Multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation

Abstract

The application discloses a multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation, and particularly relates to the technical field of machine learning, and is characterized in that, for EEG samples with labeled source domains and unlabeled target domains, a plurality of multi-view features are obtained through a plurality of feature extraction; after being mapped by a TSK-FS antecedent network, an inter-domain connection is constructed by using a transfer soft variable embedded consequent learning; a data structure is preserved through a local-global structure preservation term, so that the discriminative neighborhood relationship of original data is preserved to the greatest extent in the transfer process; a target function is constructed in combination with a multi-view learning strategy, and is iteratively optimized through an enhanced Lagrange multiplier algorithm, and finally, an output result is output by using a given classifier.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of machine learning, and particularly relates to a multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation. BACKGROUND

[0002] Motor imagery brain-computer interface (MI-BCI) system realizes intention decoding through pattern recognition of non-invasive multi-channel EEG signals, and shows broad application prospects in the fields of neural rehabilitation, prosthesis control and human-computer interaction. However, the traditional MI-EEG classification method (such as common spatial pattern (CSP) and LDA / SVM) only performs well under the same subject and the same data set, and is difficult to cope with the inherent non-stationary of EEG signal, a large amount of noise, inter-individual and cross-session / cross-data set distribution difference, resulting in significant decline of model generalization performance, and difficult to meet the actual application requirements.

[0003] In order to deal with the uncertainty and noise interference in EEG data, researchers introduce fuzzy system into the MI-EEG classification task. For example, the prior art (T. Nguyen, I. Hettiarachchi, A. Khatami, et al. Classification of multi-class BCI data by common spatial pattern and fuzzy system[J]. IEEE Access, vol. 6, pp. 27873-27884, 2018.) uses CSP combined with TSK fuzzy system to alleviate signal interference, and the prior art (E. Jiang, T. Huang, X. Yin. A combination of deep learning models and type-2 fuzzy for EEG motor imagery classification through spatiotemporal-frequency features[J]. Journal of Medical Engineering & Technology, vol. 48, no. 7, pp. 262-275, 2025.) proposes a deep fuzzy architecture combining Type-2 fuzzy activation function and Bayesian hyperparameter optimization, which greatly improves the classification accuracy. However, the existing TSK fuzzy classifier mostly relies on single domain data, directly regresses the label space through least squares or gradient descent, and the learning of consequent parameters is prone to overfitting, and lacks cross-domain adaptability.

[0004] As an effective means to alleviate the distribution difference between subjects and sessions, transfer learning has emerged a variety of strategies: global domain alignment based on maximum mean difference (MMD), marginal difference reduction using Riemann tangent space mapping, and dynamic construction of EEG channel functional connectivity graph through graph convolution network. However, these methods usually only focus on global distribution or local geometric alignment, ignoring the preservation of class discriminative structure, making it difficult to balance the local neighborhood relationship and global discriminative information of data, and the cross-domain performance is still limited.

[0005] At the same time, multi-view learning significantly enhances the MI-EEG classification performance by fusing multiple feature perspectives such as spatial domain (tangent space mapping), frequency domain (power spectral density), nonlinearity (multiscale entropy), and deep learning (MLP). For example, cross-frequency interaction framework, multi-view sparse learning, and Euclidean / Riemann manifold feature fusion method effectively capture complementary information. However, such methods rely on pre-defined frequency bands or channel subsets and static view weights, and cannot dynamically balance the contributions of different views in the cross-domain scenario, resulting in insufficient information utilization.

[0006] In summary, existing technologies have advantages in fuzzy classification, transfer learning, and multi-view learning, but cannot simultaneously solve the challenges of non-stationarity, uncertainty, and cross-domain generalization of EEG signals in a unified framework. How to construct a cross-domain fuzzy classifier that preserves discriminative structure, balances local and global, and dynamically optimizes multi-view contributions is the technical problem to be solved by the present invention. SUMMARY

[0007] To this end, the present invention provides a multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation. By closely integrating multi-view feature fusion with transfer learning and fuzzy reasoning, the present invention not only theoretically proposes a transfer soft variable embedding mechanism that balances local geometric structure and global discriminative information, but also significantly improves the classification robustness and generalization ability of MI-EEG signals across subjects, sessions, and datasets in practice, to solve the problems raised in the background technology.

[0008] To achieve the above purpose, the present invention provides the following technical solution: a multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation, comprising the following steps:

[0009] Step 1: For EEG samples with labeled source domain and unlabeled target domain, obtain multiple multi-view features through multiple feature extraction;

[0010] Step 2: After mapping by TSK-FS antecedent network, use transfer soft variable embedding-based consequent learning to construct inter-domain connections;

[0011] Step 3: The local neighborhood affinity between uniform samples in the fuzzy space is modeled by the inner graph to enhance the intra-class compactness, and the difference of inter-class samples is characterized by repulsive constraints, so as to realize the local structure preservation and global discrimination enhancement; the discriminative neighborhood relationship of the original data is preserved to the greatest extent in the migration process; a low-rank global regularization term is introduced to constrain the total rank of the source sub-class to realize the global data structure compactness in the soft variable space; the local discriminative structure matrix and the global low-rank constraint are integrated through the local-global structure preservation term to realize discriminative feature learning.

[0012] Step 4: The adaptive view fusion is realized by using Shannon entropy to measure the weight of each view, and the target function is constructed by integrating the posterior learning, local-global structure preservation and multi-view learning strategy, and the final output result is obtained by using the given classifier through the enhanced Lagrange multiplier algorithm iterative optimization.

[0013] Preferably, step 1 specifically comprises:

[0014] The labeled source domain and the unlabeled target domain obtain M multi-view feature representations through a plurality of feature extraction methods, and are respectively denoted as and , wherein the source domain and the unlabeled mth view can be specifically denoted as and , wherein and respectively represent the number of EEG samples in the two domains, , and the feature of each view is mapped to a new feature space through the antecedent network of TSK-FS, and according to the definition matrix, and are respectively converted into new features and , wherein the subscripts and correspond to the labeled source domain and the unlabeled target domain.

[0015] Preferably, step 2 specifically comprises:

[0016] The traditional fuzzy posterior parameter learning method directly maps the fuzzy features to the strict label space; in order to build the connection between the source domain and the target domain, and also to enhance the flexibility of feature expression, the source domain and the target domain are mapped to the soft variable space through the posterior learning:

[0017] (1);

[0018] , wherein is a regularization parameter, represents the posterior parameter, denotes the label association matrix, denotes the Frobenius norm square, measuring the difference between matrices; the first term of formula (12) ensures the fidelity of the fuzzy feature mapping; is the label matrix, is the transpose of the label matrix; the second term supervises the class separability of the soft variable matrix by the label matrix Y;

[0019] To bridge the gap between domains, a cross-domain linear representation is established:

[0020] (2);

[0021] wherein is the representation matrix connecting the source domain and the target domain to establish the inter-domain relationship;

[0022] To capture more cross-domain correlation, the low-rank constraint is adopted for ; the purposes are: (1) to improve the compactness of the cross-domain representation and realize the de-redundancy of knowledge transfer by using only the most representative source samples to sparsely reconstruct the target samples; (2) to induce to form a block diagonal structure, revealing the potential class structure in the soft variable space; in addition, since the number of classes is less than the number of training samples and the number of fuzzy rules, the soft variable matrix inherently satisfies the low-rank feature;

[0023] The consequent learning representation constructed based on this is:

[0024] (3);

[0025] wherein is a regularization parameter, denotes the matrix rank, 1 denotes a full 1 vector, and I denotes a unit matrix.

[0026] Preferably, step 3 specifically comprises:

[0027] Preserving the inherent local geometric structure and global discriminative information is crucial to improving cross-domain adaptability; therefore, the application enhances the local structure preservation and global discriminative enhancement by constructing the intrinsic graph of and the penalty graph of ; the intrinsic graph enhances the intra-class compactness by modeling the local neighborhood affinity between uniform samples in the fuzzy space, and the penalty graph characterizes the difference of heterogeneous samples by repulsion constraint, thereby realizing the local structure preservation and global discriminative enhancement in coordination;

[0028] the intrinsic graph are derived based on the k-nearest neighbor criterion, whose elements are defined as and , respectively,

[0029] (4) ;

[0030] (5) ;

[0031] where, denotes the vector representation of the j-th sample in the s-th source domain at the m-th view, i and j are sample indices, and the intrinsic graph and the penalty graph are employed to preserve the local geometry among cross-domain samples, ensuring that similar samples keep close while dissimilar samples are pushed apart;

[0032] The local structure preserving term is expressed as:

[0033] (6) ;

[0034] where, denotes the matrix trace; is the transpose of the posterior parameter; preserving the global structure of data is another key objective for subsequent parameter learning; to achieve compact global data structure in the soft variable space, a low-rank global regularization term is introduced to constrain the total rank of source sub-classes to approximate the global data rank in the soft variable space:

[0035] (7) ;

[0036] First, by employing global low-rank consistency, it inherently preserves the low-dimensional manifold structure, which is particularly important for handling unlabeled target domain data; second, by enforcing sub-class specific low-rank reconstruction within the source domain, it effectively reduces the intra-class distance and promotes the separation among sub-classes;

[0037] Thus the local-global structure preserving term is:

[0038] (8) ;

[0039] where, denotes the fuzzy feature matrix of the k-th sub-class in the s-th source domain at the m-th view mapped to the new feature space; denotes the union of the mapped features of the source and target domains;

[0040] The definition , is the local discriminant structure matrix of the mth view (m must be greater than or equal to 1 in theory, and greater than or equal to 2 in practice, and m is maximally taken as 4 in the present application), is the intrinsic graph Laplacian matrix and the difference between the penalty graph Laplacian matrix , which embodies the constraint requirements of local intra-class compactness and inter-class separation; formula (8) is:

[0041] (9).

[0042] Preferably, step 4 specifically comprises:

[0043] The pair-wise constraints on the result parameters of different views are used to facilitate the coordinated optimization of the feature transformation coefficient matrix :

[0044] (10) ;

[0045] Then, a view weight penalty term based on Shannon entropy is used to measure the weight of each view:

[0046] (11) ;

[0047] wherein is a view weight matrix;

[0048] Based on the back-end learning of the migration soft variable embedding, the local-global structure preservation and the multi-view learning strategy, the objective function of the multi-view transfer TSK fuzzy classifier MVT-TSK-SVSP is represented as:

[0049] (12) ;

[0050] wherein , and are regularization parameters;

[0051] Since the Rank function is non-convex and discrete, it is difficult to directly optimize equation (12), and therefore a kernel norm is used to replace the rank operation; equation (12) is written as:

[0052] (13) ;

[0053] According to the definition of the kernel norm, , wherein , . , wherein , , wherein .

[0054] To facilitate the model solution, an auxiliary variable is added and Equation (13) is written as:

[0055] (14);

[0056] Equation (14) is solved using the augmented Lagrange multiplier algorithm; the unconstrained optimization problem of equation (14) is written as,

[0057] (15);

[0058] The optimization process using the iterative strategy is as follows:

[0059] 1) Update : Simplify the optimization of equation (15) into the following subproblem:

[0060] (16);

[0061] We get:

[0062] (17);

[0063] 2) Update : Simplify the optimization of equation (15) into the following subproblem:

[0064] (18);

[0065] After rearrangement, equation (18) is expressed as:

[0066] (19);

[0067] We get:

[0068] (20);

[0069] Considering the constraint , since the constraint of column normalization , is expressed as .

[0070] 3) Update : Simplify the optimization of equation (15) into the following subproblem:

[0071] (21);

[0072] We can get,

[0073] (22);

[0074] 4) Update : Simplify the optimization of equation (15) to the following sub-problems Update :

[0075] (23);

[0076] where is a penalty parameter;

[0077] resulting in:

[0078] (24);

[0079] 5) Update : Simplify the optimization of equation (15) to the following sub-problems:

[0080] (25);

[0081] Let

[0082] resulting in:

[0083] (26);

[0084] 6) Update the Lagrange multiplier:

[0085] (27);

[0086] After the 1)-6) parameter iterations of the iterative strategy, the optimal solution of the consequent parameters and the perspective weight are obtained; for the unlabeled target domain samples , the final output result is ; the decision function is expressed as ; As a given classifier, the present application uses a nearest neighbor classifier.

[0087] The multi-channel spatial features, frequency domain power spectrum, nonlinear entropy features and perspective of deep learning extracted multi-element complementary information are dynamically weighted, and the shortcomings of traditional single perspective method in interactive modeling of signal diversity and complexity are solved; secondly, through low rank graph embedding and structure preserving constraint, the invention can preserve the discriminant neighborhood relationship of the original data to the greatest extent in the migration process, avoiding the degradation risk caused by ignoring the class structure in the conventional domain alignment method; thirdly, the introduction of soft variable embedding makes it possible to smoothly transition and adaptively correct the source domain knowledge in the target domain, greatly reducing the dependence on a large amount of labeled data, shortening the system calibration time and reducing user fatigue; in addition, the defuzzification output of the TSK fuzzy system combines nonlinear mapping and rule-based reasoning with strong interpretability, which is helpful for real-time decoding and real-time feedback control, and provides efficient, stable and transparent decision support for closed-loop BCI applications. Compared with the prior art, the present application not only technically breaks through the data distribution difference and uncertainty challenges faced by the existing MI-BCI cross-domain classification, but also lays a solid foundation for subsequent intelligent neural rehabilitation, prosthesis control and human-computer collaborative system development based on fuzzy migration and multi-perspective learning, has important theoretical value and wide application prospect.

[0088] Specifically includes:

[0089] 1. Multi-perspective feature soft variable embedding mechanism

[0090] For the first time, the spatial domain (CSP), the frequency domain (power spectrum density), the nonlinear entropy feature and the deep feature are uniformly mapped to the soft variable space of the Takagi-Sugeno-Kang fuzzy system, the contribution of each perspective in the classification decision is dynamically adjusted through adaptive weight learning, and the utilization efficiency of the complementary information of the MI-EEG signal is greatly improved.

[0091] 2. Local-global structure preservation of low-rank graph embedding

[0092] A multi-perspective local neighborhood and global discriminant structure preservation method based on low-rank graph regularization is proposed, which not only aligns the marginal distribution between the source domain and the target domain, but also strictly maintains the intra-class similarity and inter-class separability, realizing seamless migration of cross-domain discriminant structure.

[0093] 3. Perspective consistency cross-domain constraint

[0094] The perspective consistency loss term is innovatively introduced to constrain the soft variable representation of different perspectives on the same sample to remain consistent, effectively suppressing the overfitting phenomenon of a single perspective, and significantly improving the model robustness in cross-subject / cross-session scenarios.

[0095] 4. Migration soft variable driven consequent parameter reuse

[0096] In the TSK back-end parameter learning, the similarity weighting migration is performed on the learned back-end parameters of the source domain, the parameter training complexity under the small sample condition of the target domain is reduced, and the soft variable embedding is used to further correct the back-end output, thereby breaking the bottleneck of easy overfitting of the traditional least square regression.

[0097] 5. End-to-end alternating iterative optimization strategy

[0098] The application designs an efficient iterative algorithm combining alternating minimization and closed-form update solution, which can simultaneously optimize the fuzzy antecedent (membership degree parameter) and the back-end (linear regression parameter), avoids the problems of slow convergence and easy falling into local optimum of the common gradient descent, and realizes fast convergence and high precision.

[0099] 6. Real-time online decoding and incremental updating capability

[0100] For the closed-loop BCI application scenario, a perspective weight and back-end parameter fast updating method based on incremental learning is proposed, online fine-tuning is realized when new subjects or new session data arrive, and the real-time response capability of the system to the changes of the environment and the user state is ensured.

[0101] 7. Wide adaptability and scalability

[0102] The application has good modular design and can seamlessly connect other feature extractors (such as graph neural networks, time-frequency joint convolutional networks) and domain adaptation technologies, and is easy to extend to multi-task or multi-class MI-EEG classification, other bioelectric signal (such as MEG, sEMG) cross-domain decoding and other scenes.

[0103] The above jointly construct an end-to-end MI-EEG classification framework that takes into account multi-perspective information fusion, discriminative structure preservation and efficient cross-domain adaptation, significantly improves the generalization performance and real-time performance of the brain-computer interface system in a real environment, and meets the technical requirements of high performance, low delay and cross-domain robust decoding under the motor imagination task. BRIEF DESCRIPTION OF DRAWINGS

[0104] Figure 1 A fuzzy rule comparison schematic diagram of a BCI-2a data set provided by the application is shown in the figure;

[0105] Figure 2 A fuzzy rule comparison schematic diagram of an OpenBMI data set provided by the application is shown in the figure;

[0106] Figure 3 A fuzzy rule comparison schematic diagram of BCI-2a to OpenBMI provided by the application is shown in the figure;

[0107] Figure 4 A fuzzy rule comparison schematic diagram of OpenBMI to BCI-2a provided by the application is shown in the figure. DETAILED DESCRIPTION

[0108] The present application is herein described, by way of example only, with reference to embodiments thereof. It is to be understood that there is no intention to limit the application to the specific embodiments therein described, for this can be practiced with still other embodiments with recognition of the evident modifications that can be made therefore, without departing from the spirit of the application. It is therefore contemplated to cover by the present application any and all modifications coming within the scope of the present application.

[0109] TSK fuzzy model consists of three parts: antecedent part, consequent part and rule base. TSK can handle fuzzy input and fuzzy output, and make decisions through fuzzy reasoning. In classification problems, a multi-input multi-output rule is represented as,

[0110] (1) ;

[0111] where r (r = 1,..., R) represents the number of fuzzy rules. K and d represent the number of classes and dimensions of samples, respectively.

[0112] The antecedent of a rule is a set of fuzzy sets of input variables. The fuzzy set of the jth dimension of the rth rule is represented as . The consequent of a rule represents the deterministic value of the output variable. The consequent parameter , is the consequent parameter vector of the kth output in the rth rule.

[0113] In the first layer of the model, TSK model calculates the membership degree of each fuzzy set in the antecedent according to the input variables. Using Gaussian function, the membership function of the jth dimension of the mth fuzzy rule is represented as:

[0114] (2) ;

[0115] where and are the center and width of the membership function, respectively.

[0116] The second layer of the model is responsible for calculating the firing strength of fuzzy rules :

[0117] (3) ;

[0118] The third layer of the model is responsible for calculating the firing strength of defuzzified fuzzy rules . When using the normalization method, we can get,

[0119] (4) ;​

[0120] The 4th layer of the model is responsible for calculating the output of the fuzzy rules (fuzzy features), according to the fuzzy rule trigger intensity and the antecedent parameters, and the output of the 4th layer is

[0121] (5);

[0122] The following matrix is defined

[0123] (6);

[0124] (7);

[0125] (8);

[0126] The output result of the 5th layer of the model is represented as

[0127] (9);

[0128] For a classification problem, the class label of the test sample z is represented as the component corresponding to the maximum value of the K output nodes .

[0129] The TSK fuzzy model needs to optimize parameters related to the antecedent parameters and the consequent parameters C. The antecedent parameters are usually obtained using a clustering method. If Fuzzy C-means Clustering (FCM) is used, is equal to the FCM clustering center, The calculation formula of

[0130] (10);

[0131] where is the fuzzy membership obtained by clustering.

[0132] The traditional TSK fuzzy model usually uses gradient descent method to optimize the antecedent and consequent parameters. In recent years, some scholars use clustering method to optimize the antecedent parameters and least squares method to optimize the consequent parameters. This method has the characteristics of strong universality, good generalization ability and strong stability.

[0133] According to formula (4), the mapping of the original data set X in the fuzzy space is , where . Then, according to the least squares loss function, the optimization of the consequent parameters of the TSK fuzzy model is represented as

[0134] (11);

[0135] where is a regularization parameter.

[0136] The application provides a multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation, comprising the following steps:

[0137] Step 1: for the EEG samples of the labeled source domain and the unlabeled target domain, a plurality of multi-view features are obtained through a plurality of feature extraction methods;

[0138] In the MVT-TSK-SVSP model, the labeled source domain and the unlabeled target domain obtain M multi-view feature representations through a plurality of feature extraction methods, and are respectively denoted as and wherein the source domain and the unlabeled mth view can be specifically denoted as and wherein and denote the number of EEG samples in the two domains, denotes a sample set; the features of each view are mapped to a new feature space through the antecedent network of the TSK-FS, and according to formula (8), and are respectively converted into new features and wherein the subscripts and correspond to the labeled source domain and the unlabeled target domain.

[0139] Step 2: after being mapped through the TSK-FS antecedent network, a transfer soft variable embedding type consequent learning is adopted to construct the inter-domain connection;

[0140] The conventional fuzzy consequent parameter learning method directly maps the fuzzy features to a strict label space; in order to construct the connection between the source domain and the target domain and also to enhance the flexibility of feature expression, the source domain and the target domain are mapped to a soft variable space through consequent learning:

[0141] (12);

[0142] wherein is a regularization parameter, denotes a consequent parameter, denotes a label correlation matrix, denotes the square of the Frobenius norm, which measures the difference between matrices; the first term of formula (12) guarantees the fidelity of the fuzzy feature mapping; is a label matrix, is the transpose of the label matrix; the second term supervises the class separability of the soft variable matrix through the label matrix Y;

[0143] In order to bridge the gap between the domains, a cross-domain linear representation is established:

[0144] (13);

[0145] wherein is a representation matrix connecting source domain and target domain to establish inter-domain relationship;

[0146] To capture more cross-domain correlation, we adopt low-rank constraint on The purposes are: (1) to improve the compactness of cross-domain representation by using only the most representative source samples to sparsely reconstruct the target samples, to realize the de-redundancy of knowledge transfer; (2) to induce Block diagonal structure to reveal the potential class structure in the soft variable space; in addition, since the number of classes is less than the number of training samples and the number of fuzzy rules, the soft variable matrix inherently satisfies the low-rank feature;

[0147] The consequent learning representation constructed based on this is:

[0148] (14);

[0149] wherein is a regularization parameter, represents the rank of the matrix, 1 represents a full 1 vector, and I represents a unit matrix.

[0150] Step 3: Enhance the intra-class compactness by modeling the local neighborhood affinity between uniform samples in the fuzzy space through the intrinsic graph, and punish the graph to represent the difference of the different class samples through repulsion constraint, so as to realize the local structure preservation and global discriminant enhancement; reserve the data structure through the discriminant structure, realize the maximum reservation of the discriminant neighborhood relationship of the original data in the migration process; introduce a low-rank global regularization term to constrain the total rank of the source subclass to realize the global data structure compactness in the soft variable space; integrate the local discriminant structure matrix and the global low-rank constraint through the local-global structure preservation term to realize discriminant feature learning;

[0151] Reserving the inherent local geometric structure and global discriminant information is crucial to improve cross-domain adaptability; therefore, the present application constructs the intrinsic graph and the penalty graph , the intrinsic graph enhances the intra-class compactness by modeling the local neighborhood affinity between uniform samples in the fuzzy space, and the penalty graph represents the difference of the different class samples through repulsion constraint, so as to realize the local structure preservation and global discriminant enhancement;

[0152] The intrinsic graph and the penalty graph are obtained based on the k-nearest neighbor criterion, and the element and are defined as,

[0153] (15);

[0154] (16);

[0155] where, denotes the vector representation of the jth sample in the source domain s under the mth view, i and j are sample indices, and the intrinsic graph and the penalty graph are employed to preserve the local geometry among cross-domain samples, ensuring that similar samples keep close while dissimilar samples are pushed apart;

[0156] The local structure preserving term is denoted as:

[0157] (17);

[0158] where, denotes the matrix trace; is the transpose of the posterior parameter;

[0159] Preserving the global structure of data is another key objective for subsequent parameter learning; to achieve a compact global data structure in the soft variable space, a low-rank global regularization term is introduced, which constrains the total rank of source sub-classes to approximate the global data rank in the soft variable space:

[0160] (18);

[0161] First, by employing global low-rank consistency, it inherently preserves the low-dimensional manifold structure, which is particularly important for handling unlabeled target domain data; second, by enforcing sub-class specific low-rank reconstruction within the source domain, it effectively reduces the intra-class distance and promotes the separation among sub-classes;

[0162] Thus the local-global structure preserving term is:

[0163] (19);

[0164] where, denotes the fuzzy feature matrix of the sample set of the kth sub-class in the mth view of the source domain s mapped to the new feature space; denotes the union of the mapped features of the source and target domains;

[0165] Define , denotes the local discriminative structure matrix of the mth view, which is the intrinsic graph Laplacian matrix and the penalty graph Laplacian matrix the difference of the two, which satisfies the constraint of local intra-class compactness and inter-class separation; and equation (19) is:

[0166] (20).

[0167] Step 4: The feature transformation coefficient matrix is promoted to be optimized coordinately by using pair-wise constraints on the result parameters of different views, and adaptive view fusion is achieved by using Shannon entropy to measure the weight of each view. The target function is constructed by combining multi-view learning strategy with the integration of posterior learning and local-global structure preservation, and is iteratively optimized by enhanced Lagrange multiplier algorithm. Finally, the given classifier outputs the result.

[0168] In order to effectively utilize different features of MI-EEG and reduce the potential information loss in transfer learning, the designed fuzzy classifier introduces a multi-view learning mechanism which strengthens the consistency of semantic between views and dynamically balances the contribution of view-specific.

[0169] In particular, pair-wise constraints on the result parameters of different views are used to promote the coordinated optimization of the feature transformation coefficient matrix :

[0170] (21) ;

[0171] Then, a view weight penalty term based on Shannon entropy is used to measure the weight of each view:

[0172] (22) ;

[0173] wherein is the view weight matrix;

[0174] Based on the posterior learning of transfer soft variable embedding, local-global structure preservation and multi-view learning strategy, the target function of the multi-view transfer TSK fuzzy classifier MVT-TSK-SVSP is represented as:

[0175] (23) ;

[0176] wherein , and are regularization parameters;

[0177] Since the Rank function is non-convex and discrete, it is difficult to directly optimize equation (23), so the kernel norm is used to replace the rank operation; equation (23) is written as:

[0178] (24) ;

[0179] According to the definition of the kernel norm, where , . where , where .

[0180] To facilitate the model solution, auxiliary variables and are added, and equation (24) is written as:

[0181] (25);

[0182] Equation (25) is solved using the augmented Lagrangian multiplier algorithm; the unconstrained optimization problem of equation (25) is written as,

[0183] (26);

[0184] The optimization process using the iterative strategy is as follows:

[0185] 1) Update : Simplify the optimization of equation (26) into the following subproblem:

[0186] (27);

[0187] We get:

[0188] (28);

[0189] 2) Update : Simplify the optimization of equation (26) into the following subproblem:

[0190] (29);

[0191] After rearrangement, equation (29) is expressed as:

[0192] (30);

[0193] We get:

[0194] (31);

[0195] Considering the constraint , since the constraint of column normalization , is expressed as .

[0196] 3) Update : Simplify the optimization of equation (26) into the following subproblem:

[0197] (32);

[0198] can be obtained,

[0199] (33);

[0200] 4) Update : the optimization of formula (26) is simplified into the following sub-problems Update :

[0201] (34);

[0202] wherein is a penalty parameter;

[0203] obtained:

[0204] (35);

[0205] 5) Update : the optimization of formula (26) is simplified into the following sub-problems:

[0206] (36);

[0207] Let

[0208] obtained:

[0209] (37);

[0210] 6) Update the Lagrange multiplier:

[0211] (38);

[0212] After the 1)-6) parameter iterations of the iteration strategy, the optimal solution of the consequent parameter and the perspective weight is obtained; for the unlabeled target domain sample , the final output result is ; the decision function is expressed as ; As a given classifier, the present application uses a nearest neighbor classifier.

[0213] In order to comprehensively and objectively evaluate the classification performance of the MVT-TSK-SVSP model of the present application under the MI-EEG cross-person, cross-dataset and different configurations, the following evaluation indexes are mainly used:

[0214] (1) Accuracy. In this embodiment, the accuracy (ACC) is used as the evaluation index of the model performance. The average accuracy value is given for all cross-subject (BCI-2a, OpenBMI) and cross-dataset (BCI-2a→OpenBMI, OpenBMI→BCI-2a) experiments to measure the overall performance of different methods in each scenario. The accuracy refers to the proportion of the number of samples correctly predicted by the model to the total number of samples, reflecting the overall classification performance of the model. The calculation formula is:

[0215] ;

[0216] Where TP (True Positive) is the true class, indicating the number of samples correctly predicted as positive class by the model; TN (True Negative) is the true negative class, indicating the number of samples correctly predicted as negative class by the model; FP (False Positive) is the false positive class, indicating the number of samples incorrectly predicted as positive class by the model; FN (False Negative) is the false negative class, indicating the number of samples incorrectly predicted as negative class by the model.

[0217] (2) Cohen’s Kappa coefficient (Kappa). A statistical index that measures the consistency between the classification results of the model and random classification, which can eliminate the bias caused by accidental correctness, and thus more objectively reflects the reliability of the classifier. The Kappa value is reported in cross-subject and cross-dataset experiments to supplement the accuracy evaluation.

[0218] The experimental environment is the basic condition for conducting experiments, and the experimental environment of this embodiment is described as follows:

[0219]

[0220] The comparison methods in this embodiment are divided into three groups: multi-view learning, transfer learning, and multi-view transfer learning, including:

[0221] 1) MVFFR: a multi-view EEG representation method that combines multiple features with a multi-view feature fusion strategy.

[0222] 2) LR-CR²VS-TSK: a multi-view TSK fuzzy system that uses label relaxation and double sparse regularization (cross rule and cross view) to optimize fuzzy rule generation and subsequent parameter selection.

[0223] 3) METL: manifold embedding-based transfer learning, which synchronizes domain geometric structure alignment and classification parameter optimization.

[0224] 4) FWR-JPDA: A transfer learning method that integrates domain adaptation into feature extraction using a dual regularization strategy. It addresses the distribution difference in the cross-domain MI-EEG scenario.

[0225] 5) MMDA: Multi-manifold alignment transfer learning enhances cross-disciplinary classification by maximizing intra-class compactness and inter-class separability.

[0226] 6) MVTL-LSR: Multi-view transfer learning with latent space regularization ensures multi-view complementarity and cross-person knowledge transfer through consistency constraints.

[0227] 7) O-MV-T-TSK-FS: Online multi-view transfer TSK fuzzy system dynamically optimizes fuzzy rules and aligns cross-domain feature distribution to reduce individual differences.

[0228] In the experiment, the regularization parameter is searched in the range of The number of fuzzy rules in each view is searched in the range of The weighting factor is set to 2. The corresponding parameters in the comparison algorithm adopt their default settings. This embodiment uses classification accuracy and Kappa coefficient to evaluate the model performance.

[0229] A. Cross-person comparison experiment

[0230] This embodiment performs a cross-person comparison experiment by designating the MI-EEG data of one subject as the target domain and all remaining subject data as the source domain. The experimental results of the BCI-2a and OpenBMI datasets are summarized in Tables I and II, respectively. The evaluation of the two datasets shows that the proposed TSK classifier performs well in both average accuracy and Kappa coefficient. Specifically, on the BCI-2a dataset, the classifier of this embodiment improves the accuracy by 11.27% and the kappa gain by 0.1296 compared to the MVFFR method, while the accuracy and kappa are improved by 2.17% and 0.0320, respectively, compared to the O-MV-T-TSK-FS method. Similar results are observed on the OpenBMI dataset, where the classifier of this embodiment has an accuracy of 7.63% higher than MVFFR and a kappa of 0.1108 higher, and has an accuracy of 2.26% and a kappa of 0.0175 higher than O-MV-T-TSK-FS.

[0231] The comparative analysis shows that the multi-view transfer learning method is always superior to the traditional multi-view learning or traditional transfer learning single-modal method. The traditional multi-view learning is affected by the training bias due to the domain distribution difference and limited target domain samples, while the traditional transfer learning is difficult to handle linear feature concatenation, which ignores the nonlinear interaction and aggravates the dimension challenge. In contrast, the proposed TSK classifier integrates fuzzy classification, cross-domain adaptation and multi-view learning. Firstly, it replaces the traditional maximum mean discrepancy technology with the inter-domain linear representation by integrating graph embedding and low-rank constraint. The joint modeling framework simultaneously captures the local geometric relationship and global structural consistency in the data. Secondly, it combines an adaptive weighting mechanism to take advantage of the unique discriminative ability of multiple feature views while ensuring the consistency and collaboration advantage among views.

[0232] Table I Classification accuracy (%) and kappa of cross-subject experiments on BCI-2a dataset

[0233]

[0234] Table II Classification accuracy (%) and kappa of cross-subject experiments on OpenBMI dataset

[0235]

[0236] B. Cross-dataset experiments

[0237] This example performs cross-dataset comparison experiments by assigning the EEG data of all subjects in one dataset (e.g., BCI-2a or OpenBMI) as the source domain and the subject data in another dataset as the target domain. The experiment selects 21 subjects for evaluation. To implement the cross-dataset classifier training, systematic alignment processing is applied to the original MI-EEG data, including class space alignment (only left and right hands are retained in the BCI-2a dataset to ensure consistency of binary classification) and spatial topology coordination (22 common electrode channels are selected according to compatibility analysis of EEG cap configurations). Tables III and IV summarize the experimental results of BCI-2a to OpenBMI and OpenBMI to BCI-2a, respectively. As shown in Tables III and IV, compared with the cross-subject results in Tables I and II, the classification accuracy and Kappa of all algorithms are reduced. This performance degradation is due to the significant cross-dataset differences in EEG acquisition devices, experimental paradigms, subject physiology, and environmental conditions, coupled with the inherent inter-subject differences, which collectively amplify the challenges of EEG signal recognition. Despite these complexities, the proposed TSK fuzzy classifier achieves the highest classification accuracy and Kappa. Compared with the MVFFR with the lowest performance, our classifier improves the average accuracy by 11.13% and Kappa by 0.1296, while outperforming the second best O-MV-T-TSK-FS by 1.78% and 0.0280 in accuracy and Kappa, respectively.

[0238] Table III Classification accuracy (%) and kappa of BCI-2a to OpenBMI cross-dataset experiments

[0239]

[0240] Table IV Classification accuracy (%) and kappa of OpenBMI to BCI-2a cross-dataset experiments

[0241]

[0242] C. Analysis of the number of fuzzy rules

[0243] The number of rules largely determines the performance of the TSK fuzzy classifier, as it directly shapes the model’s interpretability and generalization ability. Since O-MV-T-TSK-FS is a multi-view transfer TSK model, this example compares it with the classifiers of this example. Their classification accuracy is compared with the number of rules adjusted from 2 to 12 in increments. The experimental results are as follows Figures 1-4The classification accuracy can be seen to vary with the number of rules in this embodiment. The MVT-TSK-SVSP classifier of this embodiment achieves the best accuracy with fewer rules, demonstrating its ability to balance simplicity and effectiveness.

[0244] The proposed MVT-TSK-SVSP classifier provides a breakthrough and effective approach to solve the MI-EEG classification challenge. By skillfully combining fuzzy classifiers, transfer learning, and multi-view learning techniques, this classifier achieves cross-domain distribution alignment, ensures multi-view consistency, and leverages complementary information to collectively improve the performance of MI-EEG classification. The core of this framework is the result learning mechanism of transfer soft variable embedding, which replaces the traditional label regression based on TSK rules with discriminative feature space construction. The proposed method significantly reduces the overfitting risk in cross-domain scenarios while preserving task-related information. In addition, the low-rank constraint local-global structure preservation mechanism of the embedding graph captures the domain-invariant global correlation and fine-grained local geometric patterns, ensuring robust knowledge transfer. The multi-view learning component combines maximum entropy regularization and view consistency constraints to dynamically optimize the view-specific contributions while maintaining inter-view consistency.

[0245] Two MI-EEG datasets were used in this embodiment: BCI Competition IV-2a (BCI-2a) and OpenBMI. The BCI-2a dataset contains MI-EEG data from nine healthy subjects performing four different motor imagery tasks (left hand, right hand, foot, and tongue movement). EEG signals were recorded using a 22-channel Ag / AgCl electrode cap at a sampling rate of 250 Hz. Each subject attended two sessions on different days, each session consisting of 6 runs. Data were extracted from the 2-6 second interval of the MI execution phase and downsampled to 250 Hz for subsequent analysis.

[0246] The OpenBMI dataset includes MI-EEG data from 54 subjects performing two classes of MI tasks (left hand and right hand). Each participant completed two sessions, each session involving 400 trials (100 trials per hand). A single trial consisted of a 3-second preparation phase and a 4-second execution phase. EEG signals were recorded using a 62-channel electrode cap at a raw sampling rate of 1000 Hz, which was then downsampled to 250 Hz. Similar to BCI-2a, the OpenBMI dataset analyzed data from a 4-second interval, covering the preparation and execution phases.

[0247] The experiment adopts a multi-dimensional feature extraction method to comprehensively characterize the EEG signals including four complementary perspectives. For the spatial domain features, the spatial relationship between electrode channels is analyzed using tangent space mapping (TSM), which captures the geometric patterns in the MI signal covariance structure. For the frequency domain features, the power spectral density (PSD) quantifies the energy distribution over the physiologically relevant frequency bands, revealing the oscillatory characteristics of the MI process. For the nonlinear features, the multiscale entropy (MDE) assesses the nonlinear dynamics, measuring the signal complexity variation across time scales to detect subtle neural state transitions. For the deep learning features, a multilayer perceptron (MLP) learns hierarchical temporal patterns from the raw EEG signals.

[0248] The present application combines multi-perspective feature fusion with transfer learning and fuzzy reasoning, not only theoretically proposes a transfer soft variable embedding mechanism that takes into account local geometric structure and global discriminative information, but also significantly improves the classification robustness and generalization ability of MI-EEG signals across subjects, sessions, and datasets in practice. First, the multi-channel spatial features, frequency domain power spectrum, nonlinear entropy features, and deep learning extraction perspectives of multi-complementary information are dynamically weighted, solving the shortcomings of traditional single perspective methods in interactive modeling of signal diversity and complexity. Second, through low-rank graph embedding and structure preserving constraints, the present application can preserve the discriminative neighborhood relationship of the original data to the greatest extent during the transfer process, avoiding the degradation risk caused by ignoring the class structure in conventional domain alignment methods. Third, the introduction of soft variable embedding makes it possible to smoothly transition and adaptively correct the source domain knowledge in the target domain, greatly reducing the dependence on a large amount of labeled data, shortening the system calibration time and reducing user fatigue. In addition, the defuzzification output of the TSK fuzzy system combines nonlinear mapping and rule-based reasoning with strong interpretability, which is helpful for real-time decoding and real-time feedback control, providing efficient, stable, and transparent decision support for closed-loop BCI applications. In summary, the present application not only technically breaks through the data distribution difference and uncertainty challenges faced by existing MI-BCI cross-domain classification, but also lays a solid foundation for subsequent intelligent neuro-rehabilitation, prosthetic control, and human-machine collaborative system development based on fuzzy transfer and multi-perspective learning, with important theoretical value and wide application prospects.

[0249] Although the present application has been described in detail in the foregoing description with general principles and specific embodiments, some modifications or improvements can be made to it on the basis of the present application, which is obvious to those skilled in the art. Therefore, these modifications or improvements made on the basis of not deviating from the spirit of the present application, all belong to the scope of protection claimed by the present application.

Claims

1. A multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation, characterized by: Includes the following steps: Step 1: For EEG samples with labeled source domain and unlabeled target domain, obtain multiple multi-view features through various feature extraction methods; Step 2: After mapping the TSK-FS preamble network, inter-domain connections are constructed using transfer soft variable embedded consequent learning; Step 3: Enhance intra-class compactness by modeling the local neighborhood affinity between uniform samples in the fuzzy space through the intrinsic graph, and characterize the differences between dissimilar samples through the exclusion constraint of the penalty graph, thereby synergistically achieving local structure preservation and global discrimination enhancement; By preserving the data structure through discriminative structure, the discriminative neighborhood relationships of the original data are preserved to the greatest extent during the migration process; a low-rank global regularization term is introduced to constrain the total rank of the source subclasses to achieve the compactness of the global data structure in the soft variable space; and a local-global structure preservation term is used to integrate the local discriminative structure matrix and the global low-rank constraint to achieve discriminative feature learning. Step 4: By pairwise constraints on the parameters of the results from different perspectives, the coordinated optimization of the feature transformation coefficient matrix is ​​promoted. Shannon entropy is used to measure the weight of each perspective to achieve adaptive perspective fusion. The objective function is constructed by integrating consequent learning, local-global structure preservation and multi-perspective learning strategies. The result is then iteratively optimized by the enhanced Lagrange multiplier algorithm and finally output using the given classifier.

2. The multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation according to claim 1, characterized in that: Step 1 specifically includes: The labeled source domain and the unlabeled target domain are each represented by M multi-view features using various feature extraction methods, denoted as follows: and The source domain and the m-th unlabeled view can be specifically represented as: and ,in and These represent the number of EEG samples in the two domains, respectively. This represents the sample set; the features of each viewpoint are mapped to a new feature space through the TSK-FS preflight network, according to the defined matrix. and Convert them into new features respectively and , where subscript and This corresponds to the tagged source domain and the untagged target domain.

3. The multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation according to claim 2, characterized in that: Step 2 specifically includes: To establish a connection between the source and target domains, and to enhance the flexibility of feature representation, consequent learning maps the source and target domains to a soft variable space: (1)； in, It is a regularization parameter. Indicates the consequent parameter. Represents the label association matrix. The square of the Frobenius norm is used to measure the difference between matrices; the first term in equation (1) guarantees the fidelity of the fuzzy feature mapping. It is a label matrix. It is the transpose of the label matrix; the second term supervises the soft variable matrix through the label matrix Y. Category separability; To bridge the differences between domains, a cross-domain linear representation is established: (2)； in It is a representation matrix that connects the source domain and the target domain to establish inter-domain relationships; The consequent learning representation constructed based on this is as follows: (3)； in It is a regularization parameter. Let represent the rank of the matrix, 1 represent a vector of all 1s, and I represent the identity matrix.

4. The multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation according to claim 3, characterized in that: Step 3 specifically includes: Inner Diagram and punishment picture All are obtained based on the k-nearest neighbor criterion, and their elements and They are defined as follows: (4)； (5)； in, This represents the vector form of the j-th sample in the source domain s from the m-th viewpoint, where i and j are sample indices, using an intrinsic graph. and punishment picture This preserves the local geometry between cross-domain samples, ensuring that new features of similar samples remain close, while features of different samples are pushed apart; The local structure preservation term is represented as: (6)； in, Represents the trace of a matrix; It is the transpose of the consequent parameter; to achieve a compact global data structure in the soft variable space, a low-rank global regularization term is introduced to constrain the total rank of the source subclass to approximate the global data rank in the soft variable space: (7)； Therefore, the discriminant structure, i.e., the local-global structure preservation term, is: (8)； in, It represents the fuzzy feature matrix that maps the sample set of the k-th subclass under the m-th view in the source domain s to the new feature space; This represents the set of features after mapping the source and target domains; definition , This represents the local discriminant structure matrix of the m-th viewpoint, where m is greater than or equal to 1, and is the intrinsic graph Laplacian matrix. With the penalty graph Laplace matrix The difference embodies the constraints of local intra-class compactness and inter-class separation; Equation (8) is: (9)。 5. The multi-view transfer interpretable method based on soft variable embedding and discriminative structure preservation according to claim 4, characterized in that: Step 4 specifically includes: Using pairwise constraints on the result parameters from different perspectives to facilitate the eigentransform coefficient matrix Coordination optimization: (10)； Then, a viewpoint weight penalty term based on Shannon entropy is used to measure the weight of each viewpoint: (11)； in It is the viewpoint weight matrix; Based on consequent learning through transfer soft variable embedding, local-global structure preservation, and multi-view learning strategies, the objective function of the multi-view transfer TSK fuzzy classifier MVT-TSK-SVSP is expressed as: (12)； in , and It is a regularization parameter; Due to the nonconvexity and discreteness of the rank function, it is difficult to directly optimize equation (12). Therefore, the nuclear norm is used to replace the rank operation; equation (12) is written as: (13)； According to the definition of nuclear norm, , in , . , in , , in . To facilitate model solving, auxiliary variables are added. and Equation (13) can be written as: (14)； Equation (14) is solved using the enhanced Lagrange multiplier algorithm; the unconstrained optimization problem of equation (14) is written as follows: (15)； in, , , All are Lagrange multipliers; The optimization process using the iterative strategy is as follows; 1) Update The optimization of equation (15) can be simplified into the following subproblems: (16)； get: (17)； 2) Update The optimization of equation (15) can be simplified into the following subproblems: (18)； After rearrangement, equation (18) can be expressed as: (19)； get: (20)； Considering constraints Due to column normalization constraints , Represented as . 3) Update The optimization of equation (15) can be simplified into the following subproblems: (21)； It can be obtained, (22)； 4) Update The optimization of equation (15) is simplified into the following subproblem: Update : (23)； in It is a penalty parameter; get: (24)； 5) Update The optimization of equation (15) can be simplified into the following subproblems: (25)； Let ; get: (26)； 6) Update the Lagrange multiplier: (27)； After iterating through parameters 1)-6) of the iterative strategy, the consequent parameters are obtained. and perspective weight The optimal solution for unlabeled target domain samples; The final output result is The decision function is expressed as follows: ; As a given classifier.

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