A brain network analysis method based on decoupling representation of symmetric positive definite manifold

Abstract

The application discloses a brain network analysis method based on decoupling representation of symmetric positive definite manifold, and belongs to the field of medical image processing. The analysis method comprises the following steps: acquiring functional magnetic resonance brain image data of a subject in a resting state, performing pretreatment, dividing a region of interest according to an anatomical template of a brain structure, and obtaining a time sequence of blood oxygen level dependent signals of each region of interest; constructing a brain function connection network by calculating a Pearson correlation coefficient between pairs of regions of interest, generating an FC matrix located on an SPD manifold space; using an SPD manifold encoder, preliminarily extracting feature information in the FC matrix, and using an SPD manifold decoder for reconstruction; sending the features output by the SPD manifold encoder to a decoupling representation module for decoupling, separating out site-independent and site-specific SPD manifold features; projecting the extracted site-independent SPD manifold features back to a tangent plane space, sending the features into two full connection layers, and adopting Softmax as an activation function to obtain a classification result.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of medical image processing, and particularly relates to a brain network analysis method based on decoupling representation of symmetric positive definite manifold. BACKGROUND

[0002] Resting-state functional magnetic resonance imaging (rs-fMRI) is a non-invasive neuroimaging technique that indirectly reflects neuronal activity by measuring blood oxygen level dependent signals, and can effectively reveal the connection mode of brain function in the resting state. Studies have shown that the brain functional connectivity of patients with mental disorders such as autism spectrum disorder, schizophrenia, depression and hyperactivity disorder is abnormal, so the functional connectivity (FC) analysis based on functional magnetic resonance imaging has important significance for understanding the pathological mechanism of brain diseases and realizing early intervention of diseases.

[0003] When constructing a brain network using rs-fMRI data, the first step is usually to define nodes, and one of the common methods for defining brain nodes is to divide the brain into several regions of interest (ROI) using an anatomical template that gives the structure of the brain. Then, the connection edges are constructed between the nodes, the blood oxygen dependent signal of the fMRI data in each ROI is extracted, and the correlation (such as Pearson correlation) between the pair of ROIs is calculated as the connection edge. In traditional FC network analysis, the upper triangle or lower triangle of the FC matrix is usually taken for vectorization operation, so as to perform subsequent regression or classification tasks. However, such operation will lose the topological structure information contained in the FC. Although the convolution or graph structure analysis method can capture certain topological structure information, it can only focus on the interaction between local brain regions and cannot process the FC as a whole. SUMMARY

[0004] In view of the deficiencies of the prior art, the purpose of the present application is to provide a brain network analysis method based on decoupling representation of symmetric positive definite manifold.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] A brain network analysis method based on decoupling representation of symmetric positive definite manifold, comprising the following steps:

[0007] Obtaining functional magnetic resonance brain image data of a subject in a resting state, preprocessing, dividing regions of interest according to an anatomical template of brain structure, and obtaining a time sequence of blood oxygen level dependent signals of each region of interest;

[0008] The brain function connection network is constructed by calculating the Pearson correlation coefficient between pairs of interest regions, and an FC matrix located in the SPD manifold space is generated.

[0009] The SPD manifold encoder is used to preliminarily extract the feature information in the FC matrix, and the SPD manifold decoder is used for reconstruction.

[0010] The features output by the SPD manifold encoder are sent to the decoupling representation module for decoupling, and the site-independent and site-specific SPD manifold features are separated.

[0011] The extracted site-independent SPD manifold features are projected back to the tangent plane space, sent to two fully connected layers, and the Softmax function is used as the activation function to obtain the classification result.

[0012] Further, the calculation formula of the Pearson correlation coefficient between pairs of interest regions is:

[0013]

[0014] In the formula, ρ(X, Y) represents the degree of linear correlation between brain region X and brain region Y, and the value is between-1 and 1; μ x and μ Y are the average values of the blood oxygen level dependent signals of brain region X and brain region Y in the time series, and X and Y represent the blood oxygen level dependent signal values of brain region X and brain region Y in the time series at each time point.

[0015] Further, the SPD manifold encoder includes three layers, the first two layers each include a group of BiMap layers and RegEig layers, and the last layer only includes one BiMap layer; the BiMap layer performs dimension transformation on each input SPD feature; the RegEig layer processes the eigenvalues in the SPD matrix.

[0016] Further, the geodesic distance is used to measure the intermediate features generated by the SPD manifold encoder, and the calculation formula is:

[0017]

[0018] D LEM (X i , X j )=‖log(X j )-log(X i )‖ F

[0019] In the formula, is the loss function for measuring the intermediate features generated by the SPD manifold encoder, represents the SPD matrix at the kth stage in the encoding process, N B and Ns respectively represent the size of a batch and the number of stages, i is the index of data in a batch, a is the index of the anchor sample selected from the batch data; N pos is the number of positive pairs, N neg is the number of negative pairs; L is the true label of the case; D LEM is the geodesic distance; X i and X i represent two SPD matrices that need to calculate the geodesic distance, the subscript F represents the Frobenius norm of the calculated matrix.

[0020] Further, the SPD manifold decoder is used to reconstruct the output of the last layer of the encoder, and the global reconstruction loss is used for measurement:

[0021]

[0022] wherein, is the loss function for measuring the FC of the reconstructed FC and the original input, X, respectively are the FC obtained by calculating the Pearson correlation coefficient at the beginning and the FC reconstructed by using the SPD manifold decoder at the end.

[0023] Further, the decoupling process is supervised by the domain generalization loss and the local reconstruction loss;

[0024] Domain generalization loss:

[0025]

[0026]

[0027]

[0028] wherein, is the loss function for supervising the quality of domain-invariant features, is the loss function for supervising the quality of domain-specific features, is the loss function for supervising the quality of the above two types of features. X co and X sp respectively represent the decoupled site-independent and site-specific information, S is the site label;

[0029] Local reconstruction loss:

[0030]

[0031] wherein, is the loss function for measuring the reconstructed SPD features to be decoupled and the SPD features before decoupling, X to -disentagle and respectively refer to the SPD features before decoupling and the reconstructed SPD features before decoupling.

[0032] Further, the formula for projecting back to the tangent plane space is:

[0033] P=log(X)=φlog(∧)φ T

[0034] where P is the matrix feature X located on the SPD manifold space projecting back to the matrix feature on the tangent plane space, and is obtained by performing eigenvalue decomposition on the matrix X to obtain the eigenvalue and eigenvector matrix, that is, X=φ T ∧φ.

[0035] Further, the cross-entropy loss function is used to evaluate the classification performance:

[0036]

[0037] where, is the loss function for measuring the classification performance, L refers to the true label of the sample about whether suffering from ASD, p refers to the predicted value obtained by the model, and Log() is the traditional logarithm operation in the Euclidean space.

[0038] Further, the overall loss function is as follows:

[0039]

[0040] where, α, β, λ are the weight coefficients of the model in each class loss, θ1, θ2 are the coefficients of the model in the global reconstruction and local reconstruction tasks.

[0041] A brain network analysis system based on decoupling representation of symmetric positive definite manifold, comprising:

[0042] A data acquisition and processing module: acquires functional magnetic resonance brain image data of a subject in a resting state, performs preprocessing, divides the region of interest according to the anatomical template of the brain structure, and obtains the time sequence of the blood oxygen level dependent signal of each region of interest;

[0043] An FC matrix construction module: constructs a brain functional connection network by calculating the Pearson correlation coefficient between pairs of regions of interest, and generates an FC matrix located on the SPD manifold space;

[0044] A feature extraction module: uses an SPD manifold encoder to preliminarily extract feature information in the FC matrix, and uses an SPD manifold decoder for reconstruction;

[0045] Feature decoupling module: the features output by the SPD manifold encoder are sent to the decoupling representation module for decoupling to separate site-independent and site-specific SPD manifold features;

[0046] And the analysis module: the extracted site-independent SPD manifold features are projected back to the tangent plane space, sent to two fully connected layers, and the Softmax function is used as the activation function to obtain the classification result.

[0047] The beneficial effects of the present application are:

[0048] 1. Unlike traditional functional connectivity analysis methods, the obtained FC matrix is processed as a whole in the SPD manifold space to capture its global topological structure information.

[0049] 2. Unlike traditional classification tasks that directly use classification loss to constrain the learned features, feature constraint is performed in the feature decoding stage, so that the learned intermediate features have better representation ability; unlike previous single-site data-based functional connectivity processing methods, a decoupling representation module located in the SPD manifold is designed to capture site common information for multi-site FC analysis.

[0050] 3. The present application can make progress in FC analysis of brain networks and is beneficial to the judgment of brain diseases. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0052] Figure 1 The flowchart of the symmetric positive definite manifold decoupling representation network (SPD-DRNet) provided by the present application is shown.

[0053] Figure 2 The structure diagram of the SPD manifold encoder and decoder used by the present application is shown.

[0054] Figure 3 The flowchart of the decoupling representation module working in the symmetric positive definite manifold space provided by the present application is shown.

[0055] Figure 4 The ROC curve of the model obtained by using the leave-one-out method on the NYU, UM, and USM sites in the embodiment of the present application is shown.

[0056] Figure 5 The algorithm flowchart of the present application is shown. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0058] As shown in the figure, a brain network analysis method based on decoupling representation of symmetric positive definite manifold includes the following steps: Figure 1

[0059] S1, for each sample, obtain the functional magnetic resonance brain image data of the subject in a resting state, pre-process, divide the region of interest according to the anatomical template of the brain structure, and obtain the time series of the blood oxygen level dependent signal of each region of interest;

[0060] The pre-processing step includes slice time and head motion correction, noise signal regression, and time filtering. Then, the generated rs-fMRI is normalized to MNI (Montreal Neurological Institute) space through a nonlinear registration algorithm (i.e. ANTS). Subsequently, the brain is divided into 116 regions of interest (ROI) based on the anatomical automatic labeling (AAL) template, and the average time series of each ROI is extracted to constitute the time series data of the subject's brain region as a whole;

[0061] The data form of each site is N x R x T, where N is the number of samples, R represents the number of regions of interest, and T is the length of the time series.

[0062] S2, construct a brain functional connection network by calculating the Pearson correlation coefficient between pairs of regions of interest, and generate an FC matrix located in the SPD manifold space;

[0063] By calculating the Pearson correlation coefficient, the functional connection matrix of each subject is obtained. The calculation formula of the Pearson correlation coefficient of brain region X and brain region Y is as follows:

[0064]

[0065] In the formula, ρ(X, Y) represents the degree of linear correlation between brain region X and brain region Y, and its value is between -1 and 1. The higher the value, the tighter the correlation, and the correlation value of the brain region with itself is 1. X and μ Y ​is the average of the blood oxygen level dependent signals of brain region X and brain region Y in time series, X and Y represent the blood oxygen level dependent signal values of brain region X and brain region Y in time series at each time point. The FC matrix constructed by calculating the Pearson correlation is naturally located in the SPD manifold space, without feature mapping.

[0066] In the above manner, the data of each site will be converted into an N x R x R tensor, and the constructed FC matrix is directly located in the symmetric positive definite (SPD) manifold space, without feature mapping.

[0067] S3, using an SPD manifold encoder, preliminarily extracts feature information in the FC matrix, and using an SPD manifold decoder for reconstruction, to improve the learned feature representation ability;

[0068] The SPD manifold encoder includes three layers, the first two layers each include a set of BiMap layers and RegEig layers, and the last layer only includes one BiMap layer; the BiMap layer is similar to the Dense layer in the conventional neural network, which transforms the dimension of each input SPD feature to reduce the data dimension, reduce the calculation cost, and compress the feature representation to discard the redundant information in the encoder module. The RegEig layer is a layer similar to the nonlinear activation function, which performs the function of the nonlinear activation function in the conventional neural network by processing the eigenvalues in the SPD matrix; specifically, it is responsible for truncating the smaller positive eigenvalues of each input SPD matrix. The specific operation of the BiMap layer is:

[0069]

[0070] wherein, and denote the input and output SPD manifold features, denotes a projection matrix; in order to ensure that the obtained matrix X k can also be located in the SPD manifold space, W k needs to satisfy the column full rank property to ensure the positive definiteness of X k ; however, it is difficult to directly optimize W k located in the potential non-compact StiefeL manifold, because the distance metric on the manifold space has no upper bound at this time; as a typical countermeasure, an additional semi-orthogonal constraint can be imposed on W k , so that the weight space becomes a compact StiefeL manifold, and W k located in such a manifold space provides the potential to produce an optimal solution.

[0071] The specific operation of the RegEig layer is:

[0072] Xk =φmgx(∈I, ∧)φ T

[0073] In the formula, ∈ is a small activation threshold and is a hyperparameter; I and ∧ represent the identity matrix and matrix X, respectively. k This layer is a diagonal matrix composed of all eigenvalues; it is equivalent to performing a nonlinear activation operation on the features located on the SPD manifold space.

[0074] To ensure that the SPD manifold encoder can obtain more representative features, the intermediate features generated by the encoder are measured to improve their representational power. Specifically, the geodesic distance on the SPD manifold is used to measure the intermediate features generated by the decoder. The geodesic distance is calculated as follows:

[0075] D LEM (X i X j )=‖log(X j )-log(X i )|| F

[0076] Among them, D LEM X is the geodesic distance. i and X j This represents two SPD matrices for which geodesic distances need to be calculated, and the subscript F indicates the Frobenius norm of the calculated matrix.

[0077] Geodesic distance can be used to measure intermediate features generated by the SPD manifold encoder. The basic idea is that samples with the same label are closer in the SPD manifold coding space, and vice versa. The calculation formula is as follows:

[0078]

[0079] in, To measure the loss function of the intermediate features generated by the SPD manifold encoder, N represents the SPD matrix at stage k in the encoding process. B and N s represents the batch size and the number of stages, respectively. `i` is the index of a data point within a batch, and `a` is the index of the selected anchor sample within the batch data. Sample pairs are constructed within a batch of data using the anchor sample; samples with the same label as the anchor sample are positive class pairs, otherwise they are negative class pairs; N pos N represents the number of positive pairs. negis the number of negative pairs; L is the true label of the case (sick or healthy); To evaluate the quality of the learned intermediate representation, the manifold distance metric LEM is used to simulate the metric strategy, that is, to make the SPD matrices of the same class at different stages closer in the manifold space, and the SPD matrices of different classes farther apart.

[0080] To further enhance the features learned here, the SPD manifold decoder is used to reconstruct the output of the last layer of the encoder. The overall structure of the SPD manifold encoder-decoder is shown in Figure 2 , which introduces skip connections similar to the U-Net structure design. A reconstruction loss acting on the global is used for measurement:

[0081]

[0082] where, is the loss function that measures the FC of the reconstructed and the FC of the original input, X, is the FC obtained by calculating the Pearson correlation coefficient at the beginning and the FC reconstructed by the SPD manifold decoder at the end, respectively.

[0083] S4, the features output by the SPD manifold encoder are sent to the decoupling representation module to separate the site-independent and site-specific SPD manifold features;

[0084] The features obtained in the SPD manifold encoder are input into a decoupling representation module that works directly in the SPD manifold space, aiming to let the model eliminate the differences between sites and extract common features that can be used on unknown sites. As shown in Figure 3 , the decoupling representation module decouples the SPD features of the last encoding stage. To achieve the decoupling process, a double-branch process is designed, each branch consisting of a separate SPD block; The two branches finally obtain two decoupled SPD matrices, which are the same size as the original input feature size. Through the two branches, two generated matrices containing site-independent and site-specific information are obtained.

[0085] To constrain the decoupling process, a domain generalization loss is used to add constraints on site-independent and site-specific features. The specific formula is as follows:

[0086]

[0087]

[0088]

[0089] where, is the loss function for supervising the quality of domain-invariant features, is the loss function for supervising the quality of domain-specific features, To supervise the loss of the above two kinds of feature quality, Xco and Xsp represent the decoupled site-independent and site-specific information respectively, and S is the site label (i.e. the label of the site, such as S = 1 indicates that the data comes from site 1). The same strategy as that for supervising the intermediate features is used to constrain the two learned features. Generally speaking, only the part with site-independent features needs to be extracted for further analysis, without considering the site-specific information. However, in the decoupling process, using domain-specific features can avoid information loss. If there is no reasonable constraint on the specific domain features, the learned common features may become one-sided, because emphasizing learning common representations may ignore the need to maintain the original information in the decoupling process. That is, such common representations may over-satisfy the optimization goal of the loss function, and lose the rich and key information contained in the original features. To solve this problem, the usual practice is to use reconstruction to ensure the quality of the learned features, i.e. the lost information can be recovered to the original input. In Figure 3 In the method, the obtained domain-invariant features and domain-specific features are arranged according to the main diagonal to form a block matrix, and the remaining part is filled with zeros to form a new SPD matrix. Such a matrix does not violate the definition of the SPD matrix. The matrix is sent to a BiMap layer to recover to the size of the matrix before decoupling, forming a reconstructed SPD matrix. The reconstruction loss measures the numerical consistency between the two matrices, and the specific formula is as follows:

[0090]

[0091] wherein, is the loss function for measuring the reconstructed SPD features to be decoupled and the SPD features before decoupling, Xto-disentangle and respectively refer to the SPD features before decoupling (i.e. the last output of the SPD manifold encoder) and the reconstructed SPD features, which are subjected to a local reconstruction task here.

[0092] The site-independent and site-specific information is obtained, and the decoupling process is supervised by the domain generalization loss and the local reconstruction loss.

[0093] S5, the extracted site-independent SPD manifold features are projected back to the tangent plane space, sent to two fully connected layers, and the Softmax function is used as the activation function to obtain the classification result:

[0094] The formula for projecting back to the tangent plane space is as follows:

[0095] P = log (X) = φ log (A) φ T

[0096] In the formula, p is the matrix feature X located on the SPD manifold space projected back to the matrix feature on the tangent plane space, and is obtained by eigenvalue decomposition of matrix X, that is, X = φ T and φ. In this way, matrix X can be mapped to the tangent space, ensuring the feasibility of subsequent processing using the Euclidean space method.

[0097] The sizes of the two fully connected layers are 256 and 2 respectively, and the output value conversion of classification is realized by sending the fully connected layer into the Softmax function. In the present application, the features projected back to the tangent plane space are flattened to form an N x K shaped tensor data, which is changed to N x 256 and N x 2 respectively by two fully connected layers. Finally, N x 2 is sent into the Softmax function to map the elements in the two-dimensional tensor to the binary space of {0, 1}.

[0098] The cross-entropy loss function is used to evaluate the classification performance:

[0099]

[0100] wherein, is the loss function for measuring the classification performance, L refers to the true label of the sample about whether suffering from ASD (0 represents suffering from the disease, and 1 represents healthy), p refers to the prediction value obtained by the model, and Log() here is the traditional logarithm operation in the Euclidean space.

[0101] the overall optimization target of the model proposed in the present application is represented by , which can be specifically represented as:

[0102]

[0103] wherein, α, β, λ are the weight coefficients of balancing the losses of the model in each type, θ1, θ2 are the coefficients of balancing the global reconstruction and local reconstruction tasks of the model, and these coefficients are all hyperparameters. The overall optimization target of the model is to minimize

[0104] Embodiment:

[0105] In the present embodiment, the ABIDE dataset is taken as the training sample to illustrate the brain network analysis process based on the decoupled representation of the symmetric positive definite manifold, including the following steps:

[0106] Step 1: Obtain data.

[0107] Download and prepare the ABIDE dataset.

[0108] All effective rs-fMRI samples in this study are from the ABIDE (Autism Brain Imaging Data Exchange) dataset. Table 1 gives the sample information of each site. The ABIDE database collects data from 17 different collection sites, and this application uses 1102 rs-fMRI data, including 531 autism patients and 571 normal controls (NCs). The data used is provided by the Preprocessed Connectome Project Initiative and preprocessed by C-PAC. The preprocessing steps include slice time and head motion correction, noise signal regression, and temporal filtering. Then, the generated rs-fMRI is normalized to MNI (Montreal Neurological Institute) space by a nonlinear registration algorithm (i.e. ANTS). Subsequently, the Anatomical Automatic Labeling (AAL) template divides the brain into 116 regions of interest (ROIs), and extracts the average time series of each ROI to form the overall time series data of the subject's brain region. The names and data amounts of each site used are shown in Table 1:

[0109] Table 1. Statistical information of ABIDE dataset samples (M represents male, and F represents female)

[0110]

[0111]

[0112] Second step: Constructing functional connection matrix.

[0113] The leave-one-out method is used to divide the training set and test set for multi-site data. At this time, the data of each site is a tensor with a shape of N x R x T, and by calculating the Pearson correlation coefficient, the data of each site is converted to a shape of N x R x R. For single subject data, the shape is a symmetric matrix of R x R.

[0114] Third step: Establishing a classification network.

[0115] The network mainly includes an SPD manifold encoder, a decoupling representation module and a fully connected layer. The SPD manifold encoder has three layers, the first two layers each include a set of BiMap layers and RegEig layers, and the last layer only includes a BiMap layer. In the encoding process, the intermediate features generated by the encoder are measured using geodesic distance to improve the representation ability of the features. The decoupling representation module directly acts on the SPD manifold space, and the features generated by the SPD manifold encoder are sent to two independent branches, each branch includes a set of BiMap layers and RegEig layers, and each branch obtains station-independent and station-specific information, and the decoupling process is supervised by domain generalization loss and reconstruction loss. Finally, the station-independent features obtained from the SPD manifold space are projected back to the tangent plane space to obtain the representation in the Euclidean space, and are sent to two fully connected layers to convert the classification output value using Softmax.

[0116] Step 4: Set network parameters.

[0117] The network model is implemented under the PyTorch framework, where the Pytorch version is 1.13.1, the CUDA version is 11.7, the training batch size is 16, the dropout in the two fully connected layers is 0.2, in the three encoding stages, the size of the SPD matrix changes from 116x116 to 96x96 to 66x66 to 26x26, the ∈ in the RegEig layer is set to 1e-4, the α and β in the overall loss function are set to 1, the λ is set to 1e-2, the θ1 and θ2 are set to 0.5 and 0.5, respectively. Under this configuration, the model is trained to obtain the trained high-order brain network classification network.

[0118] Step 5: Use the trained symmetric positive definite manifold decoupling representation network to classify and predict samples.

[0119] Through the learning and training of steps 3-4, the optimal network model parameters are obtained by manual parameter tuning, and the test sample data in the data set is predicted for classification.

[0120] The leave-one-out training method is used to simulate the generalization ability of the model on unknown sites. Specifically, for the data of 17 sites in the ABIDE dataset, a certain site is taken as the test set, and the remaining site data is taken as the training set. In order to prevent the influence of data bias, the leave-one-out method is used for training and evaluation for all sites, a total of 17 rounds of experiments. The present application performs a classification task: ADHD vs. NC classification task. In performance evaluation, seven indicators are used, which are accuracy ACC (all samples are correctly classified), sensitivity SEN (the proportion of all patients correctly classified by the model), specificity SPE (the proportion of all normal people correctly classified by the model), balance BAC (the average of sensitivity and specificity), positive example precision PPV (the proportion of patients predicted by the model that meet the true label), and negative example precision NPV (the proportion of normal people predicted by the model that meet the true label), and the area under the receiver operating characteristic curve (AUC). Take the average of the 17 rounds of results of each indicator as the final result. At the same time, in order to verify the effectiveness of the model (SPD-DR-Net) proposed in the present application, the baseline model SPDNet using SPD manifold learning is compared, and the encoder-decoder model based on vectorization method, namely ASD-Diag Net and DAE model, is also compared. In addition, the method using convolution and graph structure, namely BrainCNN and BrainGNN model, is also compared. The method of using federated learning to analyze multi-site fMRI data, Fed, is also compared. The comparison results of the above six methods are shown in Table 2.

[0121] Table 2 Comparison results of six methods in ADHD vs. NC classification task

[0122]

[0123] As can be seen from Table 2, the method proposed in the present application has better classification performance than the other six methods in all indicators, and the best values of each indicator are highlighted. Specifically, the performance of the proposed method is better than that of the model based on the vectorization method of the encoder-decoder structure network (i.e., ASD-Diag Net and DAE), which indicates that the SPD manifold can better capture the topological structure information in the FC matrix compared to the method of directly vectorizing the FC. In addition, the proposed method is better than the model using convolution and graph structure analysis function connection (i.e., BrianCNN and BrainGNN), which shows that the proposed model can better mine the structural information contained in the FC. Moreover, the performance of the proposed method is also better than the baseline model SPDNet based on the SPD manifold learning method. And the performance of the proposed model is also better than the Fed model using federated learning to analyze multi-site data, which shows that the method based on SPD manifold learning can better extract generalizable features compared to the Euclidean space method. In order to verify the classification ability of the obtained model, the ROC curves of the proposed model and the other six comparison methods are plotted to show the classification performance of the proposed model for positive samples (case samples), as shown in Figure 4 In order to embody the stability and reliability of the classification performance of the model, the ROC curves obtained after leave-one-out training are plotted for the first four sites with the largest amount of data, i.e., the NYU, UM, USM, and UCLA sites, each with 184, 145, 101, and 99 data, respectively, as shown in Figure 4 In these four sites with more data, the AUC of the proposed model can still be maintained at a relatively high value (0.771, 0.779, 0.853, and 0.729, respectively), which further indicates that the proposed model has good classification performance.

[0124] In the description of the present specification, the description of the terms "one embodiment", "example", "specific example", and the like means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0125] The basic principles, main features, and advantages of the present application are shown and described above. It should be understood by those skilled in the art that the present application is not limited by the above embodiments, and the above embodiments and descriptions in the specification are only illustrative of the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. A brain network analysis method based on decoupled representation of symmetric positive definite manifolds, characterized in that, Includes the following steps: We acquired functional magnetic resonance brain imaging data of subjects in a resting state, preprocessed the data, divided regions of interest according to the anatomical template of brain structure, and obtained the time series of blood oxygenation level dependent signals for each region of interest. By calculating the Pearson correlation coefficient between paired regions of interest, a brain functional connectivity network is constructed, generating an FC matrix located on the SPD manifold space. The feature information in the FC matrix is ​​initially extracted using the SPD manifold encoder, and then reconstructed using the SPD manifold decoder. The features output by the SPD manifold encoder are sent to the decoupling representation module for decoupling, separating the site-independent and site-specific SPD manifold features. The extracted site-independent SPD manifold features are projected back into the tangent plane space, fed into two fully connected layers, and Softmax is used as the activation function to obtain the classification results. The decoupling process is supervised by domain generalization loss and local reconstruction loss; Domain generalization loss: Where, N B This represents the batch size, where i is the index of a data point within the batch, and a is the index of the selected anchor sample within the batch data; N pos N represents the number of positive pairs. neg L is the number of negative pairs; D is the true label of the case; LEM For geodesic distance, The loss function is the feature quality invariant in the supervised domain. The loss function is a feature quality specific to the supervised domain. The loss function to supervise the quality of the two types of features mentioned above; X co and X sp These represent the decoupled site-independent and site-specific information, respectively, with S being the site tag; Local reconstruction loss: in, To measure the loss function of the reconstructed SPD features to be decoupled and the SPD features before decoupling, X to -disentagle and These refer to the SPD features before decoupling and the SPD features before decoupling after reconstruction, respectively.

2. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 1, characterized in that, The formula for calculating the Pearson correlation coefficient between paired regions of interest is: In the formula, ρ(X,Y) represents the degree of linear correlation between brain region X and brain region Y, and its value is between -1 and 1; μ X With μ Y X represents the average value of the blood oxygenation level dependent signal in brain regions X and Y over time series, where X and Y represent the blood oxygenation level dependent signal values ​​in brain regions X and Y at various time points over time series.

3. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 1, characterized in that, The SPD manifold encoder consists of three layers. The first two layers each contain a set of BiMap layers and a RegEig layer, while the last layer contains only a BiMap layer. The BiMap layer transforms the dimensions of each input SPD feature, and the RegEig layer processes the feature values ​​in the SPD matrix.

4. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 3, characterized in that, The intermediate features generated by the SPD manifold encoder are measured using geodesic distance, and the calculation formula is as follows: D LEM (X i ,X j )=||log(X j )-log(X i )|| F In the formula, To measure the loss function of the intermediate features generated by the SPD manifold encoder, N represents the SPD matrix at stage k in the encoding process. B and N S Representing the batch size and the number of stages respectively, i is the index of a data point within a batch, and a is the index of the selected anchor sample within the batch data; N pos N represents the number of positive pairs. neg L represents the number of negative pairs; L is the true label of the case. D LEM X represents the geodesic distance; i and X j This represents two SPD matrices for which geodesic distances need to be calculated, and the subscript F indicates the Frobenius norm of the calculated matrix.

5. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 4, characterized in that, The output of the last layer of the encoder is reconstructed using the SPD manifold decoder, and the global reconstruction loss is used as the metric: in, To measure the loss function X of the reconstructed FC and the original input FC, These are the FC obtained initially by calculating the Pearson correlation coefficient and the FC reconstructed using the SPD manifold decoder, respectively.

6. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 5, characterized in that, The formula for projecting back to the tangent plane space is: P=log(X)=Φlog(Λ)Φ T In the formula, P is the matrix feature X projected back to the tangent plane space from the SPD manifold space. and This is achieved by performing eigenvalue decomposition on matrix X to obtain the eigenvalue and eigenvector matrix, i.e., X = Φ. T ΛΦ.

7. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 5, characterized in that, Evaluate classification performance using the cross-entropy loss function: in, The loss function is used to measure classification performance. L refers to the true label of the sample regarding whether it has ASD, p refers to the predicted value obtained by the model, and Log() is the traditional logarithm operation in Euclidean space.

8. The brain network analysis method based on decoupled representation of a symmetric positive definite manifold according to claim 7, characterized in that, The overall loss function is as follows: Where α, β, and λ are the weighting coefficients of the trade-off model for various types of losses, and θ1 and θ2 are the coefficients of the trade-off model between global reconstruction and local reconstruction tasks.

9. A brain network analysis system based on decoupled representation of a symmetric positive definite manifold, capable of performing the method according to any one of claims 1-8, characterized in that, include: Data acquisition and processing module: acquires functional magnetic resonance brain imaging data of subjects in a resting state, performs preprocessing, divides regions of interest according to the anatomical template of brain structure, and obtains the time series of blood oxygen level dependent signals for each region of interest; FC matrix construction module: By calculating the Pearson correlation coefficient between paired regions of interest, a brain functional connectivity network is constructed, generating an FC matrix located on the SPD manifold space; Feature extraction module: Using the SPD manifold encoder, the feature information in the FC matrix is ​​initially extracted, and then reconstructed using the SPD manifold decoder; Feature decoupling module: The features output by the SPD manifold encoder are sent to the decoupling representation module for decoupling, separating the site-independent and site-specific SPD manifold features; In addition, the analysis module: the extracted site-independent SPD manifold features are projected back into the tangent plane space, fed into two fully connected layers, and Softmax is used as the activation function to obtain the classification results.

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