CN114254676A - Source domain selection method for multi-source electroencephalogram migration - Google Patents

Source domain selection method for multi-source electroencephalogram migration Download PDF

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CN114254676A
CN114254676A CN202111564098.XA CN202111564098A CN114254676A CN 114254676 A CN114254676 A CN 114254676A CN 202111564098 A CN202111564098 A CN 202111564098A CN 114254676 A CN114254676 A CN 114254676A
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佘青山
蔡寅昊
洪宽华
范影乐
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Abstract

The invention discloses a source domain selection method for multi-source electroencephalogram migration. After the popular characteristics are obtained, classification model training is carried out on each source domain by taking the structure risk minimization and the conditional probability distribution difference minimization of the source domain and the target domain as target functions, each classifier predicts the target domain respectively, the prediction results of different source domains are integrated in a voting mode, after the first iteration, each source domain trains a classifier respectively, and finally a multi-source classifier is generated by voting, so that the LSA conditions are met, the LSA is carried out once, the mobility estimated values of different source domains are obtained, k source domains are removed, and in the subsequent iteration, the classifier is trained for the rest source domains repeatedly only, so that the operation efficiency is improved.

Description

Source domain selection method for multi-source electroencephalogram migration
Technical Field
The invention belongs to the field of research of a nervous system motion control mechanism, and relates to electroencephalogram signal preprocessing, electroencephalogram feature extraction, manifold feature alignment and extraction and multi-source migration framework design, so that multi-source electroencephalogram migration learning is carried out.
Background
The brain is used as a central center for controlling activities of human mind, behavior, emotion and the like, analyzes and processes information acquired from an external environment, and completes communication with the outside through a neuromuscular pathway. However, spinal cord injury, amyotrophic lateral sclerosis, stroke, parkinson's disease and brain trauma often cause damage or impairment to nerve central function, resulting in different degrees of disorders of perception, sensation, speech, movement, and the like. On one hand, the breakthrough of Brain Computer Interface (BCI) technology is expected to realize function compensation and function reconstruction by directly establishing high-precision information interaction and control between the Brain and external equipment; on the other hand, active rehabilitation training based on the BCI technology can enhance nerve remodeling, promote rehabilitation of patients for recovering limb motor functions, improve life quality and happiness index of patients, and has important significance to patients, families and society.
In the BCI system, a core problem is that a large amount of marked electroencephalogram data are needed for model training of a traditional supervised classifier, and too long training time brings great psychological and physiological burden to a patient, so that the development and application of the BCI system are hindered. Therefore, how to design and realize an electroencephalogram signal analysis model with strong self-adaption capability, high recognition rate and short user training time becomes one of the common key basic scientific problems to be solved urgently in the practical process of the BCI system, and further research and development of the method are needed.
Aiming at the problems of training time and recognition performance existing in electroencephalogram signal decoding, the invention develops multi-source manifold feature transfer learning research in a brain-computer interface from a transfer learning theory, enhances the generalization capability of a transfer model and the robustness of a classifier, realizes the transfer from a healthy subject to a healthy subject or a patient, and improves the system performance of the brain-computer interface.
In recent years, the research application of transfer learning in BCI is endless. Among them, the use of riemann geometry in BCI becomes popular, the covariance matrix is taken as a Symmetric Positive Definite (SPD) matrix, and the covariance matrix of each (EEG) test can be regarded as a point on the SPD manifold. Zanini et al propose a Riemann Alignment (RA) framework for calibrating EEG covariance matrices from different source domains. However, these riemann space-based methods are computationally intensive and are not compatible with machine learning methods in the euclidean space. In experiments, we can find that even though the simplest migration learning algorithm is used, a good source domain is helpful to obtain very high classification accuracy, and thus the quality of the source domain is very important. However, in practice we are likely to have multiple source domains, just as BCI devices tend to have many previously used tag data. Therefore, when there are a plurality of source domains, good source domains are more likely to be included. In multi-source migration, due to the expansion of data, a good source domain can reduce the influence of negative migration caused by a bad source domain, and multi-source migration learning can generally obtain more stable and higher classification accuracy than STS migration learning. In recent years, multi-source unsupervised domain adaptive migration learning has received increasing attention, such as (Yao, & Doretto, 2010; Lin, An, & Zhang, 2013; Li et al, 2019; Zhu, zhong, & Wang, 2019; Zhang, & Wu, 2020). On the other hand, when there are many source domains, a good source domain is included, and a bad source domain also exists, so a domain selection method is needed to determine the performance of the source domain on the target domain, the good source domain is selected for migration, and the bad source domain which may bring negative migration is abandoned. Existing studies propose some Domain selection methods, such as similarity metric based methods, including Domain Rank (Rank Of Domains, ROD) (Gong et al, 2010), Domain Transfer Evaluation (DTE) (Zhang & Wu,2020), and performance based methods Of testing, such as (Yao, & Doretto, 2010).
Disclosure of Invention
The invention aims to provide a source domain selection method for multi-source electroencephalogram migration, which is named as Label Similarity Analysis (LSA).
In order to achieve the purpose, the method mainly comprises the following steps:
step (1), extracting electroencephalogram manifold features;
the method specifically comprises the following steps: aligning different source domains and target domains on the SPD manifold by calculating the covariance matrix of each sample electroencephalogram signal, and extracting the feature of a tangent space; reconstructing the extracted tangent space characteristics back to Grassmann manifold, and extracting Grassmann manifold characteristics to achieve the purpose of minimizing the edge probability distribution of a source domain and a target domain;
step (2), shifting manifold characteristics;
migrating the stream characteristics according to the manifold characteristics of the minimized source domain and target domain edge probability distribution obtained in the step (1), and minimizing the conditional probability distribution of the source domain and the target domain;
selecting a source domain;
after the first iteration, performing one-time LSA to obtain mobility estimated values of different source domains; removing k source domains according to the mobility estimated value, and repeating the iteration of the remaining source domain training classifier in the subsequent iteration;
the LSA specifically comprises:
and obtaining the single-source classifier and the multi-source classifier of each source domain through the multi-source migration framework, comparing the prediction result of the single-source classifier trained in each source domain with the prediction result of the multi-source classifier, and calculating the estimated value of the migratability of different source domains.
Preferably, the single-source classifier and the multi-source classifier of each source domain are obtained through the multi-source migration framework, the prediction result of the single-source classifier trained in each source domain is compared with the prediction result of the multi-source classifier, and the estimated value of the migration performance of different source domains is calculated;
the method specifically comprises the following steps: the label of the target domain reality is expressed as
Figure BDA0003421584440000031
Single-source classifier f trained in each domainsAnd final vote generated multi-source classifier fmWhat is needed isThe measured labels are respectively shown as
Figure BDA0003421584440000032
And
Figure BDA0003421584440000033
using sim (-) to represent similarity between two labels, e.g. yrealAnd ypsThe similarity calculation method comprises
Figure BDA0003421584440000034
Figure BDA0003421584440000035
ntNumber of samples representing target domain
The migratability of a source domain is estimated by the STS migration classification accuracy,
Accuracy＝sim(yreal,yps)/nt (26)
higher STS migration classification precision means higher migratability; based on the assumptions for the three types of distribution of the samples, the results are obtained
Figure BDA0003421584440000036
Said
Figure BDA0003421584440000037
Respectively representing the predictive labels of the single-source classifier for the samples of the first class and the third class,
Figure BDA0003421584440000038
respectively representing the predictive labels of the multi-source classifier on the first class samples and the third class samples,
Figure BDA0003421584440000039
respectively representing a first class and a third classThe true label of the sample.
And
Figure BDA00034215844400000310
as seen from the formulas (27) and (28),
Figure BDA00034215844400000311
higher means that the source domain is highly migratable; target Domain tag yreaIs unknown, is there a possibility to find a reliable analysis method to represent the source domain's migratability? In the multi-source migration learning, the existence of a plurality of source domains obviously improves the classification performance and stability of single-source migration, mainly because the multi-source migration learning has higher accuracy in predicting the 2 nd sample,
Figure BDA0003421584440000041
if a single source classifier can predict the label of the 2 nd sample as accurately as a multi-source classifier, i.e.
Figure BDA0003421584440000042
Higher, the probability that the source domain has higher migratability is higher;
based on the above analysis and assumptions, predictive label y of multi-source classifier is usedpmTo identify the migratability of different source domains;
Figure BDA0003421584440000043
bringing formula (27) into formula (29) as long as sim (y)ps,ypm) High means that
Figure BDA0003421584440000044
High, i.e., the migratability of one source domain is high;
hence the jth source domain
Figure BDA0003421584440000045
And the target domain
Figure BDA0003421584440000046
Can be migrated between
Figure BDA0003421584440000047
The calculation is as follows:
Figure BDA0003421584440000048
wherein
Figure BDA0003421584440000049
f is a classification algorithm.
Preferably, f is linear discriminant analysis or support vector machine.
Preferably, the extraction of the electroencephalogram manifold characteristics specifically comprises the following steps:
the covariance matrix of the EEG signal of one experiment is recorded as P, P ═ XXTAnd P is an SPD matrix; by using
Figure BDA00034215844400000410
And
Figure BDA00034215844400000411
representing a source domain
Figure BDA00034215844400000412
And target and domain
Figure BDA00034215844400000413
Covariance matrix of all samples, one-dimensional distribution of distances over SPD manifold, MsAnd MtIs the mean value of the distribution of the domains,
Figure BDA00034215844400000414
and
Figure BDA00034215844400000415
representing covariance matrix distributionSelecting reversible matrixes A and B as linear transformation to align the distribution means of the domains; after the linear transformation, the samples of the source domain and the target domain are
Figure BDA00034215844400000416
And
Figure BDA00034215844400000417
according to the congruence invariance characteristic of Riemann distance, the covariance matrixes of all the characteristics are changed only on the reference position of the space, so that the source domain and the target domain are transformed
Figure BDA00034215844400000418
And
Figure BDA00034215844400000419
unchanged, transformed source domain distribution as
Figure BDA00034215844400000420
Target domain distribution
Figure BDA00034215844400000421
Is composed of
Figure BDA00034215844400000422
Using the KL divergence measure the difference in distribution from the target domain, the objective function that minimizes the marginal probability distribution is:
Figure BDA0003421584440000051
wherein KL (. cndot.) is the calculation of KL divergence using the probability density of a standard normal distribution
Figure BDA0003421584440000052
x represents the covariance matrix of the last experiment of the SPD manifold;
calculation of KL divergence
Figure BDA0003421584440000053
And
Figure BDA0003421584440000054
the formula (2) and the formula (3) are brought into the formula (1), and the objective function is simplified into
Figure BDA0003421584440000055
When A isTMsA＝BTMtB, the objective function can obtain an optimal solution, such as:
Figure BDA0003421584440000056
and
Figure BDA0003421584440000057
wherein E is a unit matrix, each domain is aligned to the distribution mean of the domain in the formula (6) by the method, and the source domain samples are all aligned to the target domain in the formula (7), and the method adopts the alignment mode of the formula (6), so that the source domain and the target domain samples are whitened by the multi-covariance matrix after the alignment;
after aligning the distribution mean, the covariance matrices of all samples in the source domain and the target domain are respectively
Figure BDA0003421584440000058
And
Figure BDA0003421584440000059
ns，ntthe number of samples in the source domain and the target domain respectively, and is expressed by the formula (8))
Figure BDA00034215844400000510
The calculation results in that,
Figure BDA00034215844400000511
the covariance matrix of the i-th experiment representing the source domain,
Figure BDA00034215844400000512
a covariance matrix representing a j-th experiment of the target domain;
projecting the aligned covariance matrix to a tangent space to obtain tangent space characteristics, converting the original two-dimensional covariance matrix characteristics into a one-dimensional vector form, and calculating according to the formula (9);
Figure BDA0003421584440000061
where upper () is the upper triangular portion of the SPD matrix taken at c
Figure BDA0003421584440000062
The operation of (1); the obtained tangent space characteristics of the source domain and the target domain are respectively
Figure BDA0003421584440000063
And
Figure BDA0003421584440000064
finally, the obtained one-dimensional tangent space characteristics are reconstructed back to the Grassmann manifold space
z＝g(x)＝Φ(t)Tx (10)
Calculating the feature map G by equation (11)
Figure BDA0003421584440000065
Finally, Grassmann manifold characteristics are obtained through the formula (12)
Figure BDA0003421584440000066
The finally obtained Grassmann manifold characteristic z eliminates the distribution variance of the source and target domains as much as possible
Figure BDA0003421584440000067
And
Figure BDA0003421584440000068
the difference in (a).
Preferably, the manifold feature migration specifically includes:
in the second step, the manifold features are migrated to minimize the conditional probability distribution of the source domain and the target domain; the objective function of the classifier f is determined as shown in equation (13), and the SRM classifier is used to minimize the conditional probability distribution of the source domain and the target domain,
Figure BDA0003421584440000069
wherein the first two terms are SRM classifiers and the third term represents the source domain
Figure BDA00034215844400000610
And a target domain
Figure BDA00034215844400000611
Conditional probability distribution difference therebetween;
wherein the SRM classifier is represented as
Figure BDA00034215844400000612
Wherein E is a diagonal matrix for recording labels, and in case of unbalanced sample classes, samples belonging to a class with a smaller number of samples can obtain a larger weight;
Figure BDA0003421584440000071
wherein n iss,(c＝1)And ns,(c＝2)Respectively representing the number of samples belonging to class 1 and class 2 in the source domain;
the third term can be expressed as
Figure BDA0003421584440000072
Wherein
Figure BDA0003421584440000073
Representing the conditional probability distribution alignment of class c samples;
using the theory of characterization, one of the classifiers f becomes
Figure BDA0003421584440000074
Where K is mapped to Hilbert space from original feature vectors
Figure BDA0003421584440000075
Is selected from the group consisting of (a) a core,
Figure BDA0003421584440000076
is the corresponding coefficient vector;
thus, equation (16) can be written as
Figure BDA0003421584440000077
Wherein
Figure BDA0003421584440000078
Represents the norm of Frobenious,
Figure BDA0003421584440000079
is a kernel matrix where Kij＝K(zi,zj), Y＝[y1,…,yn]Is a pseudo label of the source domain label and the target domain, n ═ ns+ntTr (-) is the trace of the matrix;
formula (17) is written as
Figure BDA00034215844400000710
Wherein M iscIs a MMD matrix
Figure BDA00034215844400000711
Wherein
Figure BDA0003421584440000081
and
Figure BDA0003421584440000082
Respectively representing samples belonging to class c in a source domain and a target domain;
the formula (18) and the formula (19) are brought into the formula (13), and the objective function of the classifier is
Figure BDA0003421584440000083
By derivation, pair
Figure BDA0003421584440000084
To minimize the objective function, obtain the optimal solution as
α＝((E+λMc)K+σI)-1EYT (22)
The prediction information of the classifier can be obtained by bringing the formula (22) into the formula (17).
Compared with the traditional method for analyzing the coupling among muscles, the method has the following advantages:
1. the method is simple and intuitive, is more accurate and effective compared with the existing unsupervised source domain selection method, and can be matched with the SRM classifier to mine the label information of the source domain.
2. The method can be well combined with the proposed multi-source migration framework, can complete source domain selection in the middle process of multi-source migration, and consumes little computing time.
Drawings
FIG. 1 shows the distribution of three samples of a target domain and their true labels;
FIG. 2 is a flow chart of the present invention patent;
FIG. 3 is a graph of the results of the experiments performed on five data sets according to the present invention.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings: the embodiment is implemented on the premise of the technical scheme of the invention, and a detailed implementation scheme and a specific operation process are given.
The invention provides a source domain selection method for multi-source electroencephalogram migration. As shown in fig. 2, the implementation of the present invention mainly includes three steps: (1) a multi-source migration framework; (2) performing label similarity analysis; (3) and selecting a source domain.
The respective steps are explained in detail one by one below.
The method comprises the following steps: multi-source migration framework
The covariance matrix of the EEG signal of one experiment is recorded as P, P ═ XXTAnd P is the SPD matrix. By using
Figure BDA0003421584440000085
And
Figure BDA0003421584440000086
covariance matrix representing source and target and all samples of the domain, one-dimensional distribution of distances over SPD manifold, MsAnd MtIs the domain distribution mean (the riemann mean of all samples in a domain),
Figure BDA0003421584440000087
and
Figure BDA0003421584440000088
represents the variance of the covariance matrix distribution, the larger the variance value, the more dispersed the distribution of samples representing the domain over the SPD manifold. In order to reduce the edge probability distribution of a source domain and a target domain by changing the reference position on the Riemannian manifold, reversible matrixes A and B are selected as linear transformation to carry out distribution mean alignment of the domains. After the linear transformation, the samples of the source domain and the target domain are
Figure BDA0003421584440000091
And
Figure BDA0003421584440000092
according to the congruence invariance characteristic of Riemann distance, the covariance matrixes of all the characteristics are changed only on the reference position of the space, so that the source domain and the target domain are transformed
Figure BDA0003421584440000093
And
Figure BDA0003421584440000094
unchanged, transformed distribution of
Figure BDA0003421584440000095
And
Figure BDA0003421584440000096
using the KL divergence measure the difference in distribution from the target domain, the objective function that minimizes the marginal probability distribution is:
Figure BDA0003421584440000097
where KL (. circle.) is the calculation of KL divergence probability density using a standard normal distribution
Figure BDA0003421584440000098
KL divergence can be calculated
Figure BDA0003421584440000099
And
Figure BDA00034215844400000910
the formula (2) and the formula (3) are brought into the formula (1), and the objective function is simplified into
Figure BDA00034215844400000911
When A isTMsA＝BTMtB, the objective function can obtain an optimal solution, such as:
Figure BDA00034215844400000912
and
Figure BDA00034215844400000913
wherein E is the identity matrix, as shown in fig. 2, different solutions correspond to different methods for aligning, the method for aligning in equation (6) aligns each domain to its own distribution mean, and equation (7) aligns all the samples of the source domain to the target domain, the method adopts the alignment of equation (6), because after the alignment, the multi-covariance matrix of the samples of the source domain and the target domain can be whitened.
After aligning the distribution mean, the covariance matrices of all samples in the source domain and the target domain are respectively
Figure BDA0003421584440000101
And
Figure BDA0003421584440000102
ns，ntthe number of samples in the source domain and the target domain, respectively, can be represented by the formula (8)
Figure BDA0003421584440000103
And (4) calculating.
The aligned covariance matrix can be projected to a tangent space to obtain tangent space characteristics, the original two-dimensional covariance matrix characteristics are converted into a one-dimensional vector form, and the calculation method is shown as the formula (9).
Figure BDA0003421584440000104
Where upper () is the upper triangular portion of the SPD matrix taken at c
Figure BDA0003421584440000105
The operation of (2). The obtained tangent space characteristics of the source domain and the target domain are respectively
Figure BDA0003421584440000106
And
Figure BDA0003421584440000107
finally, the obtained one-dimensional tangent space characteristics are reconstructed back to the Grassmann manifold space
z＝g(x)＝Φ(t)Tx (10)
Calculating the feature map G by equation (11)
Figure BDA0003421584440000108
Finally, Grassmann manifold characteristics are obtained through the formula (12)
Figure BDA0003421584440000109
The finally obtained Grassmann manifold characteristic z can eliminate the distribution variance of the source and target domains as much as possible
Figure BDA00034215844400001010
And
Figure BDA00034215844400001011
the difference in (a).
Step two: manifold feature migration
In the second step, the manifold features are migrated to minimize the conditional probability distribution of the source domain and the target domain. The objective function of the classifier f is shown as formula (13), the method adopts the SRM classifier to minimize the conditional probability distribution and the label similarity of the source domain and the target domain,
Figure BDA0003421584440000111
wherein the first two terms are SRM classifiers and the third term represents the source domain
Figure BDA0003421584440000112
And a target domain
Figure BDA0003421584440000113
Conditional probability distribution difference between them.
Wherein the SRM classifier can be expressed as
Figure BDA0003421584440000114
Where E is a diagonal matrix used to record labels, and in the case of sample classes that are unbalanced, samples belonging to the class with the smaller number of samples can get a larger weight.
Figure BDA0003421584440000115
Wherein n iss,(c＝1)And ns,(c＝2)Respectively representing the number of samples belonging to class 1 and class 2 in the source domain.
The third term can be expressed as
Figure BDA0003421584440000116
Wherein
Figure BDA0003421584440000117
Indicating the alignment of the conditional probability distributions for the class c samples.
Using the theory of characterization (
Figure BDA0003421584440000118
Herbrich,&Smola,2001), one of the classifiers f becomes
Figure BDA0003421584440000119
Where K is mapped to Hilbert space from original feature vectors
Figure BDA00034215844400001112
Is selected from the group consisting of (a) a core,
Figure BDA00034215844400001110
is the corresponding coefficient vector.
Thus, equation (16) can be written as
Figure BDA00034215844400001111
Wherein
Figure BDA0003421584440000121
Represents the norm of Frobenious,
Figure BDA0003421584440000122
is a kernel matrix where Kij＝K(zi,zj), Y＝[y1,…,yn]Is a pseudo label of the source domain label and the target domain, n ═ ns+ntAnd tr (-) is the trace of the matrix.
Formula (17) can be written as
Figure BDA0003421584440000123
Wherein M iscIs an MMD (maximum mean variance) matrix
Figure BDA0003421584440000124
Wherein
Figure BDA0003421584440000125
and
Figure BDA0003421584440000126
Respectively representing samples belonging to class c in the source domain and the target domain.
The formula (18) and the formula (19) are brought into the formula (13), and the objective function of the classifier is
Figure BDA0003421584440000127
By derivation, pair
Figure BDA0003421584440000128
To minimize the objective function, an optimal solution can be obtained as
α＝((E+λMc)K+σI)-1EYT (22)
The prediction information of the classifier can be obtained by bringing the formula (22) into the formula (17).
Having obtained the training method for the migration classifier, as shown in FIG. 1, the method for the migration classifierIn z source domains
Figure BDA0003421584440000129
After aligning the distribution means, there is still a difference in the conditional probability distributions of all source domains. Part of the conditional probability distribution information may be lost when their MMD matrices are computed together. Thus, the result of aligning the joint probability distribution may not be better than the result of aligning only the edge distribution. Compared with the traditional multi-source migration, the multi-source migration framework of the method does not simply put a plurality of aligned source domains together to train the classifier, but trains the classifier for each aligned source domain independently through the classifier design method of the second step, and finally accumulates the quantitative prediction value of each source domain on the target domain to obtain the final classification result. The method furthest reserves the conditional probability distribution information of each source domain, and the method adopts a quantitative classifier, so that the probability that each sample belongs to a certain class can be better described under the condition of multi-source voting. The method specifically comprises the following steps:
obtaining the covariance matrix after aligning the z source domains by the formula (8)
Figure BDA0003421584440000131
Covariance matrix aligned with target field
Figure BDA0003421584440000132
Calculating the feature of the tangent space by the formula (9)
Figure BDA0003421584440000133
Finally, Grassmann manifold feature learning is carried out through the formula (11) and the formula (12), and the manifold feature with the minimized edge probability distribution is obtained
Figure BDA0003421584440000134
Then, using the obtained manifold features, a classifier f is trained for each source domain by equation (22)iI1, 2, … z, and making quantitative votes
Figure BDA0003421584440000135
And obtaining the final multi-source classifier f.
Step two: tag similarity analysis
After the multi-source migration framework is obtained, as shown in fig. 1, in the process of the first iteration, label similarity analysis needs to be performed, and the idea and method of label similarity analysis are described in detail below.
When the learning tasks of the two domains are unrelated/similar or the data distribution of the source domain and the target domain are different, different subjects may show strong individual differences in BCI training. This may lead to Negative migration (NT) (Zhang, Deng, Zhang, & Wu, 2020). It is generally believed that a source domain has higher migratability if the knowledge it contains can help the target domain achieve higher classification accuracy. Conversely, some source domains contain data/features that are very different from the target domain and are considered to have low migratability. To avoid such negative operations, the present study proposed a test-based domain selection method, Label Similarity Analysis (LSA), to avoid the effects of poor source domains in multi-source migration. And judging whether a source domain is good or bad by comparing the labels generated by the multi-source classifier and the STS classifier. Its essence is to take advantage of the reliability of multi-source migration to help identify the migratability of each source domain.
To explore the similarities and differences between STS and multi-source migration, the present study assumed three types of target domain EEG signal signature distributions, as shown in fig. 2.
Type 1: light grey indicates some samples that are easily classified correctly.
Type 2, dark grey indicates low discriminative samples. When different source domains are migrated to help the classification of the target domain, the difference of migration effect is mainly whether the samples can be classified correctly.
And 3, black represents samples which have large distribution difference and are difficult to classify correctly.
The label of the target domain reality is expressed as
Figure BDA0003421584440000141
Single-source classifier f trained in each domainsAnd final vote generated multi-source classifier fmThe predicted labels are respectively expressed as
Figure BDA0003421584440000142
And
Figure BDA0003421584440000143
where k ═ 1,2,3 represents the three distributions of fig. 2, and sim (-) is used to represent the similarity between the two labels, e.g., yrealAnd ypsThe similarity calculation method comprises
Figure BDA0003421584440000144
Figure BDA0003421584440000145
The migration of a source domain can be estimated by STS migration classification precision
Accuracy＝sim(yreal,yps)/nt (26)
Higher accuracy means higher transferability. From the previous assumptions for the three types of distribution of the samples, one can derive
Figure BDA0003421584440000146
And
Figure BDA0003421584440000147
as can be seen from the formulas (27) and (28),
Figure BDA0003421584440000148
higher means that the source domain is highly migratable. However, the target domain label yrealIs unknown, is it possible to find a reliable analytical method to represent the source domain's migratability? In the multi-source migration learning, the existence of a plurality of source domains obviously improves the classification performance and stability of single-source migration, mainly because the multi-source migration learning has higher accuracy in predicting the 2 nd sample,
Figure BDA0003421584440000149
if a source domain can predict the label of the 2 nd sample as accurately as a multi-source classifier, i.e.
Figure BDA00034215844400001410
Higher, the probability that the source domain has higher migratability is higher.
Based on the above analysis and assumptions, the present study used the predictive label y of the multi-source classifierpmTo identify the migratability of different source domains.
Figure BDA0003421584440000151
Bringing formula (27) into formula (29) can be found as long as sim (y)ps,ypm) High means that
Figure BDA0003421584440000152
High, i.e., the migratability of one source domain is high.
Hence the jth source domain
Figure BDA0003421584440000153
And the target domain
Figure BDA0003421584440000154
Can be migrated between
Figure BDA0003421584440000155
The calculation is as follows:
Figure BDA0003421584440000156
wherein
Figure BDA0003421584440000157
f may be a classification algorithm such as Linear Discriminant Analysis (LDA) or Support Vector Machine (SVM). However, to estimate the portability of the source domain, it is time consuming to train an additional classifier to perform STS transmission and prediction. In this regard, LSA is easier to integrate into the step-proposed multi-source migration framework, as the framework has trained classifiers for each source domain exactly.
Step three: source domain selection
As shown in fig. 1, after the first iteration, each source domain is trained to obtain a classifier, and finally a multi-source classifier is generated by voting, so that the LSA condition is satisfied, at this time, the LSA is performed once to obtain mobility estimation values of different source domains, and k source domains are removed, and the values can be set by themselves. In the subsequent iteration, the training of the classifier for the rest source domain is repeated, so that the operation efficiency can be improved. Experiment:
1. data set:
in order to verify the performance of the method, the experimental part was experimented on 5 public electroencephalogram data sets. The specific description is as follows:
(1) MI1(BCI composition III Dataset IV a) the data set contained EEG signals from 5 subjects, each subject (code A1-A5) performed two motor imagery tasks requiring the imagination of right hand or foot movement following a visual cue, each group of EEG signals was recorded using 118 electrodes for 3.5s per experiment, the sampling frequency was 100Hz, and the electrode positions used the International 10/20 System. Each subject was subjected to 200 experiments in which only left and right hand EEG signals were selected for testing, and in 200 experiments, both left and right hand motor imagery were performed 100 times.
(2) MI2(BCI composition IV Dataset IIa) the data set contained EEG signals from 9 subjects (Nos. C1-C9), each of which performed four motor imagery tasks, left hand, right foot and tongue, lasting 4s per experiment. All experiments were recorded using 22 electrodes, the sampling frequency was 250Hz, and the electrode position was with the International 10/20 System. Each subject was subjected to 144 experiments in which only left and right hand EEG signals were selected for testing, and 72 of each of the 144 experiments were performed.
(3) MI3 and MI4(Cho, 2017). this data set contains EEG and EMG signals from 52 subjects (nos. S1-S52), all recorded using 64 electrodes, with a sampling frequency of 512 Hz. Each subject was subjected to 200 experiments in which only left and right hand EEG signals were selected for testing, and in 200 experiments, both left and right hand motor imagery were performed 100 times. Considering that the number of data sets of subjects is large, and furthermore, almost half of the subjects have low mobility, for the rationality of the experiment, 52 subjects were divided into a group of 10 for simple migration experiment, subjects with an average classification accuracy of less than 60% were not selected, and data of 20 subjects were finally selected, the first 10 (S1, S3, S4, S5, S9, S10, S14, S19, S20, S23) constituting MI3, and the last 10 (S24, S25, S28, S31, S33, S36, S43, S47, S48, S49) constituting MI 4.
(4) RSVP (Matran-Fernandez, & Polo, 2017): the RSVP data set contains 8-channel electroencephalographic recordings of 11 healthy subjects in a Rapid Serial Visual Presentation (RSVP) experiment. In three different experiments, images were presented at different rates (5, 6 and 10 Hz). Only the 5HZ version was used in this experiment. The goal is to classify the target image or non-target image being viewed from the electroencephalogram, e.g., images with or without an airplane. The number of images from different subjects was between 368 and 565, with a ratio of target to non-target of about 1: 10. The RSVP dataset EEG signal sample rate is 2048hz and the band pass filter is set to 0.15-28 hz.
(5) ERN (Margaux et al, 2012) ERN data sets are feedback error-dependent negativity (ERN) experiments, which are used for two classes of classification experiments for Kaggle competitions. Collected from 26 subjects and divided into a training set (16 subjects) and a test set (10 subjects). Only the training set was used in this experiment since the complete data of the test set was not accessible. The average ratio of target to non-target is about 1: 4. The 56-channel electroencephalography data sampling frequency is 200 Hz.
2. Experimental procedures and evaluation indexes:
in 5 electroencephalogram datasets, there is a classification imbalance between the ERN and RSVP datasets, so we use Balanced Classification Accuracy (BCA) to measure classification performance.
Figure BDA0003421584440000171
Wherein n ispkAnd nkThe number of samples that are true positives for class k and the number of samples for the actual class k. When the sample classes are balanced, BCA is equivalent to normal classification accuracy.
Assuming z +1 subjects in a data set, in the multi-source migration, each subject is taken as a target domain in turn, and the rest subjects are taken as source domains, so that z +1 different migration tasks are obtained, and the BCA of the z +1 migration tasks is averaged to be used as the final measure for the classification performance of a method on the data set.
To evaluate whether each source domain selection method can accurately distinguish the migratability of the source domain, the present experiment compared the proposed LSA method with the other two domain selection methods (DTE and ROD). Since different classification algorithms combined with the domain selection method produce different effects, the classifiers are all the classifiers in the first step. In each dataset, each topic is selected in turn as the target domain, the rest being considered as source domains. Firstly, calculating the similarity of a source domain and a target domain by adopting three domain selection methods; and then eliminating the source domains with the lowest similarity to the target domain one by one, gradually reducing the number of the source domains to only one, and recording the average value of the classified BCA. For example, MI1 has 7 subjects, and in each migration task, there are 6 source domains, except 1 subject as the target domain. The same is true for other data sets, and there are 6, 8, 9, 10, 15 source domains in each migration task of MI2, MI3, MI4, RSVP, ERN data sets, respectively.
3. Experimental comparison methods:
(1) rank Of Domain (ROD) (Gong et al, 2010),
(2) domain Transfer Estimation (DTE) (Zhang & Wu, 2020).
4. The experimental results are as follows:
the experimental results are shown in fig. 3, and fig. 3 shows the variation of the average BCA of 5 data sets with the decrease of the number of source domains. The mean BCA for LSAs in all data sets remained more stable than the other two comparative methods as the number of source domains was gradually reduced to 1. In MI3 in particular, as the number of source fields decreased, the average BCA increased, since the field selection method removed some bad source fields that caused negative migration. In contrast, when the number of sources is reduced to more than half, the average BCA values of ROD and DTE are significantly reduced. The result shows that compared with the two comparison methods, the LSA source domain selection method provided by the method can more accurately identify the migratability of the source domain.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention may be made by those skilled in the art without departing from the spirit of the present invention, which is defined by the claims.

Claims (5)

1. The source domain selection method for multi-source electroencephalogram migration is characterized by comprising the following steps: the method comprises the following steps:
step (1), extracting electroencephalogram manifold features;
the method specifically comprises the following steps: aligning different source domains and target domains on the SPD manifold by calculating the covariance matrix of each sample electroencephalogram signal, and extracting the feature of a tangent space; reconstructing the extracted tangent space characteristics back to Grassmann manifold, and extracting the Grassmann manifold characteristics to achieve the purpose of minimizing the edge probability distribution of the source domain and the target domain;
step (2), shifting manifold characteristics;
migrating the stream characteristics according to the manifold characteristics of the minimized source domain and target domain edge probability distribution obtained in the step (1), and minimizing the conditional probability distribution of the source domain and the target domain;
selecting a source domain;
after the first iteration, performing one-time LSA to obtain mobility estimated values of different source domains; removing k source domains according to the mobility estimated value, and repeating the iteration of the remaining source domain training classifier in the subsequent iteration;
the LSA specifically comprises:
and obtaining the single-source classifier and the multi-source classifier of each source domain through the multi-source migration framework, comparing the prediction result of the single-source classifier trained in each source domain with the prediction result of the multi-source classifier, and calculating the estimated value of the migratability of different source domains.
2. The source domain selection method for multi-source electroencephalogram migration according to claim 1, characterized in that: the single-source classifier and the multi-source classifier of each source domain are obtained through the multi-source migration framework, the prediction result of the single-source classifier trained in each source domain is compared with the prediction result of the multi-source classifier, and the estimated value of the migration performance of different source domains is calculated;
the method specifically comprises the following steps: the label of the target domain reality is expressed as
Figure FDA0003421584430000015
Single-source classifier f trained in each domainsAnd final vote generated multi-source classifier fmThe predicted labels are respectively expressed as
Figure FDA0003421584430000011
And
Figure FDA0003421584430000012
using sim (-) to represent similarity between two labels, e.g. yrealAnd ypsThe similarity calculation method comprises
Figure FDA0003421584430000013
Figure FDA0003421584430000014
ntRepresenting the number of samples of the target domain;
the migratability of a source domain is estimated by the STS migration classification accuracy,
Accuracy＝sim(yreal,yps)/nt (26)
higher STS migration classification precision means higher migratability; based on the assumptions for the three types of distribution of the samples, the results are obtained
Figure FDA0003421584430000021
Said
Figure FDA0003421584430000022
Respectively representing the predictive labels of the single-source classifier for the samples of the first class and the third class,
Figure FDA0003421584430000023
respectively representing the predictive labels of the multi-source classifier on the first class samples and the third class samples,
Figure FDA0003421584430000024
true tags representing samples of the first type and the third type, respectively;
and
Figure FDA0003421584430000025
as seen from the formulas (27) and (28),
Figure FDA0003421584430000026
higher means that the source domain is highly migratable; target Domain tag yrealIs unknown if oneSingle-source classifiers can predict the label of the 2 nd sample as accurately as multi-source classifiers, i.e.
Figure FDA0003421584430000027
Higher, the probability that the source domain has higher migratability is higher;
based on the above analysis and assumptions, predictive label y of multi-source classifier is usedpmTo identify the migratability of different source domains;
Figure FDA0003421584430000028
bringing formula (27) into formula (29) as long as sim (y)ps,ypm) High means that
Figure FDA0003421584430000029
High, i.e., the migratability of one source domain is high;
hence the jth source domain
Figure FDA00034215844300000210
And the target domain
Figure FDA00034215844300000211
Can be migrated between
Figure FDA00034215844300000212
The calculation is as follows:
Figure FDA00034215844300000213
wherein
Figure FDA00034215844300000214
f is a classification algorithm.
3. The source domain selection method for multi-source electroencephalogram migration according to claim 1, characterized in that: f is linear discriminant analysis or support vector machine.
4. The source domain selection method for multi-source electroencephalogram migration according to claim 1, characterized in that: the extraction of the electroencephalogram manifold characteristics specifically comprises the following steps:
the covariance matrix of the EEG signal of one experiment is recorded as P, P ═ XXTAnd P is an SPD matrix; by using
Figure FDA0003421584430000031
And
Figure FDA0003421584430000032
representing a source domain
Figure FDA0003421584430000033
And target and domain
Figure FDA0003421584430000034
Covariance matrix of all samples, one-dimensional distribution of distances over SPD manifold, MsAnd MtIs the mean value of the distribution of the domains,
Figure FDA0003421584430000035
and
Figure FDA0003421584430000036
representing the variance of the covariance matrix distribution, and selecting reversible matrixes A and B as linear transformation to align the distribution means of the domains; after the linear transformation, the samples of the source domain and the target domain are
Figure FDA0003421584430000037
And
Figure FDA0003421584430000038
according to the congruence invariance characteristic of Riemann distance, the covariance matrixes of all the characteristics are only at the reference position in spaceHas changed, and thus, has changed the source domain and the target domain
Figure FDA0003421584430000039
And
Figure FDA00034215844300000310
unchanged, transformed source domain distribution as
Figure FDA00034215844300000311
Target domain distribution
Figure FDA00034215844300000312
Is composed of
Figure FDA00034215844300000313
Using the KL divergence measure the difference in distribution from the target domain, the objective function that minimizes the marginal probability distribution is:
Figure FDA00034215844300000314
wherein KL (. cndot.) is the calculation of KL divergence using the probability density of a standard normal distribution
Figure FDA00034215844300000315
x represents the covariance matrix of the last experiment of the SPD manifold;
calculation of KL divergence
Figure FDA00034215844300000316
And
Figure FDA00034215844300000317
the formula (2) and the formula (3) are brought into the formula (1), and the objective function is simplified into
Figure FDA00034215844300000318
When A isTMsA＝BTMtB, the objective function can obtain an optimal solution, such as:
Figure FDA0003421584430000041
and
Figure FDA0003421584430000042
wherein E is a unit matrix, each domain is aligned to the distribution mean of the domain in the formula (6) by the method, and the source domain samples are all aligned to the target domain in the formula (7), and the method adopts the alignment mode of the formula (6), so that the source domain and the target domain samples are whitened by the multi-covariance matrix after the alignment;
after aligning the distribution mean, the covariance matrices of all samples in the source domain and the target domain are respectively
Figure FDA0003421584430000043
And
Figure FDA0003421584430000044
ns，ntthe number of samples in the source domain and the target domain, respectively, is represented by the formula (8)
Figure FDA0003421584430000045
The calculation results in that,
Figure FDA0003421584430000046
the covariance matrix of the i-th experiment representing the source domain,
Figure FDA0003421584430000047
a covariance matrix representing a j-th experiment of the target domain;
projecting the aligned covariance matrix to a tangent space to obtain tangent space characteristics, converting the original two-dimensional covariance matrix characteristics into a one-dimensional vector form, and calculating according to the formula (9);
Figure FDA0003421584430000048
where upper () is the upper triangular portion of the SPD matrix taken at c
Figure FDA0003421584430000049
The operation of (1); the obtained tangent space characteristics of the source domain and the target domain are respectively
Figure FDA00034215844300000410
And
Figure FDA00034215844300000411
finally, the obtained one-dimensional tangent space characteristics are reconstructed back to the Grassmann manifold space
z＝g(x)＝Φ(t)Tx (10)
Calculating the feature map G by equation (11)
Figure FDA00034215844300000412
Finally, Grassmann manifold characteristics are obtained through the formula (12)
Figure FDA00034215844300000413
The finally obtained Grassmann manifold characteristic z eliminates the distribution variance of the source and target domains as much as possible
Figure FDA00034215844300000414
And
Figure FDA00034215844300000415
the difference in (a).
5. The multi-source popular electroencephalogram feature transfer learning method according to claim 1, characterized in that: the manifold feature migration specifically includes:
in the second step, the manifold features are migrated to minimize the conditional probability distribution of the source domain and the target domain; the objective function of the classifier f is determined as shown in equation (13), and the SRM classifier is used to minimize the conditional probability distribution of the source domain and the target domain,
Figure FDA0003421584430000051
wherein the first two terms are SRM classifiers and the third term represents the source domain
Figure FDA0003421584430000052
And a target domain
Figure FDA0003421584430000053
Conditional probability distribution difference therebetween;
wherein the SRM classifier is represented as
Figure FDA0003421584430000054
Where E is a diagonal matrix used to record labels and belongs to a sample in the event of an unbalanced sample class
A greater weight may be obtained for a smaller number of samples of that type;
Figure FDA0003421584430000055
wherein n iss,(c＝1)And ns,(c＝2)Respectively representing the number of samples belonging to class 1 and class 2 in the source domain;
the third term can be expressed as
Figure FDA0003421584430000056
Wherein
Figure FDA0003421584430000057
Representing the conditional probability distribution alignment of class c samples;
using the theory of characterization, one of the classifiers f becomes
Figure FDA0003421584430000058
Where K is mapped to Hilbert space from original feature vectors
Figure FDA0003421584430000059
Is selected from the group consisting of (a) a core,
Figure FDA00034215844300000510
is the corresponding coefficient vector;
thus, equation (16) can be written as
Figure FDA0003421584430000061
Wherein
Figure FDA0003421584430000062
Represents the norm of Frobenious,
Figure FDA0003421584430000063
is a kernel matrix where Kij＝K(zi,zj),Y＝[y1,…,yn]Is a pseudo label of the source domain label and the target domain, n ═ ns+ntTr (-) is the trace of the matrix;
formula (17) is written as
Figure FDA0003421584430000064
Wherein M iscIs a MMD matrix
Figure FDA0003421584430000065
Wherein
Figure FDA0003421584430000066
and
Figure FDA0003421584430000067
Respectively representing samples belonging to class c in a source domain and a target domain;
the formula (18) and the formula (19) are brought into the formula (13), and the objective function of the classifier is
Figure FDA0003421584430000068
By derivation, pair
Figure FDA0003421584430000069
To minimize the objective function, obtain the optimal solution as
α＝((E+λMc)K+σI)-1EYT (22)
The prediction information of the classifier can be obtained by bringing the formula (22) into the formula (17).
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