CN112036354A - Natural action electroencephalogram recognition method based on Riemann geometry - Google Patents

Natural action electroencephalogram recognition method based on Riemann geometry Download PDF

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CN112036354A
CN112036354A CN202010938581.9A CN202010938581A CN112036354A CN 112036354 A CN112036354 A CN 112036354A CN 202010938581 A CN202010938581 A CN 202010938581A CN 112036354 A CN112036354 A CN 112036354A
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electroencephalogram
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徐宝国
王勇
张坤
刘德平
宋爱国
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Abstract

The invention discloses a natural motion electroencephalogram recognition method based on Riemann geometry, which is used for classifying and recognizing electroencephalogram signals of natural motion, analyzing, observing and removing channels with large interference after acquiring multi-channel electroencephalogram signals, then performing zero-phase band-pass filtering, intercepting an electroencephalogram signal time domain according to natural motion force information, further calculating a covariance matrix of the multi-channel electroencephalogram signals, projecting the covariance matrix onto a Riemann cut space with a Riemann mean value as a cut point, and finally finishing electroencephalogram signal classification of natural hand motion by using a contraction linear discriminant analysis algorithm in the Riemann geometric cut space.

Description

Natural action electroencephalogram recognition method based on Riemann geometry
Technical Field
The invention belongs to the technical field of electroencephalogram signal processing and application, and particularly relates to a natural motion electroencephalogram identification method based on Riemann geometry, which is used for classifying and identifying electroencephalogram signals when a user performs natural motion.
Background
The brain-computer interface technology starts from recording brain signal activity, detects natural behavior actions of a user through signal processing, sends appropriate control signals to external equipment according to the intention of the user, and controls peripheral equipment to complete corresponding operations. When the brain electrical signal of the motor-related cortex has a slow, tiny and negative drift before the self-natural action is executed, which is called as the motor-related potential (MRCP), the research shows that the brain electrical signal carries the motion information and can be used non-invasively. At present, signal processing research on motion-related potentials is relatively few, natural action electroencephalogram identification becomes a research trend, and a Riemann geometry-based method shows a good prospect compared with a traditional classification algorithm. Therefore, the method for researching natural action electroencephalogram recognition based on Riemann geometry can provide an efficient signal processing means, and has important application value and practical urgency.
Disclosure of Invention
In order to solve the problems, the invention discloses a natural action electroencephalogram identification method based on Riemann geometry, provides an efficient signal processing means, has novel and efficient algorithm and high reliability, and has important application value and actual urgency.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a natural motion electroencephalogram identification method based on Riemann geometry comprises the following steps:
(1) multichannel electroencephalogram signal acquisition
Collecting multi-channel electroencephalogram signals X (t), and setting the electroencephalogram signals of N channels as
X(t)＝[x(t)，...，x(t+L-1)]∈RN×L]
Wherein, L is the time domain length of the electroencephalogram signal after sampling, and the sampling signal at the time t is x (t) ═ x1(t)，...，xN(t)]T∈RN
(2) And (4) rejecting the channel with large interference through analysis.
In the actual electroencephalogram collection process, due to the problems of impedance problems, poor contact and the like of an electroencephalogram cap electrode, great interference can be brought to certain channels, abnormal amplitude and abnormal peak values appear in an electroencephalogram signal waveform, and the abnormal amplitude and the abnormal peak values need to be removed after observation and analysis.
(3) The remaining multi-channel signal is zero-phase filtered.
In the process of acquiring the electroencephalogram signals, power frequency interference is introduced, a 50Hz zero-phase trap filter is adopted for filtering, and in addition, because the MRCP low-frequency component (less than 2Hz) generated by natural action carries motion information, a zero-phase band-pass filter with a pass band range of 0.3 Hz-3 Hz is used for filtering noise.
(4) Electroencephalogram signal time domain interception
In the process of acquiring the electroencephalogram signals, in order to extract the time period containing the most abundant motion information, the moment when the motion starts is determined according to the force information when the natural motion is executed, and the time periods of several seconds before and after the execution is intercepted and used for calculating the subsequent covariance matrix.
(5) Computing covariance matrices for multichannel signals
In the brain-computer interface, the second-order statistical information of the electroencephalogram signal X (t) comprises separable information of brain states, and the covariance characteristic is the most common second-order statistical characteristic of the electroencephalogram signal. Therefore, the covariance characteristic of the electroencephalogram signal X (t) can be obtained as follows:
Figure BDA0002672811760000021
(6) and projecting the covariance features to a Riemann geometric tangent space, wherein tangent points are Riemann mean values.
The acquired electroencephalogram signals contain m tests, the covariance characteristics can be regarded as points Pi (i is more than or equal to 1 and less than or equal to m) on the Riemann manifold, the points Pi and the i are projected to a tangent plane taking the Riemann mean value point P as a tangent point, and the point projected to the tangent plane is recorded as a point SiThen, there are:
Si＝logP(Pi)＝P1/2log(P-1/2PiP-1/2)P1/2
in the positive definite matrix space, the riemann distance between any two points P1 and P2 is:
Figure BDA0002672811760000022
wherein σ i is P1-1The ith characteristic value of P2, then the Riemann central point of the sample can be obtained according to the Riemann geodesic distance:
Figure BDA0002672811760000023
(7) classification was performed in the cut space using shrinkage linear discriminant analysis (sLDA).
After projection, the electroencephalogram signal sample characteristics are classified by using contraction linear discriminant analysis on a Riemann geometric tangent space.
The invention has the beneficial effects that:
1. the algorithm is novel and efficient. For the motion-related potential generated by natural motion, the traditional processing algorithm mainly aims at the recognition of the amplitude of the electroencephalogram signal in the traditional classifier, but the invention extracts the effective time period of electroencephalogram analysis through natural operating force information and carries out electroencephalogram recognition in the contraction linear discrimination classifier based on the Riemann geometry method with better performance at present, thus being a novel and efficient method.
2. The reliability is high. Considering that for high dimensional data with only a small number of data points, the standard estimation of the covariance matrix may be inaccurate, degrading the classification performance, the use of shrinkage improves this possible resulting estimation error. The reliability of the method provided by the invention is greatly improved
3. Has good research prospect. In a brain-computer interface, natural action electroencephalogram recognition is taken as a hotspot research field, the natural action exploration becomes a development trend, and the method provided by the invention belongs to the most key signal processing part, so that the method has a good research prospect.
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FIG. 1 is a flow chart of a natural motion electroencephalogram identification method based on Riemann geometry.
Fig. 2 is a schematic view of the riemann manifold and tangential plane of the present invention.
List of reference numbers in fig. 2: a projected tangent point 1, a tangent plane 2 made by the projected tangent point 1, and a Riemannian manifold 3.
FIG. 3 is a flow chart of the Riemann mean point solution of the present invention.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
As shown in the figure, the natural action electroencephalogram recognition method based on Riemann geometry comprises the following steps:
(1) multi-channel electroencephalogram signal acquisition
Collecting multi-channel electroencephalogram signals X (t), and setting the electroencephalogram signals of N channels as follows:
X(t)＝[x(t)，...，x(t+L-1)]∈RN×L]
wherein, L is the time domain length of the electroencephalogram signal after sampling, and the sampling signal at the time t is x (t) ═ x1(t)，...，xN(t)]T∈RN
(2) And (4) rejecting the channel with large interference through analysis.
In the actual electroencephalogram collection process, due to the problems of impedance problems, poor contact and the like of an electroencephalogram cap electrode, great interference can be brought to certain channels, abnormal amplitude and abnormal peak values appear in an electroencephalogram signal waveform, and the abnormal amplitude and the abnormal peak values need to be removed after observation and analysis.
(3) The remaining multi-channel signal is zero-phase filtered.
In the process of acquiring the electroencephalogram signals, power frequency interference is introduced, in addition, because the MRCP generated by natural action carries motion information in low-frequency components (less than 2Hz), a 50Hz trap filter is firstly used for removing power frequency noise, and then a third-order Butterworth band-pass filter (0.3 Hz-3 Hz) is used for filtering redundant frequency band signals.
(4) Electroencephalogram signal time domain interception
In the process of acquiring the electroencephalogram signals, in order to extract the time period containing the most abundant motion information, the moment of starting the motion is determined according to the force information when the natural motion is executed, and the time period between the first two seconds of starting execution and the second two seconds of starting execution is intercepted and used for calculating the subsequent covariance matrix.
(5) Computing covariance matrices for multichannel signals
In the brain-computer interface, the second-order statistical information of the electroencephalogram signal X (t) comprises separable information of brain states, and the covariance characteristic is the most common second-order statistical characteristic of the electroencephalogram signal. Therefore, the covariance characteristic of the electroencephalogram signal X (t) can be obtained as follows:
Figure BDA0002672811760000031
(6) and projecting the covariance features to a Riemann geometric tangent space, wherein tangent points are Riemann mean values.
The acquired electroencephalogram signals comprise m tests, after the above steps are processed, the covariance characteristic of the multichannel electroencephalogram signals generated by each test is Pi (i is more than or equal to 1 and less than or equal to m), the covariance characteristics are projected to a tangent plane with a Riemann mean value point P as a tangent point, and the point projected to the tangent plane is recorded as SiThen, there are:
Si＝logP(Pi)＝P1/2log(P-1/2PiP-1/2)P1/2
as shown in fig. 2, 1 is a projected tangent point, 2 is a tangent plane made by the projected tangent point 1, and 3 is a riemann manifold.
The Riemann mean value point can be obtained according to the Riemann geodesic distance, and the calculation method is as follows:
the Riemannian distance of any two points P1 on the space of the definite matrix is recorded, and P2 is:
Figure BDA0002672811760000041
wherein σ i is P1-1The ith characteristic value of P2, the Riemann center point of the sample is
Figure BDA0002672811760000042
The above-mentioned riemann central point solution formula has no analytic solution, and the preferred scheme is to solve through iteration to obtain an approximate solution, and the iterative process is shown in fig. 3.
(7) Classification was performed in the cut space using shrinkage linear discriminant analysis (sLDA).
After projection, a systolic linear discriminant analysis was used on the riemann geometry cut space. Taking the binary case as an example, the above-mentioned projected covariance characteristic SiCorresponding to the data set
Figure BDA0002672811760000043
yiE.g. {0, 1}, let Ni、Xi、ui、∑iRespectively representing the number, the set, the mean vector and the covariance matrix of i ∈ {0, 1} class samples, and the steps are as follows:
(7.1) calculating a sample mean vector u1And u2
Figure BDA0002672811760000044
(7.2) calculating the within-class dispersion matrix Sw，
Defining a within class dispersion matrix as
Figure BDA0002672811760000045
(7.3) calculation matrix
Figure BDA0002672811760000046
To the projection matrix w
(7.4) for each sample feature in the sample set
Figure BDA00026728117600000411
Conversion into a new sample zi＝wTSi
(7.5) classifying the new samples according to a threshold, z being a more common alternative0＝(u0+u1)/2
Further, for high dimensional data with only a small number of data points, it is necessary to compensate S with a shrinkagewThe system deviation caused by medium covariance estimation is improved as follows:
unbiased estimates of mean and covariance matrices (empirical covariance matrices):
Figure BDA0002672811760000047
Figure BDA0002672811760000048
to balance the estimation error, will
Figure BDA0002672811760000049
Replacing the steps as follows:
Figure BDA00026728117600000410
wherein the shrinkage parameter gamma is ∈ [0, 1 ]]The selection can be performed by a cross-validation method, and the selectable shrinkage parameter is 0.05. I is the identity matrix and v is defined as the mean of the covariance matrix trace:
Figure BDA0002672811760000051
d is the dimension of the feature space.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.

Claims (5)

1. A natural motion electroencephalogram identification method based on Riemann geometry is characterized in that: the method comprises the following steps:
(1) multichannel electroencephalogram signal acquisition
Collecting multi-channel electroencephalogram signals X (t), and setting the electroencephalogram signals of N channels as
X(t)＝[x(t)，...，x(t+L-1)]∈RN×L]
Wherein, L is the time domain length of the electroencephalogram signal after sampling, and the sampling signal at the time t is x (t) ═ x1(t)，...，xN(t)]T∈RN；
(2) Rejection of channels with large interference by analysis
In the actual electroencephalogram acquisition process, due to the problems of impedance and poor contact of an electroencephalogram cap electrode, interference can be brought to a channel, abnormal amplitude and abnormal peak values appear in an electroencephalogram signal waveform, and the electroencephalogram signal waveform needs to be observed, analyzed and then eliminated;
(3) the remaining multi-channel signal is zero-phase filtered.
In the process of acquiring the electroencephalogram signals, power frequency interference is introduced, a 50Hz zero-phase trap filter is adopted for filtering, and in addition, because the MRCP low-frequency component generated by natural action carries motion information, a zero-phase band-pass filter with a pass band range of 0.3 Hz-3 Hz is used for filtering noise;
(4) electroencephalogram signal time domain interception
In the process of acquiring the electroencephalogram signals, in order to extract the time period containing the most abundant motion information, determining the moment when the motion starts according to the force information when the natural motion is executed, and intercepting several seconds before and after the execution starts for subsequent covariance matrix calculation;
(5) computing covariance matrices for multichannel signals
In the brain-computer interface, the second-order statistical information of the electroencephalogram signal X (t) comprises separable information of brain states, and the covariance characteristic is the most common second-order statistical characteristic of the electroencephalogram signal; therefore, the covariance characteristic of the brain electrical signal X (t) can be obtained as
Figure FDA0002672811750000011
(6) Projecting the covariance features to a Riemann geometric tangent space, wherein tangent points are Riemann mean values;
the acquired electroencephalogram signals contain m tests, and the covariance characteristics can be regarded asPoints Pi (1 ≦ i ≦ m) on the Riemannian manifold are projected on a tangent plane with the point P as a tangent point, and the point projected on the tangent plane is recorded as SiThen, there are:
Si＝logP(Pi)＝P1/2log(P-1/2PiP-1/2)P1/2
wherein the P point is a Riemann mean value point, any two points P1 on the positive definite matrix space, and the Riemann distance of P2 is as follows:
Figure FDA0002672811750000012
wherein σ i is P1-1The ith characteristic value of P2, then the Riemann central point of the sample can be obtained according to the Riemann geodesic distance:
Figure FDA0002672811750000021
(7) classification in tangent space with Linear discriminant analysis of shrinkage (sLDA)
After projection, the electroencephalogram signal sample characteristics are classified by using contraction linear discriminant analysis on a Riemann geometric tangent space.
2. The natural motion electroencephalogram recognition method based on the Riemann geometry as claimed in claim 1, wherein the Riemann cut points are Riemann mean points, no approximate solution exists in the Riemann mean points, and solution is performed through iteration.
3. The natural motion electroencephalogram identification method based on Riemann geometry according to claim 1, wherein the zero-phase filtering comprises a trap filter and a band-pass filter, and the frequency band which is not related to motion-related potential and is used for filtering power frequency interference is filtered.
4. The natural motion electroencephalogram identification method based on Riemann geometry according to claim 1, wherein the time domain interception of the electroencephalogram signal needs to use natural motion force information as a reference, and data in two seconds before and after the start of motion are selected, and the data comprise key classification information.
5. The natural motion electroencephalogram recognition method based on Riemann geometry according to claim 1, wherein the contraction parameters of the sLDA classifier are selected by using a cross-validation method to determine the contraction direction.
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