point can be obtained. The invention integrates feature extraction and classification training into a convex experience risk minimization problem, and can obtain a global optimal point.
(3) The convex optimization problem is solved by using an accelerated adjacent gradient descent method, the convergence speed is high, the calculation complexity is low, and the identification efficiency is high. In the invention, the calculation complexity for solving the problem by the accelerated adjacent gradient descent method is O (C)3) C is the number of electrodes, and the computational complexity of solving the problem by a general semi-definite programming method is O (C)6.5). Therefore, the method disclosed by the invention is low in calculation complexity and high in identification efficiency.
Drawings
Fig. 1 is a schematic structural diagram of a brain-computer interface.
Fig. 2 is a block flow diagram of the present invention.
Detailed Description
The technical solution of the present invention will be described in further detail below, but the scope of the present invention is not limited thereto.
As shown in fig. 1 and fig. 2, the method for identifying a single motor imagery electroencephalogram signal of the present invention includes the following steps:
the first step is as follows: establishing a single motor imagery electroencephalogram signal sample: the experimental data are derived from data set IVa in BCI Competition III, and the experimental data comprise five experimental objects which are respectively marked as aa, al, av, aw and ay; 118 silver/silver chloride (Ag/AgCl) reference electrodes are connected with the scalp of an experimental object, the electrodes receive and record electroencephalogram signals of the experimental object, the electroencephalogram signals are subjected to band-pass filtering at 0.05-200 Hz and are sampled to 100Hz, a quintet Butterworth band-pass filter is used for filtering at 7-30 Hz, and a time interval of 0.5-2.5 s after indication appears on a screen is used as a single imaginary moving electroencephalogram signal sample; imagining a motor electroencephalogram signal sample comprises a right hand type and a foot type, wherein a label corresponding to the right hand type is +1, and a label corresponding to the foot type is-1; the right hand class and the foot class respectively carry out 140 times of experiments, and each experimental object carries out 280 times of experiments; the 1 st experiment to 168 th experiment performed by the subject aa is used as the training set of aa, and the 169 th experiment to 280 th experiment is used as the testing set of aa; the 1 st to 224 th experiments performed by the subject al are used as the training set of the al, and the 225 th to 280 th experiments are used as the testing set of the al; the test 1-84 times of the subject av as the training set of av, and the test 85-280 times of the subject av as the testing set of av; the experiment 1-56 times carried out by the experimental subject aw is used as a training set of aw, and the experiment 57-280 times is used as a testing set of aw; the experiment 1-28 times of the experiment performed by the experimental subject ay is used as the training set of ay, and the experiment 29-280 times of the experiment is used as the testing set of ay.
The second step is that: and preprocessing the covariance matrix of the single motor imagery electroencephalogram signal sample established in the first step.
The second step comprises the following steps 201) and 202):
step 201) whitening treatment, as shown in formula (1), using the mean covariance matrix ∑ of the training set of each subject determined in the first steppCovariance matrix for each sample ∑iAnd (3) whitening treatment:
wherein,a covariance matrix representing the whitened samples;mean covariance matrix ∑ representing the training set for each subjectpTo the power of-1/2;n represents the total number of training samples per subject; i represents the serial number of the sample;
step 202) performing matrix logarithm transformation on the covariance matrix: mapping the convex cone of the covariance matrix subjected to whitening processing in the step 201) to a vector space of a symmetric matrix to obtain a covariance matrix subjected to matrix logarithm transformation:
wherein,representing a covariance matrix of each sample after matrix logarithm transformation;representation pair matrixAnd (6) carrying out logarithm calculation.
The third step: and improving an objective function of the matrix Logistic regression algorithm.
In the third step, the improved objective function is shown as formula (2):
wherein W is a weight matrix, Sym (C) is a symmetric matrix of CxC, b is a bias term, R is a real number set, n is the total number of training samples of each experimental object, e represents the base number of natural logarithm, yiLabel representing the ith training sample, XiIs the ith training sample; theta denotes the parameter set to be determined and is composed of W and b, theta: ═ (W, b), lambda1Is a regularization constant, λ, associated with a non-stationarity penalty factor2Is regularization related to the trace norm of the weight matrixConstant, S (W) is a non-stationarity penalty term,c represents 1 or 2, wherein 1 represents a right hand class, 2 represents a foot class, and ncDenotes the total number of samples in class c, NcRepresenting the number of blocks belonging to class c in each training set, wherein samples in the training sets are cut into blocks, and each block comprises u samples; symbol | | | purple*Representing and solving a trace norm;representation matrixTrace of Tr (W)T∑c) A representation matrix WT∑cWherein the superscript T denotes transpose,representing the mean covariance matrix of the k-th block belonging to class c, ∑cRepresents the mean covariance matrix of all samples belonging to class c.
The fourth step: and solving the improved objective function in the third step by an accelerated adjacent gradient descent method to obtain the classifier.
The fifth step: and (4) classifying the five test sets in the first step by using the classifier obtained in the fourth step to imagine the right hand or the feet, so as to realize the single motor imagery electroencephalogram signal identification.
A Matrix Logistic Regression algorithm (called as Matrix Logistic Regression in English, MLR for short) is different from a CSP-based identification method, and integrates feature extraction and classifier training into a unified regularized convex experience risk minimization problem to obtain a global optimal solution. Because a Logistic loss function is adopted, the MLR method can enable training samples to be far away from a decision boundary, but only different types of samples near the separation decision boundary are considered, so that the decision function values of the same type of samples cannot be guaranteed to be different, namely the generalization performance of the MLR method cannot be improved sufficiently. Since the subject inevitably produces disturbing activities such as blinking, swallowing, distraction, etc., the same kind of signals may also be greatly deviated as the experiment progresses, resulting in a reduction in the recognition accuracy. Moreover, when the MLR method solves the constructed objective function, the calculation amount is too large to be suitable for practical application.
In order to improve the robustness of the MLR method to EEG signal non-Stationary phenomena, the invention provides an improved Matrix Logistic Regression method (English is called as static Matrix Logistic Regression, which is abbreviated as sMLR). The purpose of sMLR is to obtain a classification model directly, not only to distinguish different classes of data, but also to be robust to the non-stationarity of the training data. The method mainly makes samples of different classes far away from decision boundary, and simultaneously minimizes the non-stationarity of each class of samples in a group in a decision function space. Different from the existing single motor imagery EEG identification method, the method provided by the invention can optimize the discrimination performance of the classifier and the robustness of the EEG signal non-stationarity in the same objective function. A non-stationarity penalty term is therefore introduced in the objective function of the MLR method that penalizes the non-stationarity of the EEG signal. The establishing process of the non-stationarity penalty term comprises the following steps: firstly, dividing a training set of each experimental object into a plurality of blocks, wherein each block comprises u continuous samples of the same type, then calculating the average decision function value of each block according to the non-smoothness of each sample in the training setAnd the average squared difference of the average decision function values of all samples of each class, thereby obtaining a non-stationarity penalty term, as shown in the following formula:
and adding the non-stationarity penalty term into the target function in the MLR to obtain a new target function shown in the formula (2).
The identification method of the invention firstly carries out the preprocessing of whitening and matrix logarithm transformation on the covariance matrix of the single motor imagery electroencephalogram signal sample; and then, in order to overcome the defect that the identification precision is reduced due to the non-stationarity of the EEG signal, improving an objective function of a matrix Logistic regression algorithm, solving the improved objective function by an accelerated adjacent gradient descent method, and finally obtaining a decision function to classify the data of the test set. The invention relates to an algorithm for optimizing the same objective function for feature extraction and classifier training, which can obtain a theoretical global optimum point, is robust to the non-stationarity of an EEG signal and has high identification precision. Meanwhile, in the whole method, the convergence speed is high, the calculation complexity is low, and the identification efficiency is high.
The MLR method only enables the two types of transformed training samples to be far away from the judgment hyperplane, but does not consider the change of the difference of decision function values of the same type of samples, so that the non-stationary phenomenon of the EEG signal is not robust. The sMLR method of the invention not only requires that the discriminant hyperplane can well distinguish the changed training samples, but also can make the difference of decision function values of the same type of samples small, thereby having robustness to the non-stationarity of the EEG signal and improving the generalization performance of the classifier.
The following table shows a comparison of recognition error rates of the improved matrix Logistic regression based algorithm (sMLR) of the present invention with other recognition methods. Wherein the result with the highest recognition accuracy is displayed in bold. It can be seen that the MLR and sMLR methods have better recognition accuracy than CSP-based methods. The recognition accuracy of the sMLR is respectively 9.9% higher and 2.0% higher than that of CSP and MLR methods.
TABLE 1 identification error Rate comparison Table
Claims (2)
1. A method for identifying a single motor imagery electroencephalogram signal is characterized by comprising the following steps:
the first step is as follows: establishing a single motor imagery electroencephalogram signal sample: the experimental data are derived from data set IVa in BCI Competition III, and the experimental data comprise five experimental objects which are respectively marked as aa, al, av, aw and ay; the method comprises the following steps that 118 silver/silver chloride reference electrodes are connected with the scalp of an experimental object, the electrodes receive and record electroencephalogram signals of the experimental object, band-pass filtering is carried out on the signals at 0.05-200 Hz and down-sampling is carried out to 100Hz, a five-order Butterworth band-pass filter carries out filtering at 7-30 Hz, and a time interval of 0.5-2.5 s after indication appears on a screen is used as a single imagination movement electroencephalogram signal sample; imagining a motor electroencephalogram signal sample comprises a right hand type and a foot type, wherein a label corresponding to the right hand type is +1, and a label corresponding to the foot type is-1; the right hand class and the foot class respectively carry out 140 times of experiments, and each experimental object carries out 280 times of experiments; the 1 st experiment to 168 th experiment performed by the subject aa is used as the training set of aa, and the 169 th experiment to 280 th experiment is used as the testing set of aa; the 1 st to 224 th experiments performed by the subject al are used as the training set of the al, and the 225 th to 280 th experiments are used as the testing set of the al; the test 1-84 times of the subject av as the training set of av, and the test 85-280 times of the subject av as the testing set of av; the experiment 1-56 times carried out by the experimental subject aw is used as a training set of aw, and the experiment 57-280 times is used as a testing set of aw; the experiment 1-28 times of the experiment performed by the experimental subject ay is used as the training set of ay, and the experiment 29-280 times of the experiment is used as the testing set of ay;
the second step is that: preprocessing the covariance matrix of the single motor imagery electroencephalogram signal sample established in the first step; the second step comprises the following processes:
step 201) whitening treatment, as shown in formula (1), using the mean covariance matrix ∑ of the training set of each subject determined in the first steppCovariance matrix for each sample ∑iAnd (3) whitening treatment:
wherein,a covariance matrix representing the whitened samples;mean covariance matrix ∑ representing the training set for each subjectpTo the power of-1/2;n represents the total number of training samples per subject; i represents the serial number of the sample;
step 202) performing matrix logarithm transformation on the covariance matrix: mapping the convex cone of the covariance matrix subjected to whitening processing in the step 201) to a vector space of a symmetric matrix to obtain a covariance matrix subjected to matrix logarithm transformation:
<mrow> <msub> <mover> <mi>&Sigma;</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>=</mo> <mi>log</mi> <mi> </mi> <mi>m</mi> <mrow> <mo>(</mo> <msub> <mover> <mo>&Sigma;</mo> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
wherein,representing a covariance matrix of each sample after matrix logarithm transformation;representation pair matrixCalculating a logarithm;
the third step: improving a target function of a matrix Logistic regression algorithm; in the third step, the improved objective function is shown as formula (2):
wherein W is a weight matrix, Sym (C) is a symmetric matrix of CxC, b is a bias term, R is a real number set, n is the total number of training samples of each experimental object, and e represents the base of natural logarithmNumber, yiLabel representing the ith training sample, XiIs the ith training sample; theta denotes the parameter set to be determined and is composed of W and b, theta: ═ (W, b), lambda1Is a regularization constant, λ, associated with a non-stationarity penalty factor2Is a regularization constant related to the trace norm of the weight matrix, s (w) is a non-stationarity penalty term,c represents 1 or 2, wherein 1 represents a right hand class, 2 represents a foot class, and ncDenotes the total number of samples in class c, NcRepresenting the number of blocks in each training set belonging to class c, the symbol | | | | | non-woven cells*Representing and solving a trace norm;representation matrixTrace of Tr (W)T∑c) A representation matrix WT∑cWherein the superscript T denotes transpose,representing the mean covariance matrix of the k-th block belonging to class c, ∑cRepresents the mean covariance matrix of all samples belonging to class c;
the fourth step: solving the improved objective function in the third step by an accelerated adjacent gradient descent method to obtain a classifier;
the fifth step: and (4) classifying the five test sets in the first step by using the classifier obtained in the fourth step to imagine the right hand or the feet, so as to realize the single motor imagery electroencephalogram signal identification.
2. The method for identifying the single motor imagery electroencephalogram signal according to claim 1, wherein the non-stationarity penalty term is established by the following steps: the training set for each subject was first divided into a number of blocks, each containing upsilonA continuous sample of the same type is obtained, then the instability of each sample of the same type in the training set is trained, and the average decision function value of each block is calculatedAnd the average mean square error of the average decision function values of all samples of each class is measured, so that a non-stationarity penalty term is obtained.
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