A hypergraph representation method of brain functional network

Abstract

This invention discloses a hypergraph representation method for brain functional networks. The steps include: preprocessing resting-state functional magnetic resonance imaging (fMRI) to obtain time series data for all brain regions; dividing the entire time series into multiple overlapping sub-sequence segments using a sliding window; constructing a dynamic brain functional network and transforming it into an optimization model; constructing a hypergraph of the dynamic brain functional network using the nearest neighbor algorithm; dynamically modifying the hypergraph structure through convolution operations and extracting features to obtain a new dynamic hypergraph; extracting the Laplacian matrix of the dynamic hypergraph; constructing the manifold regularization term of the Laplacian matrix and simultaneously introducing the manifold regularization term and the L1 norm regularization term into the optimization model to obtain the hypergraph representation of the brain functional network. This invention is used to represent functional interactions and higher-order relationships between multiple brain regions, determine discriminative brain functional network classification features, and effectively improve the classification performance of brain disease features.

Description

Technical Field

[0001] This invention relates to the field of biomedical information processing technology, and in particular to a hypergraph representation method for brain functional networks. Background Technology

[0002] The human brain can be viewed as a highly complex network composed of interconnected neurons, neuronal clusters, or multiple brain regions. This vast and complex network forms the physiological basis for information processing and cognitive expression. Recognizing the importance of constructing a human brain network, some neuroscientists proposed the concept of the human connectome. The human connectome aims to comprehensively and meticulously characterize the human brain at all levels, from macroscopic (brain regions) to microscopic (individual neurons), constructing a brain network map from the overall to the individual level, and further exploring the connectivity patterns within this network. In recent years, the development of graph theory-based complex network analysis has provided essential tools and analytical methods for the study of the human connectome. The two key steps in constructing a brain network are: first, how to define network nodes; and second, how to define the connections (edges) between network nodes.

[0003] With the advancement of science and technology, non-invasive brain functional imaging technology has developed rapidly, providing a broad stage for brain cognitive research using various imaging techniques. Currently, functional magnetic resonance imaging (fMRI) is widely used in the diagnosis and treatment of neurological diseases due to its high spatial resolution and non-invasive nature. fMRI technology reflects internal brain activity by measuring changes in magnetic resonance signals caused by changes in cerebral blood flow and oxygenation caused by neural activity, achieving very high spatial resolution accuracy (millimeter level). Preprocessing of fMRI images, selection of regions of interest, and extraction of average time series data are performed, followed by correlation analysis to measure functional connectivity between brain regions. The correlation between regions of interest is obtained by calculating the correlation between the average time series data of each pair of brain regions.

[0004] In the real world, almost all complex systems (such as social, biological, information, and transportation systems) can be naturally represented as networks. In recent years, brain science has experienced a boom thanks to the emerging non-invasive fMRI imaging technology. Researchers have discovered that brain functional networks constructed using fMRI possess many important network topological properties. Studying resting-state brain functional networks allows us to explore the functional organization patterns of the human brain, helping to understand the functional activity patterns of the brain in normal or diseased states, and has relatively clear physiological and pathological significance. For example, patients with brain diseases such as depression, schizophrenia, and epilepsy often exhibit abnormal brain structure accompanied by corresponding functional weakening, indicating that their brain functional networks have already changed. Different methods of constructing brain functional networks result in different network characteristics, making the construction of brain functional networks a crucial step.

[0005] Functional connectivity in the brain reflects the overall condition of the brain and plays a crucial role in exploring and researching the pathological mechanisms of various brain diseases. Traditional research methods focus only on paired relationships between two brain regions, failing to vividly represent the functional interactions or higher-order relationships between multiple brain regions. Summary of the Invention

[0006] The purpose of this invention is to provide a hypergraph representation method for brain functional networks, which overcomes the drawback that the relationships between nodes in previous brain functional network models only come from the attributes of the data itself, and explores the functional interactions and higher-order relationships between multiple brain regions.

[0007] To solve the above technical problems, the technical solution of the present invention is: a hypergraph representation method for brain functional networks, comprising the following steps:

[0008] Step 1: Acquire resting-state functional magnetic resonance imaging (fMRI) data of the brain;

[0009] Step 2: Register the resting-state functional magnetic resonance imaging data to different brain regions according to the standard partition template to obtain the time series of all brain regions;

[0010] Step 3: Use a sliding window to divide the entire time series into multiple overlapping subsequences, and then center and standardize the subsequences to obtain the time series matrix;

[0011] Step 4: Construct a dynamic brain functional network based on the time series matrix, and transform the brain functional network into an optimization model; Step 5: Construct the hypergraph G of the dynamic brain functional network using the nearest neighbor algorithm;

[0012] Step 6: Dynamically modify the hypergraph G through convolution operations, extract the features of the hypergraph G, and obtain a new dynamic hypergraph G. * Step 7: Extract the dynamic hypergraph G * Laplace matrix Ldh ;

[0013] Step 8: Construct the Laplacian matrix L of the dynamic hypergraph dh The manifold regularization term β and the L1 norm regularization term λ are simultaneously introduced into the optimization model described in step 4 to obtain the hypergraph representation of the brain functional network.

[0014] The present invention has the following beneficial effects:

[0015] I. This invention dynamically modifies the structure of a hypergraph by constructing a hypergraph and using a method of superimposing node convolution and hyperedge convolution; the Laplacian matrix of the hypergraph reflects the higher-order relationships between nodes; this invention can reflect the higher-order and dynamic characteristics of brain functional networks, providing richer information, thereby uncovering the dynamic higher-order relationships between functional connections of multiple brain regions, more vividly representing the functional interactions and higher-order relationships between multiple brain regions, reflecting the differences in network attribute indicators between brain disease patients and normal people, and determining more discriminative brain functional network classification features;

[0016] Second, by dynamically modifying the hypergraph structure through adjusted feature embeddings, many implicit relationships not included in these static relationships are considered, which can identify discriminative brain functional network classification features and effectively improve the classification performance of brain disease features. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the hypergraph representation method for brain functional networks of the present invention.

[0018] Figure 2 This is a schematic diagram of dynamic hypergraph construction in this invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Please refer to Figure 1 This invention provides a hypergraph representation method for brain functional networks. This method, from a dynamic and higher-order perspective, introduces regularization parameters of L1 norm regularization and manifold regularization into the optimization model. The method steps include:

[0021] Step 1: Acquire resting-state functional magnetic resonance imaging (fMRI) data of the brain;

[0022] Step 1 also includes a preprocessing step for the acquired resting-state functional magnetic resonance imaging (Rs-fMRI) data to remove noise signals caused by equipment, subject head movement, and biological noise during the acquisition process; the preprocessing steps include time slice correction, head movement correction, spatial normalization, spatial smoothing, delinear drift removal, and low-frequency filtering.

[0023] Step 2: Register the resting-state functional magnetic resonance imaging data to different brain regions according to the standard partition template to obtain the time series of all brain regions;

[0024] In this embodiment, the standardized brain atlas used is the internationally recognized Automated Anatomical Labeling (AAL) template. First, the whole brain is divided into 90 regions, and then the time series of each brain region is extracted.

[0025] Step 3: Divide the entire time series into multiple overlapping subsequences using a sliding window, and obtain the time series matrix after centering and standardizing the subsequences; specifically:

[0026] To obtain the dynamic functional brain network (DBFN), a sliding window is used to divide the Rs-fMRI time series into several subsequences. Assuming the total number of Rs-fMRI time points is M, the number of subsequences that can be generated is:

[0027] D=[(ML) / s]+1 (1)

[0028] In formula (1), L is the length of the sliding window and s is the step size;

[0029] The matrix composed of time series data is as follows:

[0030] X = [x1, x2, ..., x p ]∈R M×P (2)

[0031] In formula (2), P is the number of brain regions, and x p This is the time series matrix of the Pth brain region;

[0032] Define the time series of the d-th window in the i-th brain region as follows: R is a real matrix, for Centralization and Min-max standardization are performed; among them, for Centralization is represented as:

[0033]

[0034] right The Min-max normalized representation is as follows:

[0035]

[0036] In formulas (3) and (4), This represents the time series of the d-th window in the i-th brain region after centering, where d = 1, ..., D, μ d This represents the average time series value of the d-th window. Let represent the time series of the d-th window in the i-th brain region after Min-max standardization, where min and max represent the minimum and maximum values ​​of the time series of the d-th window after centering, respectively;

[0037] Bundle By concatenating the sequences, the time series matrix of the d-th window is obtained as follows:

[0038]

[0039] in, This represents the time series of the d-th window in the first brain region after Min-max standardization. This represents the time series of the d-th window in the P-th brain region (the last brain region) after Min-max standardization.

[0040] Step 4: Construct a dynamic brain functional network based on the time series matrix, and transform the brain functional network into an optimization model;

[0041] In step 4, a brain functional network is constructed using the Pearson correlation coefficient (PCC) between brain region pairs; brain regions are considered as nodes, and PCCs are considered as edges connecting them; the PCCs are calculated using the following method:

[0042] p ij =corr{x(i),x(j)} (6)

[0043] In formula (6): x(i) and x(j) represent the time series of the i-th and j-th brain regions, respectively, p ij Let x(i) and x(j) be the pairwise Pearson correlation coefficients, and corr be the Pearson correlation coefficient function.

[0044] Calculate the Pearson correlation coefficient between time series in each time window and construct a brain functional network (DBFN);

[0045] The correlation coefficient matrix of the brain functional network in the d-th window is represented by Z. (d) ≈(X (d) ) T X (d) The optimized form is:

[0046]

[0047] In formula (7), X(d) This represents the time series matrix of the d-th window.

[0048] Step 5: Construct the hypergraph G of the dynamic brain functional network using the nearest neighbor algorithm;

[0049] In step 5, the hypergraph G is represented by the incidence matrix H, which is defined by the node degree and edge degree; the incidence matrix H is constructed using the KNN algorithm.

[0050] For a given time series X, the attribute relationships between brain regions are described by a hypergraph G(V,E,W) network; the set of nodes is represented by V, the set of hyperedges is represented by E, and the set of weights of each hyperedge is represented by W; in the hypergraph G, each brain region corresponds to a node v∈V in the hypergraph, and each hyperedge contains two or more nodes to represent the interaction of multiple brain regions at the same time.

[0051] Assume H∈R |V|×|E| Let G be the vertex-edge incidence matrix of the hypergraph G, where the values ​​of the matrix elements are defined as follows:

[0052]

[0053] In formula (8), v∈V is a node of the hypergraph G, and e∈E is a hyperedge of the hypergraph G;

[0054] For the correlation matrix H, the node degree d(v) of each node i ) and the edge degree δ(e) of each hyperedge i They are represented as follows:

[0055]

[0056]

[0057] In formulas (9) and (10), e i It is the i-th hyperedge, i = 1, ..., m, where m represents the number of hyperedges; w(e i ) is the weight of the hyperedge, v i It is the i-th node.

[0058] Step 6: Dynamically modify the hypergraph G through convolution operations, extract the features of the hypergraph G, and obtain a new dynamic hypergraph G. * In step 6, the hypergraph structure is dynamically modified by superimposing node convolution and hyperedge convolution.

[0059] First, node convolutions are performed to aggregate node features onto hyperedges containing these nodes. A transformation matrix T is learned from the node features to permutate and weight the node features in the hyperedges. A multilayer perceptron is used to generate the transformation matrix T, and one-dimensional convolutions are used to compress the transformed features.

[0060]

[0061] In formula (11), X u Let x represent the node feature set, which consists of elements of the association matrix H from step 5. e The features represent adjacent hyperedges, MLP stands for perceptron function, and conv stands for convolution function;

[0062] Then, hyperedge convolution is performed to aggregate the hyperedge features into centroid node features; the weight score of each hyperedge is generated using MLP, and the output centroid node features are calculated as a weighted sum of the input hyperedge features;

[0063] w * =softmax(x e B+b) (12)

[0064]

[0065] In formulas (12) and (13), w * Here, B and b are the weights of each hyperedge, and both are learnable parameters. Softmax is a function that calculates the weights. u The centroid node features are represented by |A(u)|, which represents the size of the adjacent hyperedge set. The adjacent hyperedge set is obtained from the correlation matrix H in step 5.

[0066] Finally, node features are updated by combining node convolution and hyperedge convolution to embed new features, and a new hypergraph structure is constructed on this basis. As the feature embedding level increases and the network embedding level deepens, the hyperedge set is dynamically adjusted accordingly, ultimately resulting in a new dynamic hypergraph G. * (V * E * W * ).

[0067] Step 7: Extract the dynamic hypergraph G * Laplace matrix L dh ;

[0068] In step 7, the Laplacian matrix reflects the intrinsic geometric structure of the graph and is used for the matrix representation of the graph; the Laplacian matrix of the hypergraph reflects the higher-order relationships between nodes and is represented as follows.

[0069] L=D v -Θ (14)

[0070] In formula (14), D is the adjacency matrix of the hypergraph. v It is a node degree matrix with diagonal elements of d(v) i ), D e It is a hyperedge degree matrix with diagonal elements of δ(e i );

[0071] The normalized Laplacian matrix of a dynamic hypergraph is derived and calculated using the method for calculating the Laplacian matrix of a simple graph, as shown in formula (15):

[0072]

[0073] In formula (15), L dh It is the normalized Laplacian matrix of the dynamic hypergraph, where I is the identity matrix; D v * It is the node degree matrix of the dynamic hypergraph, D e * It is the hyper-edge degree matrix of the dynamic hypergraph, W * It is a diagonal matrix whose diagonal elements are the weights of the hyperedges of the dynamic hypergraph. For the supergraph G * The point-edge correlation matrix.

[0074] Step 8: Construct the Laplacian matrix L of the dynamic hypergraph dh The manifold regularization term is obtained, and the manifold regularization term β and the L1 norm regularization term λ are simultaneously introduced into the optimization model described in step 4 to obtain the hypergraph representation of the brain functional network.

[0075] In step 8, a manifold regularization term is constructed based on the Laplacian matrix of the dynamic hypergraph, and an L1 norm regularization term is added. The node degree and edge degree of the dynamic hypergraph are calculated to obtain the manifold regularization term of the dynamic hypergraph. A hypergraph convolution method based on the superposition of node convolution and hyperedge convolution is added to dynamically update the hypergraph structure, and the hypergraph representation of the brain functional network is obtained. The objective function is shown in formula (16).

[0076]

[0077] In formula (16), λ and β represent the regularization parameters of the L1 norm regularization term and the manifold regularization term, respectively. dh It is the normalized Laplacian matrix of the dynamic hypergraph.

[0078] In step 8, the DDBFN construction method is as follows:

[0079] Step A: Input the time series matrix X, the sliding window length L, the sliding window step size s, the hyperparameter λ of the L1 norm regularization term, the hyperparameter β of the hypergraph manifold regularization term, and the nearest neighbor number k in the KNN algorithm;

[0080] Step B: Initialize the time series matrix X of the time window. (d) Dynamic hypergraph correlation matrix H * Dynamic hypergraph Laplacian matrix L dh ;

[0081] Step C: Optimize and solve the L1 norm regularization term using the nearest neighbor operator method;

[0082] Step C1: Use gradient descent to analyze Z. (d) Perform m updates;

[0083]

[0084] In the formula, Z m-1 (d) It is Z (d) The result of the (m-1)th update Indicates Z (d) Find the partial derivative, α m It is the step size in gradient descent.

[0085] Step C2: Calculate the nearest neighbor operator for the L1 norm regularization term to apply to Z. (d) Apply a soft threshold operation to the elements in the array;

[0086] Step C3: After each gradient descent calculation, calculate Z using the nearest neighbor operator method. (d) The nearest neighbor operator is used and updated in the next iteration;

[0087] Step C4: Repeat this process until the objective function converges, at which point Z is obtained. (d) The optimal solution is to obtain DDBFN;

[0088]

[0089] In the formula, proximal represents the nearest neighbor operator method, and sgn is a function that returns the symbolic value of the numerical expression. represents the weight of the edge connecting node i and node j in the d-th window, and abs represents the absolute value function;

[0090] The constructed DDBFN is a hypergraph representation of the brain's functional network, Z (d) The optimal solution is the brain functional network of each window in the DDBFN.

[0091] Step D: Output the brain functional network Z for each window of the DDBFN (d) .

[0092] A specific embodiment is given below.

[0093] In one specific embodiment, the hypergraph representation of the brain functional network is applied to the classification of mild cognitive impairment (MCI) and normal individuals. Ten step sizes s = 1, 2, ..., 10 and ten sliding window lengths L = 10, 20, ..., 100 are set; the nearest neighbor number k takes values ​​of 1, 3, 5, 6, 7, 8, 9, 10, and 15; the regularization parameters λ and β both take values ​​in the range {2...}. -4 ,2 -3 ,2 -2 ,2 -1 The significance level for the t-test feature was set to 0.05; the parameter C of the linear kernel classifier for SVM was set to 1.

[0094] The window length is set to 80, the step size to 3, the nearest neighbor count to 9, and the regularization parameter λ = 2. -2 and β=2 -4 When constructing a DDBFN, this invention exhibits the best classification performance for MCI and normal human features.

[0095] All parts not covered in this invention are the same as or implemented using existing technologies.

[0096] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for hypergraph representation of brain functional networks, characterized in that: The steps comprise Step 1: obtaining resting-state functional magnetic resonance imaging data of the brain; Step 2: registering the resting-state functional magnetic resonance imaging data to different brain regions according to a standard partition template to obtain time series of all brain regions; Step 3: dividing the entire time series into multiple overlapping subsequences by using a sliding window, and obtaining a time series matrix after centering and standardizing the subsequences; Step 4: constructing a dynamic brain functional network according to the time series matrix, and converting the brain functional network into an optimization model; Step 5: constructing a hypergraph G of the dynamic brain functional network by using a nearest neighbor algorithm; Step 6: dynamically modify the hypergraph G through a convolution operation, extract features of the hypergraph G, and obtain a new dynamic hypergraph G * ; Step 7: Extracting the dynamic hypergraph G * Laplacian matrix L of G dh ; Step 8: Constructing Laplacian matrix L of dynamic hypergraph dh The manifold regular term β and the L1 norm regular term λ are introduced into the optimization model described in step 4 at the same time to obtain the hypergraph representation of the brain functional network.

2. The method of claim 1, wherein: In step 1, the resting-state functional magnetic resonance imaging data obtained is further preprocessed; the preprocessing steps include time layer correction, head motion correction, spatial standardization, spatial smoothing, linear drift removal and low frequency filtering.

3. The method of claim 1, wherein: In step 3, the entire time series of the resting-state functional magnetic resonance imaging data is divided into several subsequences by using a sliding window; assuming that the total number of time points of the resting-state functional magnetic resonance imaging data is M, the number of generated subsequences is D = [(M-L) / s]+1 (1) In formula (1), L is the length of the sliding window, and s is the step; The matrix composed of the time series is: X = [x1, x2,..., x p ] e R M×P (2) In formula (2), P is the number of brain regions, x p is the time series matrix of the Pth brain region; Define the time series of the dth window in the ith brain region as Centering and Min-max normalization are performed on where centering of is represented as: For Min-max standardization is represented as: In formulas (3) and (4), denotes the time series of the dth window in the ith brain region after centering, d = 1,..., D, μ d denotes the mean of the time series of the dth window, denotes the time series of the dth window in the ith brain region after Min-max normalization, min and max denote the minimum and maximum of the time series of the dth window after centering, respectively. Put concatenated to obtain the time series matrix of the dth window: wherein, denotes the time series of the dth window in the 1st brain region after Min-max normalization, denotes the time series of the dth window in the Pth brain region, i.e. the last brain region, after Min-max normalization.

4. The method of claim 3, wherein: In step 4, the brain functional network is constructed using the Pearson correlation coefficient PCC between the brain regions; The brain regions are regarded as nodes, and the PCC is regarded as the edge connecting them; The PCC is calculated using the following method: p ij = corr{x(i), x(j)} (6) In Equation (6): x(i) and x(j) represent the time series of the i-th and j-th brain regions, respectively, p ij is the pairwise Pearson correlation coefficient of x(i) and x(j), and corr is the Pearson correlation coefficient function. The Pearson correlation coefficient between the time series in each time window is calculated, and the brain functional network DBFN is constructed; The correlation coefficient matrix of the dth window brain functional network is denoted as Z (d) ≈(X (d) ) T X (d) , which is converted into an optimization form as follows: In Equation (7), X (d) represents the time series matrix of the dth window.

5. The method of claim 4, wherein: In step 5, the KNN algorithm is used to construct the hypergraph G; For a given time series X, the attribute relationship between the brain regions is described by the hypergraph G(V, E, W); the set of nodes is represented as V, the set of hyperedges is represented as E, and the set of weights of each hyperedge is represented as W; in the hypergraph G, each brain region corresponds to a node v in the hypergraph, and each hyperedge contains two or more nodes to represent the interaction of multiple brain regions at the same time; Let H ∈ R |V|×|E| is the point-edge incidence matrix of the hypergraph G, where the values of the matrix elements are defined as follows: In formula (8), v is a node of the hypergraph G, and e is a hyperedge of the hypergraph G; For the association matrix H, the node degree d(v i ) of each node and the edge degree δ(e i ) of each hyperedge are respectively represented as: In Equations (9) and (10), e i is the ith hyperedge, i = 1, …, m, where m represents the number of hyperedges; w(e i ) is the weight of the hyperedge; and v i is the ith node.

6. The method of claim 5, wherein: In step 6, the method of superimposing node convolution and hyperedge convolution is used to dynamically modify the hypergraph structure; First, node convolution is performed to aggregate node features to hyperedges containing these nodes; a transformation matrix T is learned from the node features to permute and weight the node features in the hyperedge; a multi-layer perceptron is used to generate the transformation matrix T, and a one-dimensional convolution is used to compress the transformed features: In Equation (11), X u represents the set of node features, is an element of the association matrix H in Step 5, x e represents the adjacent super-edge features, MLP represents a perception machine function, and conv represents a convolution function; Then, hyperedge convolution is performed to aggregate hyperedge features into centroid node features; The weight score of each hyperedge is generated by using an MLP, and the output centroid node feature is calculated as the weighted sum of the input hyperedge features; w * = softmax(x e B+b) (12) In formulas (12) and (13), w * is the weight of each super-edge, B and b are both learnable parameters, and softmax is a function for calculating weights; x u represents the centroid node feature, and |A(u)| represents the size of the adjacent super-edge set. Finally, the node features are updated to embed new features by combining node convolution and hyperedge convolution, and a new hypergraph structure is constructed on this basis; With the increase of feature embedding degree, the network embedding degree is deepened, and the hyperedge set is dynamically adjusted, and finally a new dynamic hypergraph G is obtained * (V * ,E * ,W * ).

7. The method of claim 6, wherein: In step 7, the Laplacian matrix reflects the internal geometric structure of the graph and is used for matrix representation of the graph; the Laplacian matrix of the hypergraph reflects the high-order relationship between the nodes and is represented as L = D v - Θ (14) In equation (14), is the adjacency matrix of the hypergraph, D v is the node degree matrix and the diagonal elements are d(v i ), D e is the hyperedge degree matrix and the diagonal elements are δ(e i ); The normalized Laplacian matrix of the dynamic hypergraph is calculated according to the calculation method of the Laplacian matrix of the graph, as shown in formula (15): In Equation (15), L dh is the normalized Laplacian matrix of the dynamic hypergraph, and I is the identity matrix. D v * is the dynamic hypergraph node degree matrix, D e * is the dynamic hypergraph hyperedge degree matrix, W * is the diagonal matrix with the dynamic hypergraph hyperedge weights on the diagonal, is the point-edge incidence matrix of the hypergraph G * .

8. The method of claim 7, wherein: In step 8, the popular regular term is constructed according to the dynamic hypergraph Laplacian matrix, and the L1 norm regular term is added, the node degree and edge degree of the dynamic hypergraph are calculated, and the manifold regular term of the dynamic hypergraph is obtained; the hypergraph convolution method based on node convolution and hyperedge convolution superposition is added to dynamically update the hypergraph structure, and the hypergraph representation form of the brain function network is obtained, and the objective function is as shown in formula (16): In equation (16), λ and β represent the regularization parameters of the L1 norm regularization term and the manifold regularization term, respectively, L dh is the normalized Laplacian matrix of the dynamic hypergraph.

9. The method of claim 8, wherein: In step 8, the hypergraph representation form DDBFN of the brain function network is constructed by: Step A: input time series matrix X, sliding window length L, sliding window step s, hyperparameter λ of L1 norm regular term, hyperparameter β of hypergraph manifold regular term, and neighbor number k in KNN algorithm; Step B: Initialize the time series matrix X of time windows (d) , dynamic hypergraph incidence matrix H * , dynamic hypergraph Laplacian matrix L dh ; Step C: using the neighbor operator method to optimize and solve the L1 norm regular term; Step C1: Update Z using gradient descent method (d) for m times; where Z m-1 (d) is Z (d) the result of the m-1th update, denotes the partial derivative of Z (d) with respect to α m is the step size in the gradient descent method; Step C2: Compute the proximity operator of the L1 norm regularizer to apply soft thresholding operation to the elements in Z (d) ; Step C3: After each gradient descent calculation, the nearest neighbor operator of Z (d) is calculated using the nearest neighbor operator method and put into the next iteration for updating; Step C4: repeat until the objective function converges, i.e. obtain Z (d) the optimal solution of DDBFN; where proximal denotes the proximal operator method, sgn is a function that returns the sign value of a numeric expression, represents the weight of the connection edge between the dth window node i and node j, and abs represents the absolute value function. Step D: Output DDBFN brain functional networks Z for each window (d) .

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