CN114818824A - Motor imagery transfer learning method based on Pluker analysis - Google Patents

Motor imagery transfer learning method based on Pluker analysis Download PDF

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CN114818824A
CN114818824A CN202210532859.1A CN202210532859A CN114818824A CN 114818824 A CN114818824 A CN 114818824A CN 202210532859 A CN202210532859 A CN 202210532859A CN 114818824 A CN114818824 A CN 114818824A
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王志恒
毛传波
都明宇
蔡世波
杨庆华
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Abstract

A motor imagery transfer learning method based on Pluker analysis comprises the following steps: 1) carrying out co-average reference and band-pass filtering pretreatment on the original electroencephalogram signals, and improving the signal-to-noise ratio; 2) respectively carrying out alignment transformation on the electroencephalogram data of the source domain and the target domain to enable the data distribution to be preliminarily aligned; 3) carrying out rotation transformation on the electroencephalogram data of the source domain to the target domain direction so as to further match the data statistical distribution; 4) and (4) obtaining a classification model by taking the electroencephalogram data of the source domain as a training set, and classifying the electroencephalogram data of the unknown label of the target domain. The method can effectively utilize the existing data of the source domain, and can obviously improve the classification accuracy of the target domain under the condition that only a small amount of known label data exists compared with the traditional machine learning method.

Description

Motor imagery transfer learning method based on Pluker analysis
Technical Field
The invention relates to the field of motor imagery transfer learning, in particular to a motor imagery cross-domain transfer learning method based on a Pluque analysis.
Background
At present, the brain-computer interface technology based on motor imagery mainly relies on machine learning technology, and the traditional machine learning model is generally based on two assumptions: (1) the test data and the training data are independently and identically distributed; (2) there is a sufficient amount of labeled data. However, because the electroencephalogram signals are weak and change greatly, the environment, the electrode position and other factors of each experiment cannot be completely consistent, so that the experimental data of the same subject in different periods have huge difference, which violates the assumption (1), and therefore, the data acquired by the subject in the past cannot be directly used under the traditional machine learning framework. In order to collect a sufficient amount of available labeling data, a calibration experiment needs to be performed for about 30 minutes before each experiment, even for experienced subjects, and the process is time-consuming and tedious and is not a little hindrance to scientific research experiments and application popularization.
To reduce the time-consuming calibration experiments, the transfer learning technique is introduced into the field of motor imagery, mainly including both cross-phase and cross-subject modalities. The basic idea is that although the statistical distribution of data varies from time period to time period/subject, with similar patterns, useful information can still be extracted from them. The difference between the two is that the classification model is derived from historical data of the same subject across time periods, and from data of different subjects across subjects. In the migration learning, a region in which past data of a target subject and data of other subjects are distributed is referred to as a source domain, and a region in which current data of the target subject is distributed is referred to as a target domain. The idea of transfer learning is to reduce the distribution difference of the target domain and the source domain data as much as possible, so that cross-domain classification identification becomes possible, the demand for calibration data is reduced, and the time consumption of calibration experiments is reduced or even cancelled.
The probuk analysis is a statistical method for analyzing the shape distribution, and is commonly used for face alignment. The working principle is that some mark points are respectively selected from two different shape distributions, and then the two mark point sets are close to each other as much as possible through translation, scaling and rotation transformation, so that the effect of aligning the two shape distributions is achieved. By referring to the idea of Pluker analysis, certain transformation processing can be carried out on the motor imagery electroencephalogram data, so that the data statistical distribution of a source domain and a target domain is close to the maximum, and cross-domain transfer learning is further implemented. At present, the Pluque analysis has less application in the field of motor imagery, and in the Riemann Pluque analysis algorithm proposed by Rodrigues et al, the processing and classification of electroencephalogram data can only be carried out in a Riemann space, but cannot be used in combination with an algorithm with excellent performance in an Euclidean space, so that the application limitation is large.
Disclosure of Invention
In order to overcome the defects of the prior art and to apply the idea of the Pluker analysis to the processing of brain electrical data in Euclidean space and expand the application range of the brain electrical data, the invention provides a motor imagery migration learning method based on the Pluker analysis.
In order to solve the technical problems, the invention provides the following technical scheme:
a motor imagery transfer learning method based on Pluke analysis comprises the following steps:
step 1): pretreatment of
Firstly, carrying out common average reference processing on an original electroencephalogram signal, and then carrying out band-pass filtering at 8-30 Hz to eliminate ocular electrical artifacts, myoelectrical artifacts and baseline drift so as to improve the signal-to-noise ratio of electroencephalogram data;
step 2): respectively carrying out alignment transformation on electroencephalogram data of a source domain and a target domain
Let x i Representing the ith preprocessed electroencephalogram data, which is an n multiplied by l matrix, wherein n represents the number of lead connections of the electroencephalogram, l represents the number of sampling points of the signal, and a covariance matrix is extracted from the ith electroencephalogram data:
Figure BDA0003638120790000021
then the Riemann mean of all sample covariance matrices is:
Figure BDA0003638120790000022
in the formula, δ (·) represents riemann distance calculation, which is defined as:
Figure BDA0003638120790000023
wherein the subscript F represents the Frobenius norm, λ r (r ═ 1,2, …, n) is
Figure BDA0003638120790000024
The real eigenvalue of (d);
the meaning of equation (2) is to find a reference matrix whose average Riemann distance to all Covariance matrix samples is the minimum, and the obtained reference matrix is the average Covariance matrix, and can be calculated and solved by using the Cooperate Toolbox of Matlab.
Finally, performing alignment transformation on each sample:
Figure BDA0003638120790000031
after the above alignment transformation, the mean covariance matrix of all samples is:
Figure BDA0003638120790000032
that is, the mean covariance matrix of all samples is an identity matrix, that is, the covariance matrix samples of each subject are distributed around the identity matrix, so that the source domain and the target domain are naturally aligned;
step 3): carrying out rotation transformation on the electroencephalogram data of the source domain to the target domain;
step 4): and (3) obtaining a classification model by taking the electroencephalogram data of the source domain as a training set, classifying the electroencephalogram data of the unknown label of the target domain, and realizing cross-domain transfer learning.
Further, in the step 3), the features of the aligned and transformed electroencephalogram data are extracted, and then the rotation transformation is performed, wherein the process is as follows:
firstly, extracting the logarithm of variance of the electroencephalogram signal of the jth channel of the ith sample after alignment transformation as a characteristic:
Figure BDA0003638120790000033
then the set of sample data for each subject is represented as:
Figure BDA0003638120790000034
wherein k represents the number of samples of the subject;
and then respectively solving the average characteristic vectors of each sample category of the source domain subject and the target domain subject:
Figure BDA0003638120790000041
c represents the number of sample categories, and it should be noted that, since the step requires the label data of the sample, only a small amount of sample data of the known label is targeted for the target domain;
the goal of the rotation transformation is to find an orthogonal matrix Q such that
Figure BDA0003638120790000042
And M are as close as possible, i.e.:
Figure BDA0003638120790000043
satisfies the following conditions:
QQ T ＝I (10)
this is an orthogonal probuck problem, with analytical solutions, and according to the singular value decomposition theorem:
Figure BDA0003638120790000044
the solution to the rotation matrix is then:
Q＝VU T (12)
and finally, performing rotation transformation on the sample data of the source domain:
f i (PA) ＝f i Q (13)。
or, in the step 3), rotation transformation is directly performed on the aligned and transformed electroencephalogram data, and the process is as follows:
firstly, solving a covariance matrix of each sample after alignment transformation:
Figure BDA0003638120790000045
and respectively solving the average covariance matrix of each sample category of the source domain subject and the target domain subject according to a formula (2):
Figure BDA0003638120790000046
note that the computation of the target domain is only for a small amount of sample data for known tags;
the goal of the rotation transformation is to find an orthogonal matrix Q such that
Figure BDA0003638120790000047
And M is as close as possible:
Figure BDA0003638120790000048
satisfies the following conditions:
QQ T ＝I (17)
the formulas (16) to (17) have no analytical solution, and are solved through a Matlab Manopt tool box;
after the rotation matrix is obtained, the rotation transformation is carried out on the sample data of the source domain according to the following formula:
Figure BDA0003638120790000051
compared with the prior art, the invention has the following technical effects: the idea of the Pluque analysis is introduced into the field of motor imagery transfer learning, the electroencephalogram data in the Euclidean space are subjected to alignment transformation and rotation transformation, the sample data statistical distribution of a source domain and a target domain is matched, and cross-domain transfer learning is achieved through combination with a machine learning algorithm with excellent effect in the Euclidean space. Compared with the traditional machine learning method, the method can effectively utilize the existing data of the source domain, and remarkably improve the classification accuracy under the condition that the target domain only has a small amount of known label data. Compared with the Riemann Pluque analysis algorithm, the method is suitable for the European space, can be combined with various classical algorithms for use, and has a wider application range.
Drawings
Fig. 1 is a schematic diagram of the principle of a transfer learning algorithm based on the bruker analysis.
Fig. 2 is a flow chart of a transfer learning algorithm that combines independent component analysis and bruker analysis.
FIG. 3 is a flow chart of a transfer learning algorithm combining co-spatial mode and Prockian analysis.
Detailed Description
The invention will be further explained with reference to the drawings.
Referring to fig. 1 to 3, a prince analysis-based motor imagery transfer learning method is shown in fig. 1, and a transfer learning algorithm principle based on the prince analysis is that a source domain and a target domain are respectively aligned and transformed, so that all sample data are uniformly distributed near the same center, and then the sample data of the source domain is rotated and transformed towards the target domain, so that the data centers of all categories of the source domain and the target domain are as close as possible. Therefore, the classification model obtained by training the source domain sample data can also have a good classification effect on the sample data of the target domain, namely, effective cross-domain transfer learning is realized.
In the implementation of the rotation transformation, two cases can be divided: firstly, extracting features from the aligned and transformed electroencephalogram data, and then performing rotation transformation; and secondly, directly performing rotation transformation on the aligned and transformed electroencephalogram data. The former is suitable for use with Independent Component Analysis (ICA) algorithms and the latter is suitable for use with common space mode (CSP) algorithms, two specific embodiments of which are described below in conjunction with fig. 2 and 3.
Example 1:
a motor imagery transfer learning method based on the Pluker analysis is disclosed, and a specific algorithm flow is shown in figure 2.
The first step is as follows: and (4) preprocessing. And performing common average reference processing on the original electroencephalogram signals, and performing 8-30 Hz band-pass filtering to eliminate ocular electrical artifacts, myoelectrical artifacts and baseline drift. Recording the preprocessed ith electroencephalogram data as x i It is a matrix of n x l, n represents the number of lead connections of the brain electricity, and l represents the number of sampling points of the signal.
The second step is that: and (4) filtering the ICA. Supposing that the number of electroencephalogram samples of a subject is k, splicing the k samples into an n x kl two-dimensional matrix end to end, and solving an ICA filter matrix W by adopting an sInfmax algorithm proposed by Wu Xiaopei et al. The algorithm has the advantages of low calculation cost and no change of the sequence of the source signals. And performing spatial filtering processing on each electroencephalogram data by using the filtering matrix:
Figure BDA0003638120790000061
the third step: and (5) carrying out alignment transformation. After the spatial filtering processing, the signal-to-noise ratio of the electroencephalogram data is further improved. Then, it needs to be subjected to an alignment transformation process. Firstly, solving a covariance matrix of each electroencephalogram data:
Figure BDA0003638120790000062
and further solving Riemann mean values of all covariance matrixes:
Figure BDA0003638120790000063
the computational solution can be performed using the Covariance Toolbox of Matlab. Finally, performing alignment transformation on each sample:
Figure BDA0003638120790000064
the fourth step: and (5) feature extraction. Extracting the logarithm of variance of the electroencephalogram signal of the jth channel of the ith sample as a feature:
Figure BDA0003638120790000065
then the set of sample data for each subject may be expressed as:
Figure BDA0003638120790000066
the fifth step: and performing rotation transformation on the source domain. Firstly, respectively solving the average feature vectors of each sample category of the source domain subject and the target domain subject:
Figure BDA0003638120790000071
where c represents the number of sample classes. It should be noted that since this step requires the label data of the sample, only a small amount of sample data for known labels is targeted to the target domain. The goal of the rotational transformation is to find an orthogonal matrix Q,so that
Figure BDA0003638120790000072
And M are as close as possible, i.e.:
Figure BDA0003638120790000073
satisfies the following conditions:
QQ T ＝I (9)
this is an orthogonal probuck problem, there is an analytic solution, and according to the singular value decomposition theorem:
Figure BDA0003638120790000074
the solution to the rotation matrix is then:
Q＝VU T (11)
and finally, performing rotation transformation on the sample data of the source domain:
f i (PA) ＝f i Q (12)
and a sixth step: and (4) performing cross-domain migration classification. The classifier adopts Linear Discriminant Analysis (LDA) which is one of the most common algorithms in the field of motor imagery, and utilizes electroencephalogram data training of a source domain to obtain a classification model so as to classify label-free data of a target domain.
Example 2:
a motor imagery transfer learning method based on the Pluker analysis is disclosed, and a specific algorithm flow is shown in figure 3.
The first step is as follows: and (4) preprocessing. The specific processing flow of this step is the same as that of embodiment 1, and thus is not described again.
The second step is that: and (5) carrying out alignment transformation. Firstly, solving a covariance matrix of each electroencephalogram data:
Figure BDA0003638120790000075
then obtaining Riemann of all covariance matrixes according to formula (3)Mean value
Figure BDA0003638120790000076
And then performing alignment transformation on each sample:
Figure BDA0003638120790000081
the third step: and performing rotation transformation on the source domain. Firstly, solving a covariance matrix of each sample after alignment transformation:
Figure BDA0003638120790000082
and respectively solving the average covariance matrix of each sample category of the source domain subject and the target domain subject according to the formula (3):
Figure BDA0003638120790000083
note that the computation of the target domain is only for a small amount of sample data for known tags. Likewise, the goal of the rotational transformation is to find an orthogonal matrix Q such that
Figure BDA0003638120790000084
And M is as close as possible:
Figure BDA0003638120790000085
satisfies the following conditions:
QQ T ＝I (18)
the equations (16) to (17) have no analytical solution and need to be solved by means of a Matlab Manopt toolbox. The method comprises the following specific steps:
1) defining a rotationfactor manifold;
2) defining a loss function, namely formula (17);
3) the gradient was automatically calculated using an automatic differentiation tool (Manopt version 7.0, Matlab R2021a later version is required);
4) using Steepest-depth to solve, and the default maximum iteration number is 1000.
After the rotation matrix is obtained, the rotation transformation is carried out on the sample data of the source domain according to the following formula:
Figure BDA0003638120790000086
the fourth step: and extracting the CSP characteristics. And obtaining the CSP spatial filter W by using the sample data of the source domain, and respectively performing spatial filtering and feature extraction on the sample data of the source domain and the target domain. Since the CSP is a classical algorithm in the field of motor imagery, the relevant equations will not be presented here.
The fifth step: and (4) performing cross-domain migration classification. Similarly, an LDA classification model is obtained by utilizing the electroencephalogram data training of the source domain, and the target domain label-free data is classified.
The embodiments described in this specification are merely illustrative of implementations of the inventive concepts, which are intended for purposes of illustration only. The scope of the present invention should not be construed as being limited to the particular forms set forth in the examples, but rather as being defined by the claims and the equivalents thereof which can occur to those skilled in the art upon consideration of the present inventive concept.

Claims (3)

1. A motor imagery transfer learning method based on a Pluker analysis is characterized by comprising the following steps:
step 1): pretreatment of
Firstly, carrying out co-average reference processing on an original electroencephalogram signal, and then carrying out 8-30 Hz band-pass filtering;
step 2): respectively carrying out alignment transformation on electroencephalogram data of a source domain and a target domain
Let x i Representing the ith preprocessed electroencephalogram data, which is an n multiplied by l matrix, wherein n represents the number of lead connections of the electroencephalogram, l represents the number of sampling points of the signal, and a covariance matrix is extracted from the ith electroencephalogram data:
Figure FDA0003638120780000011
then the Riemann mean of all sample covariance matrices is:
Figure FDA0003638120780000012
in the formula, δ (·) represents riemann distance calculation, which is defined as:
Figure FDA0003638120780000013
wherein the subscript F represents the Frobenius norm, λ r (r ═ 1,2, …, n) is
Figure FDA0003638120780000014
The real eigenvalue of (d);
the meaning of the formula (2) is to find a reference matrix, the average Riemann distance from the reference matrix to all covariance matrix samples is minimum, and the obtained reference matrix is the average covariance matrix;
finally, performing alignment transformation on each sample:
Figure FDA0003638120780000015
after the alignment transformation, the mean covariance matrix of all samples is:
Figure FDA0003638120780000016
that is, the mean covariance matrix of all samples is an identity matrix, and the covariance matrix samples of each subject are distributed near the identity matrix, so that the source domain and the target domain are naturally aligned;
step 3): carrying out rotation transformation on the electroencephalogram data of the source domain to the target domain;
step 4): and (3) obtaining a classification model by taking the electroencephalogram data of the source domain as a training set, classifying the electroencephalogram data of the unknown label of the target domain, and realizing cross-domain transfer learning.
2. The method for motor imagery transfer learning based on pluker analysis according to claim 1, wherein in step 3), the alignment-transformed electroencephalogram data are first subjected to feature extraction, and then subjected to rotation transformation, and the process is as follows:
firstly, extracting the logarithm of variance of the electroencephalogram signal of the jth channel of the ith sample after alignment transformation as a characteristic:
Figure FDA0003638120780000017
then the set of sample data for each subject is represented as:
Figure FDA0003638120780000021
wherein k represents the number of samples of the subject;
and then respectively solving the average characteristic vectors of each sample category of the source domain subject and the target domain subject:
Figure FDA0003638120780000022
c represents the number of sample categories, and it should be noted that, since the step requires the label data of the sample, only a small amount of sample data of the known label is targeted for the target domain;
the goal of the rotation transformation is to find an orthogonal matrix Q such that
Figure FDA0003638120780000023
And M are as close as possible, i.e.:
Figure FDA0003638120780000024
satisfies the following conditions:
QQ T ＝I (10)
this is an orthogonal probuck problem, with analytical solutions, and according to the singular value decomposition theorem:
Figure FDA0003638120780000025
the solution to the rotation matrix is then:
Q＝VU T (12)
and finally, performing rotation transformation on the sample data of the source domain:
f i (PA) ＝f i Q (13)。
3. the method for motor imagery transfer learning based on pluronic analysis according to claim 1, wherein in step 3), the rotation transformation is directly performed on the aligned transformed electroencephalogram data, and the process is as follows:
firstly, solving a covariance matrix of each sample after alignment transformation:
Figure FDA0003638120780000026
and respectively solving the average covariance matrix of each sample category of the source domain subject and the target domain subject according to a formula (2):
Figure FDA0003638120780000027
note that the computation of the target domain is only for a small amount of sample data for known tags;
rotateThe transformation aims to find an orthogonal matrix Q such that
Figure FDA0003638120780000028
And M is as close as possible:
Figure FDA0003638120780000029
satisfies the following conditions:
QQ T ＝I (17)
the formulas (16) to (17) have no analytic solution, and are solved through a Matlab Manopt tool box;
after the rotation matrix is obtained, the rotation transformation is carried out on the sample data of the source domain according to the following formula:
Figure FDA00036381207800000210
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* Cited by examiner, † Cited by third party
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CN115526340A (en) * 2022-11-25 2022-12-27 北京烽火万家科技有限公司 Method and device for steady-state visual evoked potential paradigm transfer learning
CN116049639A (en) * 2023-03-31 2023-05-02 同心智医科技(北京)有限公司 Selective migration learning method and device for electroencephalogram signals and storage medium
CN117082188A (en) * 2023-10-12 2023-11-17 广东工业大学 Consistency video generation method and related device based on Pruk analysis
CN117195040A (en) * 2023-08-25 2023-12-08 浙江大学 Brain-computer interface transfer learning method based on resting state electroencephalogram data calibration

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115526340A (en) * 2022-11-25 2022-12-27 北京烽火万家科技有限公司 Method and device for steady-state visual evoked potential paradigm transfer learning
CN116049639A (en) * 2023-03-31 2023-05-02 同心智医科技(北京)有限公司 Selective migration learning method and device for electroencephalogram signals and storage medium
CN117195040A (en) * 2023-08-25 2023-12-08 浙江大学 Brain-computer interface transfer learning method based on resting state electroencephalogram data calibration
CN117195040B (en) * 2023-08-25 2024-05-17 浙江大学 Brain-computer interface transfer learning method based on resting state electroencephalogram data calibration
CN117082188A (en) * 2023-10-12 2023-11-17 广东工业大学 Consistency video generation method and related device based on Pruk analysis
CN117082188B (en) * 2023-10-12 2024-01-30 广东工业大学 Consistency video generation method and related device based on Pruk analysis

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