EEG Signal Classification Method Based on Metric Geometry Alignment Transfer Learning

Abstract

The present invention relates to an EEG signal classification method based on metric geometric alignment transfer learning. Metric learning is used to analyze the relationship between labeled samples and their neighboring samples and measure the similarity between the two. First, two projection matrices are used to map source domain samples and target domain samples into a shared subspace, and marginal probability distribution alignment and conditional probability distribution alignment are performed simultaneously. The distance between the source domain and the target domain is minimized to reduce the distribution difference, and the local structure is maintained by the Laplacian matrix. Then, the Mahalanobis distance metric is used to calculate the metric matrix for the labeled source domain samples in the shared subspace, so that the intra-class distance is minimized and the inter-class distance is maximized. Finally, the optimization target is obtained. The present invention has broad application prospects in EEG signal processing and brain-computer interface systems.

Description

Technical Field

[0001] The invention belongs to the field of pattern recognition and is a method for classifying electroencephalogram (EEG) signals using metric learning and local similarity. Background Art

[0002] Brain-computer interface technology (BCI) is an important means of realizing human-computer interaction through electroencephalogram (EEG) signal analysis. Emotion recognition is a typical paradigm in BCI technology. It uses EEG information to identify emotional states. In order to accurately identify the pattern of emotions, it is necessary to find a suitable algorithm to accurately describe the distribution of data structure. For this purpose, many machine learning algorithms have been applied to EEG signal analysis and can complete certain discrimination tasks.

[0003] To effectively distinguish distinct patterns in a set of EEG signals, numerous machine learning algorithms have been applied to classify them, including linear discriminant analysis, neural networks, support vector machines, nonlinear Bayesian classifiers, and nearest neighbor classifiers. However, due to external interference during signal acquisition and changes in neuronal function caused by brain plasticity, EEG signals are highly time-varying, non-stationary, and inter-individually heterogeneous. Furthermore, traditional supervised classifiers require a large amount of labeled EEG data for model training. Therefore, the design and implementation of EEG signal analysis models with strong adaptability, high recognition rates, and minimal user training time require further research. To further enhance the model's adaptability and stability, model training requires the inclusion of unlabeled EEG signals to address the issue of time-varying signals. Therefore, the use of semi-supervised algorithms for EEG signal analysis has become increasingly meaningful. Semi-supervised algorithms can simultaneously utilize information from both labeled and unlabeled samples for model training. Using information from unlabeled samples can better explore the data distribution of samples, thereby improving classification accuracy. In recent years, an increasing number of semi-supervised algorithms have been applied to EEG classification research. Nicolas-Alonso et al. utilized an adaptive semi-supervised classification method to address the non-stationary effects of multi-class motor imagery EEG signals. This method can gradually enhance model performance by adding unlabeled samples to training through online accumulation. To meet the requirements of online BCI analysis, a spectral regression and discriminant analysis method was used to reduce computational costs. Experimental results confirmed that the proposed analysis system has strong classification performance. Tian et al. combined clustering and popularity hypotheses and designed a transductive support vector machine (TSVM) using a multi-class kernel learning method. They applied this to EEG classification and achieved promising results. To analyze the relationship between EEG signals and emotional body expressions, Xu et al. used stacked autoencoders and semi-supervised deep belief networks to analyze the correlation between the two. Experimental results confirmed that this method can effectively extract EEG features related to emotional state and accurately distinguish them. These methods have achieved good results in EEG classification research, but as semi-supervised learning algorithms, they fail to adequately consider the impact of sample geometry distribution on the model.

[0004] When the source and target domains have different distributions, domain adaptation algorithms mitigate the performance degradation caused by domain transfer by learning a domain-invariant representation. Therefore, feature extraction methods with knowledge transfer capabilities have attracted widespread attention. Pan et al. proposed the Transfer Component Analysis (TCA) method, which aims to achieve cross-domain knowledge transfer by minimizing the maximum mean difference, narrowing the gap between the source and target domains while preserving the variance of the original data. Long et al. designed a Joint Distribution Domain Adaptation (JDA) algorithm that combines joint distribution with PCA to construct a low-dimensional feature subspace. This algorithm minimizes the marginal distribution and conditional probability distribution while iteratively optimizing labels. Wang et al. proposed the Balanced Distribution Adaptation (BDA) method, which adaptively exploits the importance of marginal and conditional probability distributions to mitigate data distribution differences. Zhang et al. proposed the Manifold Embedding Knowledge Transfer (MEKT) method, which first aligned the covariance matrix of EEG data on a Riemannian manifold and extracted features on the tangent space. This method performs domain adaptation by minimizing the joint probability distribution between the source and target domains while preserving the geometric structure of the original EEG data. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the present invention proposes a metric-based geometric alignment transfer learning method for EEG signal classification.

[0006] The present invention comprises the following steps:

[0007] Step (1) constructs the Mahalanobis metric matrix to maintain the separability of the source domain.

[0008] The formula for Mahalanobis distance is as follows:

[0009]

[0010] Among them, x i and x j is the differential entropy feature sample pair of EEG signal, M=A T A, is a positive semidefinite matrix;

[0011]

[0012]

[0013] M s Represents the measurement matrix of the source domain, M t represents the measurement matrix of the target domain; X s represents the source domain, X t represents the target domain; the optimization objectives are as follows:

[0014] min tr(MM s)+tr(M -1 M t ) (4)

[0015] The metric matrix A is used to map samples, source domain samples x i After mapping, we get x′ i , x′ i =x i A.

[0016] This metric learning is equivalent to finding a linear transformation by which the source domain is projected into a low-dimensional subspace while maintaining the separability of the source domain, that is, samples from the same class remain close, while samples from different classes are far away.

[0017] Step (2) uses the source domain and target domain data in the subspace to align the joint probability distribution.

[0018] The joint distribution MMD is used to calculate the joint distribution difference, directly considering the joint distribution of the source domain and the target domain instead of the traditional marginal distribution and conditional probability distribution. The joint distribution MMD is expressed as follows:

[0019]

[0020] in and denote the labeled data belonging to the cth category in the source domain and the target domain, respectively. and Represents the number of samples belonging to the cth class in the source domain and the target domain, N s and N t represents the number of samples in the source domain and the target domain, E and B are the transformation matrices in the latent space.

[0021] After encoding the source domain and target domain labels using one-hot encoding, we can get:

[0022]

[0023] Where X represents the labeled data in the source domain, and Z represents the labeled data in the target domain;

[0024]

[0025] Y s represents the label of the source domain, Y T The label representing the target domain;

[0026] Step (3): Construct the Laplace regularization term

[0027] The similarity of sample geometric properties is used to simulate the manifold geometry of the source and target domains.

[0028] The similarity between samples is:

[0029]

[0030] in, σ i For sample x i The distance between it and its nearest neighbor, N k (x i ) are k neighboring samples.

[0031] The Laplace regularization term is defined as follows:

[0032]

[0033] Where W is the value of ω ij The similarity matrix is composed of D, which is a diagonal matrix, and L u =DW.

[0034] Step (4) combines steps (1), (2) and (3) to obtain the final optimization objective function.

[0035] Combining the above regularization terms, the final optimization objective is expressed as follows:

[0036]

[0037] Where α is a trade-off parameter.

[0038] For the objective function established in Equation (10), matrix operations and an iterative optimization algorithm are used to learn the matrices M, E, and B. Specifically, during the iteration, the projection matrices E and B are first updated using gradient descent, followed by the metric matrix M. Thus, the objective function is updated in each iteration until its change is less than a predetermined threshold ε. For parameter α, a leave-one-out optimization method is proposed.

[0039] Finally, the emotional EEG signals are classified using the k-nearest neighbor classifier under the metric matrix M, and the emotional EEG features are divided into three categories: neutral, positive and negative.

[0040] Compared with existing emotion recognition EEG signal classification methods, the present invention has the following characteristics:

[0041] Using metric learning, a Mahalanobis metric matrix is constructed to maintain the separability of the source domain, keeping samples of the same type close and samples of different types apart. The local structure is preserved by the Laplacian matrix, and the similarity in the geometric properties of samples is exploited to simulate the manifold geometry of the source and target domains. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is an implementation flow chart of the present invention. DETAILED DESCRIPTION

[0043] The metric-based local linear embedding transfer learning method of the present invention is described in detail below with reference to the accompanying drawings. Figure 1 Implementation flowchart.

[0044] like Figure 1 The implementation of the method of the present invention mainly includes four steps: (1) constructing a Mahalanobis metric matrix in the source domain to maintain the separability of the source domain; (2) aligning the joint distribution MMD of the subspace source domain and the target domain; (3) constructing a Laplacian matrix to maintain the local structure; (4) combining various regularization terms to obtain the optimization target.

[0045] The following describes each step in detail.

[0046] Step (1) constructs the Mahalanobis metric matrix to maintain the separability of the source domain.

[0047] The formula for Mahalanobis distance is as follows:

[0048]

[0049] Among them, x i and x j is the differential entropy of any EEG signal, M = A T A, is a positive semidefinite matrix;

[0050]

[0051]

[0052] M s Represents the measurement matrix of the source domain, M t represents the measurement matrix of the target domain; X s represents the source domain, X t represents the target domain;

[0053] The optimization goals are as follows:

[0054] min tr(MM s )+tr(M -1 M t ) (4)

[0055] The metric matrix A is used to map samples, source domain samples x i After mapping, we get x′ i , x′ i =x i A.

[0056] Step (2) uses the source domain and target domain data in the subspace to align the joint probability distribution.

[0057] The joint distribution MMD is used to calculate the joint distribution difference, directly considering the joint distribution of the source domain and the target domain instead of the traditional marginal distribution and conditional probability distribution. The joint distribution MMD is expressed as follows:

[0058]

[0059] in and denote the labeled data belonging to the cth category in the source domain and the target domain, respectively. and Represents the number of samples belonging to the cth class in the source domain and the target domain, N s and N t represents the number of samples in the source domain and the target domain, E and B are the transformation matrices in the latent space.

[0060] After encoding the source domain and target domain labels using one-hot encoding, we can get:

[0061]

[0062] Where X represents the labeled data in the source domain, and Z represents the labeled data in the target domain;

[0063]

[0064] Y s represents the label of the source domain, Y T The label representing the target domain;

[0065] Step (3): Construct the Laplace regularization term

[0066] The similarity of sample geometric properties is used to simulate the manifold geometry of the source and target domains.

[0067] The similarity between samples is:

[0068]

[0069] in, σ i For sample x i The distance between it and its nearest neighbor, N k (x i ) are k neighbors

[0070] sample.

[0071] The Laplace regularization term is defined as follows:

[0072]

[0073] Where W is the value of ω ij The similarity matrix is composed of D, which is a diagonal matrix, and Lu =DW.

[0074] Step (4) combines steps (1), (2) and (3) to obtain the final optimization objective function.

[0075] Combining the above regularization terms, the final optimization objective is expressed as follows:

[0076]

[0077] Where α is a trade-off parameter.

[0078] For the objective function established in Equation (10), matrix operations and an iterative optimization algorithm are used to learn the matrices M, E, and B. Specifically, during the iteration, the projection matrices E and B are first updated using gradient descent, followed by the metric matrix M. Thus, the objective function is updated in each iteration until its change is less than a predetermined threshold ε. For parameter α, a leave-one-out optimization method is proposed.

[0079] Finally, the emotional EEG signals are classified using the k-nearest neighbor classifier under the metric matrix M, and the emotional EEG features are divided into three categories: neutral, positive and negative.

[0080] In summary, the present invention proposes a metric-based geometric alignment transfer learning method. Metric learning is used to analyze the relationship between labeled samples and their neighboring samples and measure the similarity between the two. First, two projection matrices are used to map the source domain samples and some labeled target domain samples into a shared subspace. At the same time, marginal probability distribution alignment and conditional probability distribution alignment are performed to minimize the distance between the source and target domains to reduce the distribution difference, and the local structure is maintained through the Laplacian matrix. Then, the Mahalanobis distance metric is used to calculate the metric matrix for the labeled source domain samples in the shared subspace, so that the intra-class distance is minimized and the inter-class distance is maximized. Finally, the emotional EEG signals are classified using the k-nearest neighbor classifier under the metric matrix M.

Claims

1. An EEG signal classification method based on metric-based geometric alignment transfer learning, characterized by: The method comprises the following steps: Step (1), construct the Mahalanobis metric matrix to maintain the separability of the source domain; The formula for Mahalanobis distance is as follows: Among them, x i ' and x j is any pair of differential entropy features of EEG signals, M=A T A, is a positive semidefinite matrix; M s Represents the measurement matrix of the source domain, M t represents the measurement matrix of the target domain; X s represents the source domain, X t represents the target domain; The optimization goals are as follows: min tr(MM s )+tr(M -1 M t )(4) The measurement matrix A is used to map samples, source domain samples x i 'After mapping, we get x i , x i =x i 'A; Step (2) uses the source domain and target domain data in the subspace to align the joint probability distribution; The joint distribution MMD is used to calculate the joint distribution difference, directly considering the joint distribution of the source domain and the target domain instead of the traditional marginal distribution and conditional probability distribution; the joint distribution MMD is expressed as follows: in and Represent the labeled data belonging to category c in the source domain and target domain respectively; and Represents the number of samples belonging to the cth class in the source domain and the target domain, N s and N t represents the number of samples in the source domain and the target domain, E and B are the transformation matrices in the latent space; After encoding the source domain and target domain labels using one-hot encoding, we can get: Where X represents the labeled data in the source domain, and Z represents the labeled data in the target domain; Y s represents the label of the source domain, Y T The label representing the target domain; Step (3): Construct the Laplace regularization term Utilize the similarity of sample geometric properties to simulate the manifold geometry of the source domain and the target domain; The similarity between samples is: in, σ i For sample x i The distance between it and its nearest neighbor, N k (x i ) are k neighboring samples; The Laplace regularization term is defined as follows: Where W is the value of ω ij The similarity matrix is composed of D, which is a diagonal matrix, and L u =DW; Step (4), combining steps (1), (2) and (3) to obtain the final optimization objective function; Combining the above regularization terms, the final optimization objective is expressed as follows: Where α is the trade-off parameter; For the objective function established by formula (10), matrix operations and iterative optimization algorithms are used to learn matrices M, E, and B. Specifically, in the iteration, the projection matrices E and B are first updated using the gradient descent method, and then the metric matrix M is updated. Thus, the value of the objective function is updated in each iteration until its change is less than a certain threshold ε. For the parameter α, the leave-one-out method is used to optimize the parameter. Finally, the emotional EEG signals are classified using the k-nearest neighbor classifier under the metric matrix M, and the emotional EEG features are divided into three categories: neutral, positive and negative.

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