A multi-modal brain network feature classification method based on multiple data centers

Abstract

The application discloses a multi-modal brain network feature classification method based on multiple data centers, carries out preprocessing on each modality brain image data of multiple different data centers; extracts parameters in the preprocessed image, constructs each brain network; splices and aggregates the upper triangular elements of each brain network into each connection aggregation matrix; sets multiple data centers as a target domain and a source domain; uses a hypergraph-based multi-source domain adaptive algorithm to convert the sample distribution in the source domain into consistency with the target domain, and combines it with the sample in the target domain; uses a multi-task feature selection algorithm based on local ordered structure for feature selection; and uses a support vector machine algorithm based on multi-kernel learning for classification on the selected discriminant features. The method reduces the heterogeneity of multi-center brain network feature distribution; uses multi-kernel learning to fuse functional networks and structural networks to better assist brain network feature classification, and has important application value for studying cognitive function and structural disorders of the brain.

Description

Technical Field

[0001] This invention relates to biomedical image information processing, specifically to a multimodal brain network feature classification method based on multiple data centers. Background Technology

[0002] The human brain is an extremely complex system found in nature. Various neurons are connected through synapses, forming a highly complex network. Therefore, the brain network is the structural basis for various physiological and cognitive activities. With the advancement of science, the development of brain imaging technology has provided a broad platform for brain network research. Currently, researchers mainly use functional magnetic resonance imaging (fMRI) and structural magnetic resonance imaging (sMRI) to construct functional and structural networks, respectively, to study the brain. fMRI has advantages such as high spatial resolution and non-invasiveness, while sMRI images brain tissue structures by observing the distribution of proton density within the brain, thereby obtaining morphological data of the brain tissue. Both technologies are widely used in brain network research and the auxiliary diagnosis of brain diseases, and are of great significance to the development of human brain science research.

[0003] Functional networks integrate the functions of different neuronal groups or brain regions through correlations, recording the dynamic coordination of signals between different brain regions through functional connections. Structural networks, on the other hand, identify connections between brain regions based on morphological correlations, and structural connections are the material basis of network connectivity in the brain. Various neuronal activities are transmitted to the whole brain through structural networks, producing synergistic effects. Studying functional networks can explore the functional organization patterns of the human brain, helping to understand the functional activity patterns of the brain in normal or diseased states; studying structural networks helps to reveal the topological properties of the human brain's structural networks. Integrating these two types of brain network research can further accelerate human exploration of the brain, enabling a more comprehensive analysis and understanding of the pathophysiological mechanisms of brain diseases.

[0004] In recent years, data sharing has shown a growing trend, with numerous medical databases being publicly released worldwide to address various health issues. While the development of multicenter medical imaging databases has facilitated access to data to some extent, analyzing multicenter data remains challenging. Multicenter data originates from diverse sources, and most methods assume that the data comes from the same distribution. This means existing methods ignore the data heterogeneity caused by differences in scanning equipment or imaging parameters between different centers, thus failing to effectively handle heterogeneous multicenter data. This not only reduces the statistical power of the data but also weakens the credibility of multicenter data analysis research.

[0005] Existing research on multi-center heterogeneous data can be broadly categorized into two types. One type involves learning a model separately for each center and then integrating them, but this approach ignores the heterogeneity between the multi-center data. The other type addresses multi-source domain adaptation, where a model is first trained on data from different source domains, and then tested on the target domain. Unsupervised low-rank representation has been proposed for domain adaptation, transforming source domain data into the target domain using low-rank representation for subsequent learning tasks. However, existing methods neglect the complex relationships between data from different source domains, i.e., higher-order relationships, which may contain useful information to improve classification or regression performance.

[0006] In the field of machine learning, multimodal learning has attracted widespread interest from researchers. In medical imaging, researchers have begun to utilize multimodal data for disease diagnosis and analysis. Integrating data from multiple modalities can provide necessary complementary information, thereby helping to improve the diagnostic accuracy of brain diseases. Feature selection is often used to remove redundant or irrelevant features from multimodal data; however, due to the complexity of the brain and brain diseases, detecting all disease-related features from single-modal data is extremely difficult. Since different modalities reflect the same underlying pathology, they may provide complementary information to help identify abnormal brain regions. Current research explores the joint selection of features from multimodal data; however, due to the heterogeneity of different subjects with the same brain disease, considering only the relationship between data and subject labels for feature selection cannot effectively uncover the complex intrinsic relationships within the data. Furthermore, data acquisition often involves the simultaneous use of multiple imaging devices, making samples from different categories very similar in certain modalities. Features extracted using general methods are prone to repetition or similarity, resulting in low discriminative power. Summary of the Invention

[0007] Purpose of the invention: To address the above-mentioned shortcomings, this invention provides a multimodal brain network feature classification method based on multiple data centers to reduce data heterogeneity.

[0008] Technical Solution: To solve the above problems, this invention employs a multimodal brain network feature classification method based on multiple data centers, comprising the following steps:

[0009] (1) Collect brain imaging data of each modality from multiple data centers and preprocess them respectively to obtain preprocessed images of each modality in each data center;

[0010] (2) The obtained preprocessed images are divided into brain regions based on a standardized brain partitioning template. Each brain region is divided into N brain regions, and each brain region corresponds to a node in the brain network.

[0011] (3) Extract parameters from each modality of preprocessed images in each data center and construct brain networks for each modality respectively;

[0012] (4) Concatenate the upper triangular elements of each brain network into a single network with dimension [missing information]. The connection vectors; and combine all connection vectors of the same mode in each data center into a connection aggregation matrix;

[0013] (5) Select one data center as the target domain and other data centers as the source domains. Divide the connection vectors of the connection aggregation matrix in the target domain and the source domain into training sets and test sets respectively. Use the hypergraph-based multi-source domain adaptive algorithm to solve for a transformation matrix in the training set of each source domain. Transform the distribution of connection vectors in multiple source domains into the same distribution as the connection vectors in the target domain through the transformation matrix. Combine the transformed training sets in the source domains with the training sets in the target domain to form the final connection training sets for each modality.

[0014] (6) Use a multi-task feature selection algorithm based on local ordered structure to train the model and select features in the final modal connection training set; based on the model trained in the training set and the selected features, select discriminative features in the target domain test set;

[0015] (7) The selected discriminant features are classified using a support vector machine algorithm based on multi-kernel learning, and the final classification result is obtained.

[0016] Furthermore, in step (1), brain functional magnetic resonance imaging and brain structural magnetic resonance imaging are acquired from multiple data centers; brain gray matter images are obtained after preprocessing the brain structural magnetic resonance imaging.

[0017] The standardized brain partition templates in step (2) include the AAL partition template and the Brodmann partition template.

[0018] In step (3), the brain networks of each modality include brain functional networks and brain structural networks. For functional magnetic resonance images of the brain from different data centers, the average time series of different brain regions are extracted, the correlation coefficient between the average time series of each pair of brain regions is calculated, and the brain functional network of each subject is constructed. For gray matter images of the brain from different data centers, the probability density function of gray matter volume values ​​of all voxels in each brain region is estimated using the kernel density estimation method. Then, the Jensen divergence between the probability density functions of gray matter volume of each pair of brain regions is calculated. The Jensen divergence is defined as the connection weight of the structural network to evaluate the similarity of gray matter volume of different brain regions, thereby constructing the brain structural network of each subject.

[0019] The formula for calculating the Jensen divergence is as follows:

[0020]

[0021] In the formula, and Let represent the probability distributions of gray matter volumes in brain regions P and Q, respectively. and The corresponding probability density function is and D KL (.||.) represents the KL divergence between the probability density functions of gray matter volumes of any two brain regions. and The formula for calculating the KL divergence between them is:

[0022]

[0023] Furthermore, in step (5), the objective function of the m-th modality in the hypergraph-based multi-source neighborhood adaptive algorithm is as follows:

[0024]

[0025] In the formula, ||.|| * Let ||.|| be the nuclear norm of the matrix. 2,1 For matrix l 2,1 Norm, tr(.) is the trace operation of a matrix. D is the feature matrix of the training set of the target domain. m N represents the number of features of the m-th mode. T The number of training sets in the target domain. Let i = 1, ..., S be the feature matrix of the i-th source domain training set. Let be the number of training sets in the i-th source domain. Let N be the reconstruction coefficient matrix for all source domains. SLet be the number of training sets in all source domains. For the error matrix of all source domains, Let be the transformation matrix of the i-th source domain. Let be the Laplacian matrix of the hypergraph, where τ and λ are regularization parameters for the balance trinomials.

[0026] Calculate the hypergraph G of the training set in all source domains, and solve for L. h Then, by solving equation (3) using the augmented Lagrange multiplier method, we obtain Z. m E m , The optimal solution, through Transform the data in the corresponding source domain to the target domain.

[0027] Furthermore, the specific content of the locally ordered structure in step (6) is as follows: For the feature matrix X, its representation in the low-dimensional space after projection is R = WX, where W is the projection matrix of X, and a triple (xi) in X is... i ,x u ,x v The triple mapped to a lower-dimensional space can be represented as (r i ,r u ,r v The locally ordered structure can be equivalent to the following optimization problem:

[0028]

[0029] In the formula, x u and x v For x i The neighboring nodes, For x i The set of k nearest neighbors, Let dist(.,.) be the adjacency matrix, and dist(.,.) be the distance metric; Equation (4) is equivalent to min W tr(W T XLX T W); where, D is a diagonal matrix, and S is a distance matrix.

[0030] Combining the above optimization problem with feature selection and then performing joint optimization, the objective function is as follows:

[0031]

[0032] In the formula, Y is the label vector of all training sets, and X... m W represents the feature matrix of the final connection training set after combination. m For X mThe projection matrix is ​​given by α and β, where α and β are regularization parameters of the balanced three terms. Equation (5) is solved using an accelerated approximate gradient algorithm to obtain the coefficient matrix W. m The coefficient matrix W obtained by solving m The sum of squares of each row is used to obtain a column vector P. The features corresponding to values ​​greater than or equal to 0.01 in column vector P are selected to obtain discriminative features.

[0033] Furthermore, the specific classification steps in step (7) are as follows:

[0034] (1) Calculate a linear kernel matrix for each mode;

[0035] (2) Combine the linear kernel matrices of multiple modes using the following formula:

[0036]

[0037] In the formula, It is the m-th modal connection vector x i and connect vector x j kernel function, α m Let be non-negative weight parameters, and satisfy ∑ m α m =1 constraint; find α by using a grid search strategy on the training set. m The optimal value;

[0038] (3) Use the support vector machine algorithm to classify the merged hybrid kernel matrix.

[0039] Beneficial Effects: Compared with existing technologies, the significant advantage of this invention is that it utilizes a multi-source domain adaptive method based on low-rank representation to transform samples from multiple data source domains into the feature space of the target domain. Furthermore, it introduces a hypergraph Laplacian matrix, which reflects the higher-order relationships between different data centers, effectively reducing the heterogeneity of features in multimodal, multi-center brain networks. By employing a multimodal feature selection method based on locally ordered structures and using multi-kernel learning to fuse functional and structural networks to better assist in the identification of brain disease features, this invention has significant application value for studying cognitive and structural impairments in the brain. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the multimodal brain network feature classification method of the present invention. Detailed Implementation

[0041] like Figure 1 As shown in this embodiment, a multimodal brain network feature classification method based on multiple data centers includes the following steps:

[0042] (1) fMRI and sMRI data were obtained from a public dataset, which included data from multiple data centers. For the fMRI data, the SPM12 toolbox in Matlab 2018 was used for preprocessing, including head movement correction, temporal correction, registration, spatial normalization, and smoothing. Finally, low-frequency filtering was performed to reduce low-frequency drift and high-frequency biological noise. Similarly, the SPM12 toolbox was used to preprocess the T1 structural images of the sMRI data. Voxel morphology (VBM) analysis was used in SPM12 to automatically perform examination, tissue segmentation, normalization, modulation, and smoothing to obtain gray matter images of each subject. In this embodiment, fMRI and sMRI data were obtained from the FBIRN dataset, including 152 normal subjects and 154 subjects with schizophrenia (SZ). The determination of normal and SZ subjects was based on the DSM-IV diagnostic criteria. The selected subjects came from six data centers (centers 3, 9, 10, 12, 13, and 18, respectively), and the low-frequency filtering range in fMRI preprocessing was 0.01 Hz to 0.08 Hz.

[0043] (2) A standardized brain partitioning template (such as the AAL partitioning template and the Brodmann partitioning template) was selected to match the preprocessed functional magnetic resonance imaging (fMRI) images and brain gray matter images of each subject, and the images were divided into N brain regions, each corresponding to a node in the brain network. In this embodiment, the AAL partitioning template was selected to divide the brain into 90 brain regions (45 in each hemisphere), i.e., N=90, and the 90 brain regions correspond to 90 nodes in the brain network.

[0044] (3) For functional magnetic resonance images from different data centers, the average time series of different brain regions were extracted, and the correlation coefficient between the average time series of each pair of brain regions was calculated to construct the brain functional network for each subject. For gray matter images from different data centers, the probability density function of gray matter volume values ​​of all voxels in each brain region was estimated using the kernel density estimation method. Then, the Jensen divergence between the probability density functions of gray matter volume of each pair of brain regions was calculated. The Jensen divergence was defined as the connection weight of the structural network to evaluate the similarity of gray matter volume in different brain regions, thereby constructing the brain structural network for each subject. The formula for Jensen divergence is as follows:

[0045]

[0046] In the formula, and These are the probability distributions of gray matter volumes in brain regions P and Q, respectively. and The corresponding probability density function is and D KL (.||.) represents the KL divergence between the probability density functions of gray matter volumes of any two brain regions. and The formula for calculating the KL divergence between them is:

[0047]

[0048] In this embodiment, both the functional network and the structural network are 90×90 in size, with the element values ​​of the functional network being [-1,1] and the element values ​​of the structural network being [0,1].

[0049] (4) Concatenate the upper triangular elements of each functional network and structural network into a single network with dimension [missing information]. The vectors are the functional connection vector and the structural connection vector. In this embodiment, the dimension of both the functional connection vector and the structural connection vector is 4005.

[0050] (5) Combine the functional connectivity vectors and structural connectivity vectors of all subjects in different data centers to form functional connectivity aggregation matrices and structural connectivity aggregation matrices representing the data center, respectively. In this embodiment, the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 3rd center is 45×4005, the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 9th center is 59×4005, the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 10th center is 57×4005, the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 12th center is 61×4005, the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 13th center is 56×4005, and the size of the functional connectivity aggregation matrix and structural connectivity aggregation matrix of the 18th center is 28×4005.

[0051] (6) Select one data center as the target domain and the other data centers as the source domains. Divide the data in the target domain and the source domains into training sets and test sets respectively. Use a hypergraph-based multi-source domain adaptation algorithm to solve for a transformation matrix in the training set of each source domain. Transform the sample distribution in multiple source domains into a distribution consistent with that in the target domain through the transformation matrix. Combine the transformed training sets in the source domains with the training sets in the target domain to form the final functional connectivity training set and structural connectivity training set. In this embodiment, the third center is used as the target domain and the other centers are used as the source domains. Five-fold cross-validation is used to divide the training set and test set for functional connectivity and structural connectivity. When constructing the hypergraph, the k-Nearest Neighbor (KNN) algorithm is used to select the 7 vertices closest to the center vertex to form a hyperedge. The hyperparameter values ​​in the domain adaptation algorithm are all in the range of [0.010.1 1 10 100]. The grid search method is used to select the optimal parameters within the range of hyperparameter values.

[0052] In the hypergraph-based multi-source neighborhood adaptation algorithm, the objective function for the m-th mode is as follows:

[0053]

[0054] In the formula, ||.|| * Let be the nuclear norm of the matrix; ||.|| 2,1 For matrix l 2,1 Norm; tr(.) is the trace operation of a matrix; D is the feature matrix of the training set in the target domain; m N represents the number of features of the m-th mode; T The number of training sets in the target domain. i = 1, ..., S is the feature matrix of the i-th source domain training set; Let be the number of training sets in the i-th source domain; N is the reconstruction coefficient matrix for all source domains; S The number of training sets in all source domains; Let be the error matrix for all source domains; Let be the transformation matrix of the i-th source domain; The Laplacian matrix of the hypergraph;

[0055] For L h To solve this problem, we compute the hypergraph G of the training set in all source domains; G(V,C,A) consists of the set of vertices V, the set of hyperedges C, and the set of weights of each hyperedge A, where each hyperedge C... i They are all assigned a weight a(c) i For a hypergraph G, the incidence matrix Used to represent the relationship between each vertex and a hyperedge, defined as follows:

[0056]

[0057] Based on the incidence matrix M, the degree of each vertex and the degree of each hyperedge in the hypergraph are defined as follows:

[0058] d(v)=∑ c∈C a(c)M(v,c) (5

[0059] d(c)=∑ v∈V M(v,c) (6

[0060] The Laplacian matrix of the hypergraph can be obtained from equations (5) and (6), as shown below:

[0061] L h =I-Θ(7)

[0062] In the formula, L h I is the Laplacian matrix of the hypergraph, and I is the identity matrix. The solved L h In the algorithm of input formula (3), the solution method of formula (2) is the augmented Lagrange multiplier method; once Z is obtained m E m , The optimal solution can be found by... The data in the corresponding source domain is transformed to the target domain, and the training set in the transformed source domain and the training set in the target domain are combined to form the final training set.

[0063] (7) A multi-task feature selection algorithm based on local ordered structure is used to train the model and select features in the functional connectivity training set and the structural connectivity training set, and to select discriminative features in the functional connectivity test set and the structural connectivity test set. In this embodiment, the hyperparameter values ​​in the multi-task feature selection algorithm are all in the range of [0.01 0.11 10 100], and the optimal parameters are selected using a grid search method within the range of hyperparameter values.

[0064] The specific content of the locally ordered structure is as follows:

[0065] 1) Define R = WX as the projection of X into a low-dimensional space, where X is the feature matrix composed of n samples, and W is the projection matrix of X; define a triple (x i ,x u ,x v ) by x i and its neighbor node x u and x v The triplet, mapped to a lower-dimensional space, can be represented as (r i ,r u ,r v Define dist(.,.) as a distance metric, where dist(x) = ... i ,x u )≤dist(x i ,x v When ), there is dist(r) i ,r u )≤dist(r i ,r v If x i The locally ordered structure is preserved, and this locally ordered structure is beneficial to x. i The classification is necessary; otherwise, the structure is not conducive to x. i The classification; locally ordered structures can be equivalent to the following optimization problem:

[0066]

[0067] In the formula, For x i The set of k nearest neighbors, It is an adjacency matrix;

[0068] 2) Solve The elements in the text are accessed using the following methods:

[0069]

[0070] In the formula,

[0071] 3) Embed F in equation (9) into the mapping process to obtain the distance matrix S:

[0072]

[0073] Equation (8) is redefined as:

[0074]

[0075] Use S i,u Substitution formula (11) yields:

[0076]

[0077] 4) Combine the two equations in equation (12) into:

[0078]

[0079] Equation (13) can be rewritten as:

[0080]

[0081] Equation (14) can also be equivalent to min W tr(W T XLX T W), where D is a diagonal matrix.

[0082] Combining the above optimization problem with feature selection and then performing joint optimization can preserve the locally ordered structure and perform effective feature selection; since different modes have related and similar structures, l is added to the final objective function. 2,1 The norm regularization term, combined with the sparsity feature, gives the overall objective function as shown in equation (15):

[0083]

[0084] In the formula, Y is the label vector of all training sets. The accelerated approximate gradient algorithm is used to solve equation (15). When selecting common features associated with the task, the sum of squares of each row of the coefficient matrix W obtained by the solution is used to obtain the column vector P. If the value in the column vector P is greater than or equal to 0.01, the feature corresponding to this value is selected, thereby selecting the discriminative feature in the two modality test sets.

[0085] (8) The features selected from the functional connectivity test set and the structural connectivity test set are used to classify patients with brain diseases and normal people using a support vector machine algorithm based on multi-kernel learning, and the final classification results are obtained.

[0086] The specific steps are as follows:

[0087] 8.1) Calculate a linear kernel matrix for each mode;

[0088] 8.2) Merge kernel functions for multiple modes; the merging method is as follows:

[0089]

[0090] In the formula, It is the m-th modal sample x i and sample x j kernel function, α m It is a non-negative weight parameter, and satisfies ∑ m α m =1 constraint; find α by using a grid search strategy on the training set. m The optimal value;

[0091] 8.3) Use the support vector machine algorithm on the merged hybrid kernel to classify patients with brain diseases and normal people.

[0092] In this embodiment, the linear kernel support vector machine is implemented using the LIBSVM toolbox, with a search step size of 0.1 in multi-kernel learning. In classification, SZ subjects are generally used as positive class samples, and normal subjects as negative class samples. Four evaluation metrics—accuracy (ACC), sensitivity (SEN), specificity (SPE), and area under the curve (AUC)—are used to measure classification performance. The classification results are validated by repeatedly performing five 5-fold cross-validation steps.

[0093] Tables 1 and 2 show the classification performance of the embodiments of the present invention on the Function Biomedical Informatics Research Network (FBIRN) dataset, comparing the performance of a multi-task feature selection algorithm based solely on locally ordered structures with other multi-task feature selection algorithms, as well as the combined performance of a hypergraph-based multi-source domain adaptation algorithm with other multi-task feature selection algorithms. The comparison methods are as follows: Functional connectivity classification (FC(single)), Structural connectivity classification (SC(single)), Feature selection and classification using ttest (ttest), Feature selection and classification using Lasso (Lasso), Feature selection and classification using a multi-task feature selection algorithm (M3L), Feature selection and classification using a manifold-regularized multi-task feature selection algorithm (M2TFS), Feature selection and classification using a hypergraph-regularized multi-task feature selection algorithm (HMTFS), Feature selection and classification using a discriminative multi-task feature selection algorithm (DMTFS), Feature selection and classification using a clustering-based multi-task feature selection algorithm (CMTFS), and Feature selection and classification using an adaptive similarity-based multi-task feature selection algorithm. The FBIRN dataset contains 318 participants, including 161 participants with schizophrenia (SZ) and 157 normal participants. All participants were recruited from seven data centers (3, 7, 9, 10, 12, 13, 18). Data from center 7 was omitted to prevent overfitting due to its limited data. Tables 1 and 2 show that, compared to other multi-task feature selection algorithms, the locally ordered structure-based multi-task feature selection algorithm achieved the best classification performance. Furthermore, incorporating a hypergraph-based multi-source domain adaptation algorithm further demonstrates the effectiveness of the multi-source domain adaptation algorithm and the superiority of the multi-task feature selection algorithm used in this implementation.

[0094] Table 1. Classification performance of different multi-task feature selection algorithms

[0095]

[0096] Table 2 shows the classification performance of the combined hypergraph-based multi-source domain adaptation algorithm and other multi-task feature selection algorithms.

[0097]

Claims

1. A multimodal brain network feature classification method based on multiple data centers, characterized in that, Includes the following steps: (1) Collect brain imaging data of each modality from multiple data centers and preprocess them respectively to obtain preprocessed images of each modality in each data center; (2) The obtained preprocessed images are divided into brain regions based on a standardized brain partitioning template. Each brain region is divided into N brain regions, and each brain region corresponds to a node in the brain network. (3) Extract parameters from each modality of preprocessed images in each data center and construct brain networks for each modality respectively; (4) Concatenate the upper triangular elements of each brain network into a single network with dimension [missing information]. The connection vectors; and combine all connection vectors of the same mode in each data center into a connection aggregation matrix; (5) Select one data center as the target domain and the other data centers as the source domains. Divide the connection vectors of the connection aggregation matrix in the target domain and the source domain into training and test sets respectively. Use the hypergraph-based multi-source domain adaptive algorithm to solve for a transformation matrix in the training set of each source domain. Transform the distribution of connection vectors in multiple source domains into a distribution consistent with the distribution of connection vectors in the target domain through the transformation matrix. Combine the transformed training sets in the source domains with the training sets in the target domain to form the final connection training sets for each modality. In the hypergraph-based multi-source domain adaptive algorithm, the objective function of the m-th modality is as follows: (3) In the formula, Let be the nuclear norm of the matrix. For matrix l 2,1 Norm, tr(.) is the trace operation of a matrix. D is the feature matrix of the training set of the target domain. m N represents the number of features of the m-th mode. T The number of training sets in the target domain. Let be the feature matrix of the i-th source domain training set. Let be the number of training sets in the i-th source domain. Let N be the reconstruction coefficient matrix for all source domains. S Let be the number of training sets in all source domains. For the error matrix of all source domains, Let be the transformation matrix of the i-th source domain. Let be the Laplacian matrix of the hypergraph, where τ and λ are regularization parameters for the balance trinomials; The specific process of solving the objective function is as follows: calculate the hypergraph G of the training set in all source domains, and solve for L. h Then, by solving equation (3) using the augmented Lagrange multiplier method, we obtain... The optimal solution, through Transform the data in the corresponding source domain to the target domain; For L h To solve this problem, we compute the hypergraph G of the training set in all source domains; G(V,C,A) consists of the set of vertices V, the set of hyperedges C, and the set of weights of each hyperedge A, where each hyperedge C... i They are all assigned a weight a(c) i For a hypergraph G, the incidence matrix Used to represent the relationship between each vertex and a hyperedge, defined as follows: (4) Based on the incidence matrix M, the degree of each vertex and the degree of each hyperedge in the hypergraph are defined as follows: (5) (6) The Laplacian matrix of the hypergraph can be obtained from equations (5) and (6), as shown below: (7) In the formula, L h I is the Laplacian matrix of the hypergraph, and I is the identity matrix. ; (6) Use a multi-task feature selection algorithm based on local ordered structure to train the model and select features in the final modal connection training set; Based on the model trained on the training set and the selected features, discriminative features are selected in the target domain test set; (7) The selected discriminant features are classified using a support vector machine algorithm based on multi-kernel learning, and the final classification result is obtained.

2. The multimodal brain network feature classification method according to claim 1, characterized in that, In step (1), functional magnetic resonance imaging (fMRI) and structural magnetic resonance imaging (MRI) of the brain are acquired from multiple data centers; brain gray matter images are obtained after preprocessing the structural MRI images.

3. The multimodal brain network feature classification method according to claim 1, characterized in that, The standardized brain partition templates in step (2) include the AAL partition template and the Brodmann partition template.

4. The multimodal brain network feature classification method according to claim 2, characterized in that, In step (3), the brain networks of each modality include brain functional networks and brain structural networks. For functional magnetic resonance images of the brain from different data centers, the average time series of different brain regions are extracted, the correlation coefficient between the average time series of each pair of brain regions is calculated, and the brain functional network of each subject is constructed. For gray matter images of the brain from different data centers, the probability density function of gray matter volume values ​​of all voxels in each brain region is estimated using the kernel density estimation method. Then, the Jensen divergence between the probability density functions of gray matter volume of each pair of brain regions is calculated. The Jensen divergence is defined as the connection weight of the structural network to evaluate the similarity of gray matter volume of different brain regions, thereby constructing the brain structural network of each subject.

5. The multimodal brain network feature classification method according to claim 4, characterized in that, The formula for calculating the Jensen divergence is as follows: (1) In the formula, and Let represent the probability distributions of gray matter volumes in brain regions P and Q, respectively. and The corresponding probability density function is and ; To calculate the KL divergence between the probability density functions of gray matter volumes in pairs of brain regions; ; and The formula for calculating the KL divergence between them is: (2)。 6. The multimodal brain network feature classification method according to claim 1, characterized in that, The specific content of the locally ordered structure in step (6) is as follows: For the feature matrix X, its representation in the low-dimensional space after projection is R=WX, where W is the projection matrix of X, and a triplet (x) in X is... i, x u ,x v The triple mapped to a lower-dimensional space can be represented as (r i ,r u ,r v The locally ordered structure can be equivalent to the following optimization problem: (8) In the formula, x u and x v For x i The neighboring nodes, For x i The set of k nearest neighbors, Let dist(.,.) be the adjacency matrix, and dist(.,.) be the distance metric; Equation (8) is equivalent to In the formula, D is a diagonal matrix; S is a distance matrix.

7. The multimodal brain network feature classification method according to claim 6, characterized in that, The objective function for feature selection in step (6) is as follows: (15) In the formula, Y represents the label vectors of all training sets. The final connection training set feature matrix after combination. for The projection matrix is ​​given by α and β, where α and β are regularization parameters of the balanced three terms. Equation (15) is solved using an accelerated approximate gradient algorithm to obtain the coefficient matrix. The coefficient matrix obtained by solving The sum of squares of each row is used to obtain a column vector P. The features corresponding to values ​​greater than or equal to 0.01 in column vector P are selected to obtain discriminative features.

8. The multimodal brain network feature classification method according to claim 1, characterized in that, The specific classification steps in step (7) are as follows: (1) Calculate a linear kernel matrix for each mode; (2) Combine the linear kernel matrices of multiple modes using the following formula: (16) In the formula, It is the m-th modal connection vector x i and connect vector x j kernel function, α m The weights are non-negative and satisfy the following conditions: Constraints; find α by using a grid search strategy on the training set. m The optimal value; (3) Use the support vector machine algorithm to classify the merged hybrid kernel matrix.

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