Analysis and Classification Method of Brain Functional Hypernetwork Topology Structure Based on Zero Model

Abstract

The present invention proposes a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model. First, a brain functional hypernetwork is constructed. Then, a null model of the brain functional hypernetwork that retains the topological attributes of the nodes and hyperedges of the original brain functional hypernetwork to different degrees is constructed. Next, the topological attributes of the original brain functional hypernetwork and the null model of the brain functional hypernetwork are calculated, and based on specific topological attributes, the correlation of this topological attribute of the two network models is evaluated. Finally, a better topological attribute is selected according to the correlation to construct a classification model. The method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model proposed by the present invention constructs a null model of the brain functional hypernetwork. By comparing the brain functional hypernetwork model with the corresponding null model, the dependence relationship between the features of interest is explored, and the topological attributes with important functions are identified, so as to make the analysis of the structure and dynamics of the final hypernetwork more realistic and improve the classification accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and particularly relates to a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model. Background Art

[0002] Existing research has successfully applied hypernetworks to characterize the complex multivariate interactions between multiple brain regions of the human brain, thereby obtaining a more realistic brain network. However, the existing research on brain functional hypernetworks mainly focuses on the improvement of network models and the application of the improved models, and does not analyze the structure and dynamics of brain functional hypernetworks. Summary of the Invention

[0003] The present invention provides a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model, and proposes a "chain generation" mechanism and a hyperedge legality check method to randomly generate effective null models within an adjustable range, analyze the dependence relationship between features of interest from the aspects of the structure and dynamics of the brain functional hypernetwork, and discriminate the redundancy relationship between the features of interest and other features, so as to identify the features of important functions in the brain functional hypernetwork and explain the working mechanism and pathological mechanism of the human brain.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: A method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model, comprising the following steps:

[0005] Step S1, acquiring resting-state functional magnetic resonance imaging data and performing preprocessing;

[0006] Step S2, dividing the preprocessed resting-state functional magnetic resonance imaging data into brain regions according to a selected standardized brain atlas, and then extracting the average time series of each brain region;

[0007] Step S3, constructing a brain functional hypernetwork model based on the average time series of each brain region by using the k-median algorithm;

[0008] Step S4, calculating different topological attributes of the brain functional hypernetwork model, including node average degree, hyperedge average degree, node degree, hyperedge degree, node pairwise joint degree distribution, three different clustering coefficients, shortest path, hyperedge pairwise joint degree distribution, node degree-related redundancy coefficient, and hyperedge degree-related redundancy coefficient;

[0009] Step S5, converting the brain functional hypernetwork model into a bipartite graph, and combining the "chain mechanism" strategy, and respectively constructing multiple brain functional hypernetwork null models that simultaneously retain the node and hyperedge topological attributes of the brain functional hypernetwork model by using a generation method and a rewiring method;

[0010] Step S6: Calculate all topological properties of multiple brain functional hypernetwork null models, and take each topological property as an interesting topological property to evaluate the correlation of the values of this topological property in the brain functional hypernetwork model and the brain functional hypernetwork null model;

[0011] Step S7: Compare the correlations of the interesting topological properties in the brain functional hypernetwork model and the brain functional hypernetwork null model, analyze the dependence relationship of this interesting topological property with the remaining topological properties, that is, the existing redundancy relationship, and select the topological property with less redundancy as the classification feature to construct a classification model.

[0012] Further, in step S2, it specifically includes:

[0013] Step S21: Use the anatomical labeling template AAL to divide the brain regions, and divide the whole brain into 90 brain regions, where there are 45 brain regions in the left and right hemispheres respectively;

[0014] Step S22: Extract the BOLD intensities of all corresponding voxels in each brain region at different time points, and then calculate the arithmetic mean of the BOLD intensities of each voxel at different time points to obtain the average time series of each brain region.

[0015] Among them, AAL represents the Anatomical Automatic Labeling (AAL) template, and BOLD represents Blood Oxygen Level Dependent (BOLD).

[0016] Further, in step S3, it specifically includes:

[0017] Based on the average time series of each brain region, set the number of clusters k, and use the k-median algorithm to cluster the brain regions, and each class is a hyperedge;

[0018] Considering the influence of multiple levels, with a step size of 5, the number of clusters k ∈ [5, 85], and generate corresponding hyperedges at each number of clusters k, that is, generate multi-scale hyperedges at multiple k values, and all multi-scale hyperedges form the brain functional hypernetwork model.

[0019] Further, in step S5, based on the bipartite graph, according to the parameter (Q v , Q e ) value, construct brain functional hypernetwork null models that retain different topological properties in the brain functional hypernetwork model to different degrees;

[0020] When Q v = 0, construct a brain functional hypernetwork null model under the condition of retaining the node average degree of the brain functional hypernetwork model;

[0021] When Qv When Q = 1, it is to construct a brain functional hypernetwork null model while preserving the node average degree and node degree of the brain functional hypernetwork model;

[0022] When Q v = 2, it is to generate a brain functional hypernetwork null model while approximately preserving the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model on the basis of preserving the node average degree and node degree of the brain functional hypernetwork model, that is, further approximately preserving the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model to generate a brain functional hypernetwork null model on the basis of Q v = 1;

[0023] When Q v = 2.5, it is to generate a brain functional hypernetwork null model while approximately preserving the node degree - related redundancy coefficient of the brain functional hypernetwork model on the basis of preserving the node average degree and node degree of the brain functional hypernetwork model and approximately preserving the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model, that is, approximately preserving the node degree - related redundancy coefficient of the brain functional hypernetwork model to generate a brain functional hypernetwork null model on the basis of Q v = 2;

[0024] Similarly, when Q e = 0, the hyper - edge average degree of the brain functional hypernetwork model is preserved, when Q e = 1, the hyper - edge average degree and hyper - edge degree of the brain functional hypernetwork model are preserved, when Q e = 2, the pairwise joint degree distribution of the hyper - edges of the brain functional hypernetwork model is approximately preserved on the basis of Q e = 1, when Q e = 2.5, the hyper - edge degree - related redundancy coefficient of the brain functional hypernetwork model is approximately preserved on the basis of Q e = 2.

[0025] Furthermore, in step S5, it specifically includes the following steps:

[0026] Step S51: Construct a bipartite graph corresponding to the brain functional hypernetwork model, and convert the brain functional hypernetwork model into a simple bipartite graph with M + N nodes and W edges; where M represents the number of brain region nodes in the brain functional hypernetwork model, and N represents the number of hyper - edges in the brain functional hypernetwork model;

[0027] Step S52: Based on the bipartite graph, construct different null models according to different preserved topological attributes; for Q v ∈{0, 1} and Q e ∈{0, 1}, use the generation method to construct brain functional hypernetwork null models that preserve the node average degree, hyper - edge average degree, node degree, and hyper - edge degree of the brain functional hypernetwork model to different degrees;

[0028] Step S53: Use the rewiring method to construct Qv = 2 or Q e The null model of the brain functional hypernetwork when = 2, based on Q v = 1 or Q e The bipartite graph obtained when = 1 is rewired according to the topological properties to be retained, and the finally generated bipartite graph is converted into a hypernetwork, which is the corresponding null model of the brain functional hypernetwork;

[0029] Step S54: Construct Q using the rewiring method v = 2.5 or Q e The null model of the brain functional hypernetwork when = 2.5, based on Q v = 2 or Q e The bipartite graph obtained when = 2 is rewired according to the topological properties to be retained. The number of rewiring times is 500W, and the finally generated bipartite graph is converted into a hypernetwork, which is the corresponding null model of the brain functional hypernetwork.

[0030] Furthermore, in step S52, it specifically includes:

[0031] Starting from a bipartite graph with M + N nodes and no edges, and then randomly generating the edges of the bipartite graph according to the parameters (Q v , Q e ), and finally converting the generated bipartite graph into a hypernetwork, which is the corresponding null model of the brain functional hypernetwork;

[0032] Among them, (Q v , Q e ) = (0, 0) means retaining the node average degree and hyperedge average degree of the brain functional hypernetwork model to generate the corresponding bipartite graph, randomly selecting a bipartite graph node represented by a node type and a bipartite graph node represented by a hyperedge type in the bipartite graph and connecting them until W edges of the bipartite graph are generated, and finally obtaining a bipartite graph with M + N nodes and W edges;

[0033] (Q v , Q e ) = (0, 1) means retaining the node average degree, hyperedge average degree and hyperedge degree of the brain functional hypernetwork model to generate the corresponding bipartite graph, first attaching half-edges with the same number as the hyperedge degree to each bipartite graph node represented by a hyperedge in the bipartite graph, and then randomly selecting a bipartite graph node represented by a node type to connect with each remaining half-edge, and finally obtaining a bipartite graph with M + N nodes and W edges;

[0034] (Q v , Q e(Q, Q) = (1, 0) means to retain the node average degree, hyperedge average degree, and node degree of the brain functional hypernetwork model to generate the corresponding bipartite graph. In the bipartite graph, first attach half-edges with the same number as the node degree to each bipartite graph node represented by the node type, and then for each remaining half-edge, randomly select a bipartite graph node represented by a hyperedge to connect to it. Finally, a bipartite graph with M + N nodes and W edges is obtained;

[0035] (Q v , Q e ) = (1, 1) means to retain the node average degree, hyperedge average degree, hyperedge degree, and node degree of the brain functional hypernetwork model to generate the corresponding bipartite graph. In the bipartite graph, first attach half-edges with the same number as the hyperedge degree to each bipartite graph node represented by a hyperedge, attach half-edges with the same number as the node degree to each bipartite graph node represented by the node type, and then randomly select the half-edges attached to the node type and the half-edges attached to the hyperedge type and connect them until there are no unconnected half-edges. Finally, a bipartite graph with M + N nodes and W edges is obtained.

[0036] Further, in step S53, it specifically includes:

[0037] Q v ∈ {0, 1} and Q e = 2 means to approximately retain the bipartite graph generated by the hyperedge pairwise joint degree distribution of the brain functional hypernetwork model on the basis of Q v ∈ {0, 1} and Q e = 1;

[0038] When (Q v , Q e ) = (0, 2), it is to rewire the bipartite graph generated by (Q v , Q e ) = (0, 1) to approximately retain the hyperedge pairwise joint degree distribution;

[0039] When (Q v , Q e ) = (1, 2), it is to rewire the bipartite graph generated by (Q v , Q e ) = (1, 1) to approximately retain the hyperedge pairwise joint degree distribution;

[0040] The specific process of rewiring at this time is: first randomly select two edges (v, e) and (v′, e′), and satisfy v ≠ v′, e ≠ e′, and then replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the hyperedge pairwise joint degree distributions before and after the original and replacement edges decreases. The number of rewiring times is 500W;

[0041] Q v= 2 and Q e ∈ {0, 1} indicates that on the basis of Q v = 1 and Q e ∈ {0, 1}, a bipartite graph generated by approximately retaining the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model is generated;

[0042] When (Q v , Q e ) = (2, 0), it is to perform rewiring on the bipartite graph generated by (Q v , Q e ) = (1, 0) to approximately retain the pairwise joint degree distribution of the nodes;

[0043] When (Q v , Q e ) = (2, 1), it is to perform rewiring on the bipartite graph generated by (Q v , Q e ) = (1, 1) to approximately retain the pairwise joint degree distribution of the nodes;

[0044] At this time, the specific process of rewiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v ≠ v′, e ≠ e′. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the pairwise joint degree distributions of the nodes before and after the original and replaced edges decreases. The number of rewiring times is 500W;

[0045] (Q v , Q e ) = (2, 2) indicates that on the basis of (Q v , Q e ) = (1, 1), both the pairwise joint degree distribution of the hyperedges and the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model are approximately retained. Rewiring operations are performed on the basis of the bipartite graph generated by (Q v , Q e ) = (1, 1). At this time, the specific process of rewiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v ≠ v′, e ≠ e′. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the pairwise joint degree distributions of the hyperedges and the distance between the pairwise joint degree distributions of the nodes after the original and replaced edges decrease simultaneously. The number of rewiring times is 500W.

[0046] Further, in step S54, it specifically includes:

[0047] Q v ∈ {0, 1} and Q e = 2.5 indicates that on the basis of Q v ∈ {0, 1} and Q eA bipartite graph approximately retaining the hyper-edge degree-related redundancy coefficient of the brain functional hyper-network model is generated based on ;

[0048] When (Q v , Q e ) = (0, 2.5), re-wiring is performed on the bipartite graph generated when (Q v , Q e ) = (0, 2) to approximately retain the hyper-edge degree-related redundancy coefficient of the brain functional hyper-network model;

[0049] When (Q v , Q e ) = (1, 2.5), re-wiring is performed on the bipartite graph generated when (Q v , Q e ) = (1, 2) to approximately retain the hyper-edge degree-related redundancy coefficient of the brain functional hyper-network model;

[0050] The specific process of re-wiring at this time is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v ≠ v′, e ≠ e′, and the degree values of the hyper-edges e and e′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the hyper-edge degree-related redundancy coefficients before and after the original and replacement edges decreases;

[0051] Q v = 2.5 and Q e ∈ {0, 1} indicates a bipartite graph approximately retaining the node degree-related redundancy coefficient of the brain functional hyper-network model based on Q v = 2 and Q e ∈ {0, 1};

[0052] When (Q v , Q e ) = (2.5, 0), re-wiring is performed on the bipartite graph generated when (Q v , Q e ) = (2, 0) to approximately retain the node degree-related redundancy coefficient of the brain functional hyper-network model;

[0053] When (Q v , Q e ) = (2.5, 1), re-wiring is performed on the bipartite graph generated when (Q v , Q e ) = (2, 1) to approximately retain the node degree-related redundancy coefficient of the brain functional hyper-network model;

[0054] At this time, the specific process of rewiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, and the degree values of nodes v and v′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the node-degree-related redundancy coefficients before and after the original and replaced edges decreases;

[0055] (Q v ,Q e ) = (2, 2.5) means that on the basis of generating a bipartite graph with (Q v ,Q e ) = (2, 2), rewiring is performed to approximately preserve the hyperedge-degree-related redundancy coefficient of the brain functional hypernetwork model. At this time, the specific process of rewiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, the degree values of hyperedges e and e′ are the same, and the degree values of nodes v and v′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the hyperedge-degree-related redundancy coefficients before and after the original and replaced edges decreases;

[0056] (Q v ,Q e ) = (2.5, 2) means that on the basis of generating a bipartite graph with (Q v ,Q e ) = (2, 2), rewiring is performed to approximately preserve the node-degree-related redundancy coefficient of the brain functional hypernetwork model. At this time, the specific process of rewiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, the degree values of hyperedges e and e′ are the same, and the degree values of nodes v and v′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the node-degree-related redundancy coefficients before and after the original and replaced edges decreases.

[0057] According to the above steps, different (Q v ,Q e ) values are set. After generating different bipartite graphs, they are then converted into the form of a hypernetwork, and this hypernetwork is the null model that retains different topological properties.

[0058] Further, in step S6, it specifically includes:

[0059] Step S61: Select the hypernetwork topological properties of interest, including the average node degree, average hyperedge degree, node degree, hyperedge degree, pairwise joint degree distribution of nodes, pairwise joint degree distribution of hyperedges, node-degree-related redundancy coefficient, hyperedge-degree-related redundancy coefficient, clustering coefficient, and shortest path length. Then, calculate the topological properties of the brain functional hypernetwork model and the corresponding brain functional hypernetwork null model respectively;

[0060] Step S62: Calculate the correlation between the topological attributes of the brain functional hypernetwork model and the corresponding null model of the brain functional hypernetwork using the Pearson correlation analysis method.

[0061] Further, in step S7, it specifically includes:

[0062] Step S71: Select specific topological attributes based on the correlation between topological attributes. Based on the specific topological attributes, use an SVM classifier based on radial basis functions, and select the specific topological attributes with significant between-group differences after non-parametric testing as classification features to construct a classification model;

[0063] Step S72: Randomly select 90% of the samples from the sample set as the training set, and the remaining 10% of the samples as the test set, and conduct classification tests accordingly and calculate the classification accuracy; Arithmetically average the classification accuracies obtained after repeating the classification test 100 times, and then use the arithmetic mean as the classification accuracy of the classifier.

[0064] Advantages of the present invention: The present invention proposes a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model, uses node and hyperedge attributes to comprehensively characterize the topological structure of the brain functional hypernetwork, and then proposes a "chain generation" mechanism to sequentially retain different topological attributes, and generates multiple different null models of the brain functional hypernetwork in a nested manner within an adjustable range. At the same time, during the random generation of the null model, a hyperedge legality check method is proposed to test the generated null model to avoid the existence of duplicate hyperedges or empty hyperedges, so as to more accurately construct the corresponding null model. The present invention explores the topology of the brain functional hypernetwork from the perspective of the dynamic network structure to discover the dependence relationship between the topological attributes of interest and other topological attributes, identify the topological attributes of important functions, and infer the redundancy between multiple groups of topological attributes. Brief Description of the Drawings

[0065] Figure 1 It is a schematic flowchart of a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model provided by an embodiment of the present invention;

[0066] Figure 2 It is a comparison schematic diagram between the present invention and the traditional method for classifying magnetic resonance imaging data. Detailed Embodiment

[0067] In order to make the objectives, technical solutions, and advantages of the present invention clearer and more complete, the following will further elaborate on the present invention in combination with embodiments and the accompanying drawings. It should be noted that the present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to disclose the present invention in detail and completely, and to fully convey the scope of the present invention to those skilled in the art.

[0068] As shown Figure 1 in the figure, a method for analyzing and classifying the topological structure of a brain functional hypernetwork based on a null model provided by an embodiment of the present invention includes the following steps:

[0069] Step S1: Collect resting-state functional magnetic resonance imaging data, and then perform preprocessing operations on the collected data;

[0070] Step S2: Divide the preprocessed resting-state functional magnetic resonance imaging data into brain regions according to a selected standardized brain atlas, and then extract the average time series of each brain region;

[0071] Step S3: Use the k-median algorithm to construct a brain functional hypernetwork;

[0072] Step S4: Calculate different topological properties of the brain functional hypernetwork, specifically including node average degree, hyperedge average degree, node degree, hyperedge degree, node pairwise joint degree distribution, three different clustering coefficients, shortest path, hyperedge pairwise joint degree distribution, node degree-related redundancy coefficient, hyperedge degree-related redundancy coefficient;

[0073] Step S5: Convert the brain functional hypernetwork into a bipartite graph. Based on this bipartite graph, combined with the "chain mechanism" strategy, use the generation method and the rewiring method to construct multiple brain functional hypernetwork null models that simultaneously retain the node and hyperedge topological properties of the brain functional hypernetwork model;

[0074] Step S6: Calculate all topological properties of multiple brain functional hypernetwork null models, and use each topological property as an interesting topological property, and evaluate the correlation between the topological property value in the brain functional hypernetwork model and multiple null models;

[0075] Step S7: By comparing the correlation between the brain functional hypernetwork model and multiple null models in terms of the interesting topological properties of the network models, analyze the dependence relationship, that is, the existing redundancy relationship, between the interesting topological property and the remaining topological properties, and select the topological property with less redundancy as the classification feature to construct a classification model.

[0076] In a specific embodiment, in the step S1, the preprocessing operation specifically includes: discarding the initial data signal to exclude the influence of instability at the start of the device, time slice correction to correct the time difference between each scan slice, head motion correction to reduce the influence of the subject's head motion on the data, spatial normalization to avoid the influence of differences in brain structures between subjects, and low-frequency filtering to obtain the resting-state functional magnetic resonance imaging signal that can reflect spontaneous neural activity.

[0077] In a specific embodiment, the step S2 specifically includes the following steps:

[0078] Step S21: Use the AAL anatomical labeling template provided by the Montreal Neurological Institute to divide the brain regions, and divide the whole brain into 90 brain regions (45 brain regions in the left and right hemispheres respectively);

[0079] Step S22: Extract the BOLD intensities of all corresponding voxels in each brain region at different time points, and then calculate the arithmetic mean of the BOLD intensities of each voxel at different time points to obtain the average time series of each brain region.

[0080] In a specific embodiment, in step S3, constructing a brain functional hypernetwork using the k-median algorithm specifically includes the following steps:

[0081] Step S31: Specifically,

[0082] 1) Based on the brain region time series, set the number of clusters k, and randomly select k specific brain regions as the initial seed nodes S = {S 1 , S 2 ,... S k};

[0083] 2) Calculate the Manhattan distances from the remaining brain regions to the seed node S i respectively;

[0084] 3) Combine the brain region with the shortest distance to S i with S i to form a new sub-region;

[0085] 4) In the new sub-region, reset the brain region at the median in the sub-region as the physical center point of the new sub-region, and use it as the new seed node, so as to further calculate the Manhattan distances from the remaining brain regions to the new seed node;

[0086] 5) Repeat steps 3) and 4) until the new seed node does not change. Finally, the new sub-region generated by each seed node is a hyperedge.

[0087] Step S32: Considering the multi-level influence, with a step size of 5, the number of clusters k ∈ [5, 85], generate corresponding hyperedges at each number of clusters k, that is, generate multi-scale hyperedges at multiple k values, and all multi-scale hyperedges form a brain functional hypernetwork.

[0088] In a specific embodiment, in step S4, considering that some nodes and hyperedges in the brain functional hypernetwork play important roles in information transmission, and most traditional brain functional hypernetworks quantify information through node features, ignoring the topological attribute information of hyperedges. Therefore, the present invention introduces the average hyperedge degree, hyperedge degree, and proposes the hyperedge pairwise joint degree distribution and hyperedge degree-related redundancy coefficient hyperedge topological attributes, and combines node features to comprehensively characterize the topological information of the hypernetwork.

[0089] The node topological attributes and hyperedge topological attributes of the specific hypernetwork include: average node degree, node degree, pairwise joint degree distribution of nodes, node-degree-related redundancy coefficient, three different clustering coefficients, shortest path, average hyperedge degree, hyperedge degree, pairwise joint degree distribution of hyperedges, hyperedge-degree-related redundancy coefficient, and their specific definitions are as follows:

[0090]

[0091] In formula (1), avg_d node represents the average node degree of the hypernetwork; V represents the set of nodes in the hypernetwork; M represents the number of nodes in the hypernetwork; d node (v) represents the degree of node v in the hypernetwork, and the specific definition is:

[0092]

[0093] In formula (2), d node (v) represents the node degree of any node v in the hypernetwork; E represents the set of hyperedges in the hypernetwork; H(v, e) represents the incidence matrix of the hypernetwork, where the row elements represent nodes and the column elements represent hyperedges. When hyperedge e contains node v, H(v, e) = 1; otherwise, H(v, e) = 0.

[0094]

[0095] In formula (3), P node (d node , d node ′) represents the pairwise joint degree distribution of nodes in the hypernetwork; m node (d node , d node ′) represents the number of shared hyperedges between a node with degree d node and a node with degree d node ′; E represents the set of hyperedges in the hypernetwork; d edge (e) represents the degree of hyperedge e in the hypernetwork.

[0096]

[0097] In formula (4), r node (d node ) represents the node-degree-related redundancy coefficient of the hypernetwork; n node (d node ) represents the number of nodes with degree d node ; V represents the set of nodes in the hypernetwork; d node (v) represents the degree of node v in the hypernetwork; r node (v) represents the redundancy coefficient of node v in the hypernetwork, and the definition is:

[0098]

[0099] In formula (5), r node (v) represents the redundancy coefficient of any node v in the hypernetwork; d node (v) represents the degree of node v in the hypernetwork; E represents the set of hyperedges in the hypernetwork; E′ represents the set of traversed hyperedges but does not include the hyperedge e; 1 {cond} and Γ v,e,e′ ={v′∈V\{v}|H(v′,e)H(v′,e′)>0} represents the indicator function, which returns 1 if the condition cond holds, otherwise returns 0.

[0100] The calculation formulas for three different clustering coefficients (Hypergraph Cluster Coefficient, HCC) and shortest path lengths (Shortest Path, SP) are specifically expressed as follows:

[0101]

[0102] In formula (6), HCC 1 (v) represents the first type of clustering coefficient; u, t, v represent nodes; Q(v) represents the set of other nodes contained in the hyperedges containing node v; E represents the set of hyperedges in the hypernetwork, if When u,t∈e and then otherwise

[0103]

[0104] In formula (7), HCC 2 (v) represents the second type of clustering coefficient; u, t, v represent nodes; Q(v) represents the set of other nodes contained in the hyperedges containing node v; E represents the set of hyperedges in the hypernetwork, if When u,t,v∈e, then I′(u,t,v)=1, otherwise I′(u,t,v)=0.

[0105]

[0106] In formula (8), HCC 3 (v) represents the third type of clustering coefficient; v represents a node; S(v) represents the set of hyperedges containing node v; |e| represents the number of nodes contained in the hyperedge e; Q(v) represents the set of other nodes contained in the hyperedges containing node v.

[0107]

[0108] In formula (9), SP(v) represents the shortest path of any node v in the hypernetwork; V represents the set of nodes in the hypernetwork; D(u, v) represents the shortest path between nodes u and v; M represents the number of nodes in the hypernetwork.

[0109]

[0110] In formula (10), avg_d edge represents the average degree of hyperedges in the hypernetwork; E represents the set of hyperedges in the hypernetwork; d edge (e) represents the degree of hyperedge e in the hypernetwork; N represents the number of hyperedges in the hypernetwork.

[0111]

[0112] In formula (11), d edge (e) represents the hyperedge degree of hyperedge e in the hypernetwork; V represents the set of nodes in the hypernetwork; H(v, e) represents the incidence matrix of the hypernetwork, where the row elements represent nodes and the column elements represent hyperedges. When hyperedge e contains node v, H(v, e) = 1; otherwise, H(v, e) = 0.

[0113]

[0114] In formula (12), P edge (d edge , d edge ′) represents the pairwise joint degree distribution of hyperedges in the hypernetwork; m edge (d edge , d edge ′) represents the number of shared nodes of a hyperedge with degree d edge and a hyperedge with degree d edge ′; V represents the set of nodes in the hypernetwork; d node (v) represents the degree of node v in the hypernetwork.

[0115]

[0116] In formula (13), r edge (d edge ) represents the hyperedge degree-related redundancy coefficient of the hypernetwork; n edge (d edge ) represents the number of hyperedges with degree d edge ; E represents the set of hyperedges in the hypernetwork; d edge (e) represents the degree of hyperedge e in the hypernetwork; r edge (e) represents the redundancy coefficient of hyperedge e in the hypernetwork, and its specific definition is:

[0117]

[0118] In formula (14), r edge (e) represents the hyperedge redundancy coefficient of any hyperedge e in the hypernetwork; d edge (e) represents the degree of hyperedge e in the hypernetwork; V represents the set of nodes in the hypernetwork; V′ represents the set of nodes that have been traversed but does not include node v; 1 {cond} and Γ v,v′,e ={e′∈E\{e}|H(v,e′)H(v′,e′)>0} represents an indicator function that returns 1 if the condition cond holds, otherwise returns 0.

[0119] In a specific embodiment, although step S5 can comprehensively quantify the topological information of the brain functional hypernetwork by introducing hyperedge attributes and combining node attributes from multiple perspectives, due to the complex characteristics of hyperedges, the computational complexity of quantifying the topological information of the hypernetwork also increases significantly. At the same time, there may be a problem of high dependence (i.e., high redundancy) among multiple topological attributes, ultimately affecting the classification and diagnosis of brain diseases.

[0120] The present invention introduces a null model to evaluate the dependence relationship among topological attributes of brain functional hypernetworks. Without losing the topological information of the brain functional hypernetwork, topological attributes with less dependence (i.e., lower redundancy) are selected to participate in the construction of the classification model. The null model refers to a random network that has some of the same properties as a specific network. In the brain functional hypernetwork, it is to randomize the hypernetwork model under the condition of retaining specific topological attributes of the brain functional hypernetwork, and finally obtain the null model of the brain functional hypernetwork. Different null models are obtained when different specific topological attributes are retained.

[0121] The present invention generates different null models based on the chain mechanism strategy. Specifically, according to the parameter (Q v , Q e ) values, null models of the brain functional hypernetwork that retain the node topological attributes and hyperedge topological attributes of the brain functional hypernetwork model to different degrees are constructed. When Q v =0, a null model of the brain functional hypernetwork is constructed under the condition of retaining the average node degree of the brain functional hypernetwork model. When Q v =1, a null model of the brain functional hypernetwork is constructed under the condition of retaining the average node degree and node degree of the brain functional hypernetwork model. When Q v =2, a null model of the brain functional hypernetwork is generated under the condition of retaining the average node degree and node degree of the brain functional hypernetwork model, and at the same time approximately retaining the pairwise joint degree distribution of the nodes in the brain functional hypernetwork model, that is, on the basis of Q v =1, further approximately retaining the pairwise joint degree distribution of the nodes in the brain functional hypernetwork model to generate the null model of the brain functional hypernetwork. When Q vWhen Q = 2.5, a null model of the brain functional hypernetwork is generated by approximately retaining the node degree-related redundancy coefficient of the brain functional hypernetwork model while approximately retaining the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model under the condition of retaining the average node degree and node degree of the brain functional hypernetwork model, that is, on the basis of Q v = 2, approximately retaining the node degree-related redundancy coefficient of the brain functional hypernetwork model to generate a null model of the brain functional hypernetwork; similarly, when Q e = 0, the average hyperedge degree of the brain functional hypernetwork model is retained, and when Q e = 1, the average hyperedge degree and hyperedge degree of the brain functional hypernetwork model are retained. When Q e = 2, on the basis of Q e = 1, the pairwise joint degree distribution of the hyperedges of the brain functional hypernetwork model is approximately retained. When Q e = 2.5, on the basis of Q e = 2, the hyperedge degree-related redundancy coefficient of the brain functional hypernetwork model is approximately retained, which specifically includes the following steps:

[0122] Step S51: Construct a bipartite graph corresponding to the brain functional hypernetwork. Specifically, convert the brain functional hypernetwork into a simple bipartite graph with M + N nodes (where M represents the number of brain region nodes in the original brain functional hypernetwork and N represents the number of hyperedges in the original brain functional hypernetwork) and W edges. Therefore, it can be known that the nodes of the bipartite graph include two types. One is the brain region nodes of the brain functional hypernetwork model, and the other is the hyperedges of the brain functional hypernetwork model. Its edges are such that if a brain region node v is included in a certain hyperedge e, then there is an edge (v, e) in the bipartite graph |{(v, e) ∈ W}.

[0123] Step S52: Based on the bipartite graph, construct different null models according to different retained topological properties. For Q v ∈ {0, 1} and Q e ∈ {0, 1}, use the generation method to construct null models that retain the average node degree, average hyperedge degree, node degree, and hyperedge degree of the brain functional hypernetwork model to different degrees. Specifically, first start from a bipartite graph with M + N nodes and no edges, and then randomly generate the edges of the bipartite graph according to the parameters (Q v , Q e ), and finally convert the generated bipartite graph into a hypernetwork, which is the corresponding null model of the brain functional hypernetwork. Specifically:

[0124] (Q v , Q e(Q)=(0,0) means to generate the corresponding bipartite graph by retaining the node average degree and hyperedge average degree of the brain functional hypernetwork model. Specifically, in the bipartite graph, randomly select a bipartite graph node represented by a node type and a bipartite graph node represented by a hyperedge type and connect them until W edges of the bipartite graph are generated. Finally, a bipartite graph with M + N nodes (where M represents the node type in the brain functional hypernetwork, N represents the hyperedge type in the brain functional hypernetwork, and the same meaning will be used hereinafter and will not be repeated) and W edges is obtained.

[0125] (Q v ,Q e )=(0,1) means to generate the corresponding bipartite graph by retaining the node average degree, hyperedge average degree and hyperedge degree of the brain functional hypernetwork model. Specifically, in the bipartite graph, first attach half-edges with the same number as the hyperedge degree to each bipartite graph node represented by a hyperedge, then for each remaining half-edge, randomly select a bipartite graph node represented by a node type and connect it. Finally, a bipartite graph with M + N nodes and W edges is obtained.

[0126] (Q v ,Q e )=(1,0) means to generate the corresponding bipartite graph by retaining the node average degree, hyperedge average degree and node degree of the brain functional hypernetwork model. Specifically, in the bipartite graph, first attach half-edges with the same number as the node degree to each bipartite graph node represented by a node type, then for each remaining half-edge, randomly select a bipartite graph node represented by a hyperedge and connect it. Finally, a bipartite graph with M + N nodes and W edges is obtained.

[0127] (Q v ,Q e )=(1,1) means to generate the corresponding bipartite graph by retaining the node average degree, hyperedge average degree, hyperedge degree and node degree of the brain functional hypernetwork model. Specifically, in the bipartite graph, first attach half-edges with the same number as the hyperedge degree to each bipartite graph node represented by a hyperedge, attach half-edges with the same number as the node degree to each bipartite graph node represented by a node type, then randomly select the half-edges attached to the node type and the half-edges attached to the hyperedge type and connect them until there are no unconnected half-edges. Finally, a bipartite graph with M + N nodes and W edges is obtained.

[0128] Step S53: Construct Q using the rewiring method v = 2 or Q e = 2 for the null model, mainly in Q v = 1 or Q e = 1 means to further generate a bipartite graph by approximately retaining the pairwise joint degree distribution of nodes or the pairwise joint degree distribution of hyperedges of the brain functional hypernetwork model based on the bipartite graph represented. Specifically, based on Q v = 1 or Q eThe bipartite graph obtained when = 1 is re-wired according to the topological properties to be retained, and the finally generated bipartite graph is converted into a hypernetwork, which is the zero model of the corresponding brain functional hypernetwork. The detailed steps are as follows:

[0129] Q v ∈ {0, 1} and Q e = 2 indicates that on the basis of Q v ∈ {0, 1} and Q e = 1, a bipartite graph is generated by approximately retaining the pairwise joint degree distribution of the hyperedges of the brain functional hypernetwork model. Specifically, when (Q v , Q e ) = (0, 2), it is re-wired on the bipartite graph generated when (Q v , Q e ) = (0, 1) to approximately retain the pairwise joint degree distribution of the hyperedges; when (Q v , Q e ) = (1, 2), it is re-wired on the bipartite graph generated when (Q v , Q e ) = (1, 1) to approximately retain the pairwise joint degree distribution of the hyperedges. The specific process of re-wiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v ≠ v′, e ≠ e′. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the pairwise joint degree distributions of the hyperedges before and after the original and replacement edges decreases. The number of re-wiring times is 500W.

[0130] Q v = 2 and Q e ∈ {0, 1} indicates that on the basis of Q v = 1 and Q e ∈ {0, 1}, a bipartite graph is generated by approximately retaining the pairwise joint degree distribution of the nodes of the brain functional hypernetwork model. Specifically, when (Q v , Q e ) = (2, 0), it is re-wired on the bipartite graph generated when (Q v , Q e ) = (1, 0) to approximately retain the pairwise joint degree distribution of the nodes; when (Q v , Q e ) = (2, 1), it is re-wired on the bipartite graph generated when (Q v , Q e) = (1, 1), re - wiring is performed on the generated bipartite graph to approximately preserve the pairwise joint degree distribution of nodes. The specific process of re - wiring is as follows: First, randomly select two edges (v, e) and (v′, e′) with v ≠ v′ and e ≠ e′. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the pairwise joint degree distributions of nodes before and after the original and replaced edges decreases. The number of re - wiring times is 5 million.

[0131] (Q v ,Q e ) = (2, 2) means that on the basis of (Q v ,Q e ) = (1, 1), both the pairwise joint degree distribution of hyper - edges and the pairwise joint degree distribution of nodes of the brain functional hyper - network model are approximately preserved. Specifically, re - wiring operations are performed on the bipartite graph generated by (Q v ,Q e ) = (1, 1). The specific process of re - wiring is as follows: First, randomly select two edges (v, e) and (v′, e′) with v ≠ v′ and e ≠ e′. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distances between the pairwise joint degree distributions of hyper - edges and the pairwise joint degree distributions of nodes before and after the original and replaced edges both decrease. The number of re - wiring times is 5 million.

[0132] Step S54: Use the re - wiring method to construct the null model when Q v = 2.5 or Q e = 2.5. Mainly, on the basis of Q v = 2 or Q e = 2, a bipartite graph is further generated by approximately preserving the node - degree - related redundancy coefficient or the hyper - edge - degree - related redundancy coefficient of the brain functional hyper - network model. Specifically, based on the bipartite graph obtained when Q v = 2 or Q e = 2, re - wiring is performed according to the topological properties to be preserved, and the number of re - wiring times is 5 million. The finally generated bipartite graph is converted into a hyper - network, which is the corresponding null model of the brain functional hyper - network. The detailed steps are as follows:

[0133] Q v ∈{0, 1} and Q e = 2.5 means a bipartite graph generated by approximately preserving the hyper - edge - degree - related redundancy coefficient of the brain functional hyper - network model on the basis of Q v ∈{0, 1} and Q e = 2. Specifically, when (Q v ,Q e ) = (0, 2.5), it is on the basis of (Q v ,Q e)=(0,2) Generate bipartite graphs for rewiring to approximately preserve the hyper - edge - degree - related redundancy coefficient of the brain functional hyper - network model; when (Q v ,Q e )=(1,2.5), it is to re - wire on the bipartite graph generated by (Q v ,Q e )=(1,2) to approximately preserve the hyper - edge - degree - related redundancy coefficient of the brain functional hyper - network model. The specific process of re - wiring is as follows: First, randomly select two edges (v,e) and (v′,e′), and satisfy v≠v′, e≠e′, and the degree values of the hyper - edges e and e′ are the same. Then, replace (v,e) and (v′,e′) with (v,e′) and (v′,e) if and only if the distance between the hyper - edge - degree - related redundancy coefficients before and after the original and replaced edges decreases.

[0134] Q v =2.5 and Q e ∈{0,1} means generating a bipartite graph that approximately preserves the node - degree - related redundancy coefficient of the brain functional hyper - network model based on Q v =2 and Q e ∈{0,1}. Specifically, when (Q v ,Q e )=(2.5,0), it is to re - wire on the bipartite graph generated by (Q v ,Q e )=(2,0) to approximately preserve the node - degree - related redundancy coefficient of the brain functional hyper - network model; when (Q v ,Q e )=(2.5,1), it is to re - wire on the bipartite graph generated by (Q v ,Q e )=(2,1) to approximately preserve the node - degree - related redundancy coefficient of the brain functional hyper - network model. The specific process of re - wiring is as follows: First, randomly select two edges (v,e) and (v′,e′), and satisfy v≠v′, e≠e′, and the degree values of the nodes v and v′ are the same. Then, replace (v,e) and (v′,e′) with (v,e′) and (v′,e) if and only if the distance between the node - degree - related redundancy coefficients before and after the original and replaced edges decreases.

[0135] (Q v ,Q e )=(2,2.5) means in (Q v ,Q e)=(2, 2) On the basis of generating a bipartite graph, re - wiring is carried out to approximately preserve the hyper - edge - degree - related redundancy coefficient of the brain functional hyper - network model. The specific process of re - wiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, the degree values of hyper - edges e and e′ are the same, and the degree values of nodes v and v′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the hyper - edge - degree - related redundancy coefficients before and after the original and replaced edges decreases.

[0136] (Q v ,Q e )=(2.5, 2) indicates that on the basis of (Q v ,Q e )=(2, 2) generating a bipartite graph, re - wiring is carried out to approximately preserve the node - degree - related redundancy coefficient of the brain functional hyper - network model. The specific process of re - wiring is as follows: First, randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, the degree values of hyper - edges e and e′ are the same, and the degree values of nodes v and v′ are the same. Then, replace (v, e) and (v′, e′) with (v, e′) and (v′, e) if and only if the distance between the node - degree - related redundancy coefficients before and after the original and replaced edges decreases.

[0137] During the re - wiring process, the distance between each kind of topological property to be preserved is obtained through the normalized L 1 distance. The specific calculation formula is as follows:

[0138]

[0139] In formula (15), DL 1 represents the distance between the topological properties to be preserved in the brain functional hyper - network model and the re - wired hyper - network. Tat(i) represents the specific topological property vector in the brain functional hyper - network model of the i - th brain region, and Tat′(i) represents the topological property vector of the re - wired hyper - network in the i - th brain region.

[0140] According to the above steps, different (Q v ,Q e) After generating different bipartite graphs with values and then converting them into a hypernetwork form, this hypernetwork serves as a null model that retains different topological properties. In this null model, the hyperedges are all the neighbor nodes of the nodes corresponding to the hyperedge types in the bipartite graph (i.e., the nodes corresponding to the node types that are connected to the nodes corresponding to the hyperedge types), and the nodes are the brain region nodes in the brain functional hypernetwork. Its significance is to selectively retain different topological properties of the brain functional hypernetwork model and explore how the important functional characteristics of the brain functional hypernetwork represent the working mechanism and pathological mechanism of the human brain. It should be noted that in the above null model, for the four topological properties of node average degree, hyperedge average degree, node degree, and hyperedge degree, the null models of the corresponding parameters are precisely retained; while for the four topological properties of node pairwise joint degree distribution, hyperedge pairwise joint degree distribution, node degree-related redundancy coefficient, and hyperedge degree-related redundancy coefficient, the null models of the corresponding parameters are approximately retained.

[0141] In a specific embodiment, in step S6, it specifically includes:

[0142] Step S61: Calculate all topological properties of the brain functional hypernetwork model and the null model respectively.

[0143] Step S62: Take each topological property as a specific topological property, and use the Pearson correlation analysis method to calculate the correlation between the brain functional hypernetwork and the corresponding null model for this topological property. By calculating the correlation between the topological properties of the brain functional hypernetwork model and the null model, the dependence relationship between the features of interest is revealed, and it is quantified to what extent the existence or magnitude of the features of interest is caused by other features. The specific calculation formula is as follows:

[0144]

[0145] In formula (16), R represents the correlation between the hyper-brain functional hypernetwork model and the corresponding null model for the topological property; att represents the vector of the specific topological property of the brain functional hypernetwork model; att′ represents the vector of the specific topological property of the null model; cov(att, att′) represents the covariance between att and att′; σ att represents the standard deviation of att, and σ att′ represents the standard deviation of att′.

[0146] In a specific embodiment, in step S7, by comparing the correlations of the network model's interesting topological properties between the brain functional hypernetwork model and multiple null models, the dependence relationship between this interesting topological property and the remaining topological properties, that is, the existing redundancy relationship, is analyzed, and the topological property with less redundancy is selected as a classification feature to construct a classification model. The specific steps are as follows:

[0147] Step S71: By comparing the correlation of the topological properties of interest between the brain functional hypernetwork model and multiple null models, analyze the dependence relationship, i.e., the existing redundancy relationship, between the topological property of interest and the remaining topological properties, and select the topological properties with less redundancy as the superior topological properties to participate in classification.

[0148] Step S72: Based on the superior topological properties, use non-parametric tests to select the features with significant inter-group differences as classification features, and then construct a classification model using an SVM classifier based on the radial basis function.

[0149] Step S73: Randomly select 90% of the samples from the sample set as the training set, and the remaining 10% of the samples as the test set, and conduct classification tests and calculate the classification accuracy accordingly; perform an arithmetic average on the classification accuracies obtained after repeating the classification tests 100 times, and then use the arithmetic mean as the classification accuracy of the classifier.

[0150] By analyzing the correlation between the topological properties of the brain functional hypernetwork and the corresponding null models, the dependence relationships between the features of interest are obtained, namely the pairwise joint degree distribution of nodes, the node degree-related redundancy coefficient, HCC 1 、HCC 2 、HCC 3 mainly depend on the node degree, the pairwise joint degree distribution of hyperedges, the hyperedge degree-related redundancy coefficient mainly depends on the hyperedge average degree and partially depends on the hyperedge degree, HCC 1 partially depends on the node degree-related redundancy coefficient, HCC 2 、HCC 3 partially depends on the node degree-related redundancy coefficient, the hyperedge degree, and the hyperedge degree-related redundancy coefficient, while the correlation between the shortest path length and the topological properties retained by the null model is not significant, as Figure 2 shown, thus obtaining the features with important functions in the brain functional hypernetwork (node average degree, hyperedge degree, pairwise joint degree distribution of nodes, pairwise joint degree distribution of hyperedges, node degree-related redundancy coefficient, hyperedge degree-related redundancy coefficient, HCC 1 、HCC 3 、shortest path length). Classify based on the above specific topological properties, as Figure 2 shown, the classification accuracy of the present invention is significantly higher than that of the traditional magnetic resonance imaging data classification method, thus making the application value higher.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for topological structure analysis and classification of brain function supernetwork based on a zero model, characterized in that: The following steps are involved: Step S1, acquiring resting state functional magnetic resonance imaging data and performing preprocessing; Step S2, dividing the preprocessed resting-state functional magnetic resonance imaging data into brain regions according to the selected standardized brain atlas, and then extracting the average time series of each brain region; Step S3, based on the average time series of each brain region, a brain function hypernetwork model is constructed using the k-median algorithm; Step S4, calculating different topological properties of the brain function hypernetwork model, including node average degree, hyperedge average degree, node degree, hyperedge degree, node pairwise joint degree distribution, three different clustering coefficients, shortest path, hyperedge pairwise joint degree distribution, node degree correlation redundancy coefficient, and hyperedge degree correlation redundancy coefficient; Step S5, converting the brain function hypernetwork model into a bipartite graph, combining the "chain mechanism" strategy, using the generation method and the rewiring method to respectively construct a plurality of brain function hypernetwork zero models that simultaneously retain the topological properties of the brain function hypernetwork model nodes and hyperedges; Step S6, calculating all topological attributes of multiple brain function hypernetwork null models, and taking each topological attribute as a topological attribute of interest, and evaluating the correlation between the topological attribute values ​​in the brain function hypernetwork model and the brain function hypernetwork null model; Step S7, compare the correlation of the topological attributes of interest in the brain function hypernetwork model and the brain function hypernetwork null model, analyze the dependency relationship between the topological attributes of interest and the remaining topological attributes, that is, the existing redundant relationship, and select the topological attributes with less redundancy as classification features to construct a classification model.

2. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 1, characterized in that: In step S2, it specifically includes: Step S21, using the anatomical labeling template AAL to divide the brain into 90 brain regions, wherein the left hemisphere and the right hemisphere each have 45 brain regions; Step S22: extract the BOLD intensity of all voxels corresponding to each brain region at different time points, and then calculate the arithmetic mean of the BOLD intensity of each voxel at different time points to obtain the average time series of each brain region.

3. The method for analyzing and classifying the brain function supernetwork topology based on the zero model according to claim 1, characterized in that: In step S3, it specifically includes: Based on the average time series of each brain region, the number of clusters k is set, and the brain regions are clustered using the k-median algorithm, with each cluster being a hyperedge; Taking into account the influence of multiple levels, the step size is 5, and the number of clusters k∈[5,85] is changed. Corresponding hyperedges are generated under each cluster number k, that is, multi-scale hyperedges are generated under multiple k values. All multi-scale hyperedges constitute a brain function hypernetwork model.

4. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 1, characterized in that: In step S5, based on the bipartite graph, according to the parameter (Q v ,Q e ) values ​​to construct the brain function super network null model which retains different topological properties in the brain function super network model to different degrees; When Q v =0, the zero model of brain function supernetwork is constructed under the condition of retaining the average degree of nodes in the brain function supernetwork model; When Q v =1, the brain function super network null model is constructed under the condition of retaining the node average degree and node degree of the brain function super network model; When Q v = 2, the zero model of the brain function super network is generated by approximately retaining the node average degree and node degree of the brain function super network model while approximately retaining the node pairwise joint degree distribution of the brain function super network model. That is, in Q v = 1, further approximately retain the joint degree distribution of the nodes of the brain function super network model pairwise to generate the zero model of the brain function super network; When Q v = 2.5, the zero model of the brain function super network is generated by approximately retaining the node degree-related redundancy coefficient of the brain function super network model while retaining the average node degree and node degree of the brain function super network model and approximately retaining the pairwise joint degree distribution of the nodes of the brain function super network model. That is, in Q v =2 to approximately retain the node-degree related redundancy coefficient of the brain function super network model to generate a brain function super network null model; Similarly, Q e = 0, the average degree of the hyperedge of the brain function hypernetwork model is retained, Q e = 1, the hyperedge average degree and hyperedge degree of the brain function hypernetwork model are retained, Q e =2 at Q e = 1, and the joint degree distribution of the hyperedges of the brain function hypernetwork model is approximately retained. e =2.5 at Q e =2, and the hyper-edge-degree related redundancy coefficient of the brain function hyper-network model is approximately retained.

5. The method for analyzing and classifying the brain function supernetwork topology based on the zero model according to claim 4, characterized in that: In step S5, the following steps are specifically included: Step S51: construct a bipartite graph corresponding to the brain function hypernetwork model, and convert the brain function hypernetwork model into a simple binary graph containing M+N nodes and W edges; wherein M represents the number of brain region nodes in the brain function hypernetwork model, and N represents the number of hyperedges in the brain function hypernetwork model; Step S52: Based on the bipartite graph, construct different null models according to the different topological attributes to be retained; for Q v ∈{0,1} and Q e ∈{0,1}, using the generative method to construct a brain function hypernetwork null model that retains the average node degree, average hyperedge degree, node degree, and hyperedge degree of the brain function hypernetwork model to varying degrees; Step S53: Construct Q using the rewiring method v =2 or Q e = 2, based on the zero model of brain function supernetwork, v =1 or Q e = 1, rewire the bipartite graph according to the topological attributes to be retained, and convert the resulting bipartite graph into a hypernetwork, which is the corresponding brain function hypernetwork zero model; Step S54: Construct Q using the rewiring method v =2.5 or Q e = 2.5, based on the null model of brain function supernetwork, v =2 or Q e =2, the bipartite graph is rewired according to the topological attributes to be retained, the number of rewiring is 500W, and the final generated bipartite graph is converted into a hypernetwork, which is the corresponding brain function hypernetwork zero model.

6. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 5, characterized in that: In step S52, it specifically includes: Starting from a bipartite graph with M+N nodes and no edges, we then v ,Q e ) randomly generate the edges of the bipartite graph, and finally convert the generated bipartite graph into a hypernetwork, which is the zero model of the corresponding brain function hypernetwork; Among them, (Q v ,Q e )=(0,0) means that the corresponding bipartite graph is generated by retaining the node average degree and hyperedge average degree of the brain function hypernetwork model, and a bipartite graph node represented by a node type and a bipartite graph node represented by a hyperedge type are randomly selected in the bipartite graph and connected until W bipartite graph edges are generated, and finally a bipartite graph containing M+N nodes and W edges is obtained; (Q v ,Q e )=(0,1) means that the corresponding bipartite graph is generated by preserving the average node degree, average hyperedge degree and hyperedge degree of the brain function hypernetwork model. In the bipartite graph, the same number of half edges as the hyperedge degree is firstly added to the bipartite graph node represented by each hyperedge, and then for each remaining half edge, a bipartite graph node represented by a node type is randomly selected to be connected to it, and finally a bipartite graph containing M+N nodes and W edges is obtained; (Q v ,Q e )=(1,0) means that the corresponding bipartite graph is generated by preserving the average node degree, average hyperedge degree and node degree of the brain function hypernetwork model. In the bipartite graph, the same number of half edges as the node degree is first added to each bipartite graph node represented by the node type, and then for each remaining half edge, a bipartite graph node represented by a hyperedge is randomly selected to connect to it, and finally a bipartite graph containing M+N nodes and W edges is obtained; (Q v ,Q e )=(1,1) represents the generation of the corresponding bipartite graph by preserving the average node degree, average hyperedge degree, hyperedge degree and node degree of the brain function hypernetwork model. In the bipartite graph, firstly, half edges with the same number as the hyperedge degree are attached to each bipartite graph node represented by each hyperedge, and half edges with the same number as the node degree are attached to each bipartite graph node represented by each node type. Then, half edges attached to the node type and half edges attached to the hyperedge type are randomly selected and connected until there are no unconnected half edges. Finally, a bipartite graph containing M+N nodes and W edges is obtained.

7. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 6, characterized in that: In step S53, it specifically includes: Q v ∈{0,1} and Q e =2 means in Q v ∈{0,1} and Q e = 1, and approximately retains the bipartite graph generated by the joint degree distribution of the hyperedges of the brain function hypernetwork model; When (Q v ,Q e )=(0,2), it is (Q v ,Q e )=(0,1) to rewire the bipartite graph to approximately preserve the joint degree distribution of hyperedges; When (Q v ,Q e )=(1,2), it is (Q v ,Q e )=(1,1) to rewire the bipartite graph to approximately preserve the joint degree distribution of hyperedges. The specific process of rewiring at this time is: first randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, then replace (v, e) and (v′, e′) with (v, e′) and (v′, e′) if and only if the distance between the original and replaced hyperedges' joint degree distributions decreases, and the number of rewiring times is 500W; Q v =2 and Q e ∈{0,1} means in Q v =1 and Q e ∈{0,1} based on the approximately retained brain function hypernetwork model of the node two-by-two joint degree distribution generated by the bipartite graph; When (Q v ,Q e )=(2,0), it is (Q v ,Q e )=(1,0) to rewire the bipartite graph generated to approximately preserve the joint degree distribution of nodes; When (Q v ,Q e )=(2,1), it is (Q v ,Q e )=(1,1) to rewire the bipartite graph generated to approximately preserve the joint degree distribution of nodes; The specific process of rewiring at this time is: first randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, then replace (v, e) and (v′, e′) with (v, e′) and (v′, e′) if and only if the distance between the original and replaced node joint degree distributions decreases, and the number of rewiring times is 500W; (Q v ,Q e )=(2,2) means that in (Q v ,Q e )=(1,1) while approximately retaining the hyperedge pairwise joint degree distribution and node pairwise joint degree distribution of the brain function hypernetwork model. v ,Q e )=(1,1) based on the bipartite graph generated. The specific process of rewiring is as follows: first, randomly select two edges (v,e) and (v′,e′), and satisfy v≠v′ and e≠e′. Then, replace (v,e) and (v′,e′) with (v,e′) and (v′,e′) if and only if the distance between the original and replaced hyperedge pairwise joint degree distributions and the distance between the node pairwise joint degree distributions are simultaneously reduced. The number of rewiring times is 500W.

8. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 7, characterized in that: In step S54, it specifically includes: Q v ∈{0,1} and Q e =2.5 means that in Q v ∈{0,1} and Q e =2, and approximately retains the bipartite graph generated by the hyper-edge-degree correlation redundant coefficient of the brain function hyper-network model; When (Q v ,Q e )=(0,2.5), it is (Q v ,Q e )=(0,2) to rewire the bipartite graph generated to approximately retain the hyper-edge-degree related redundancy coefficient of the brain function hyper-network model; When (Q v ,Q e )=(1,2.5), it is (Q v ,Q e )=(1,2) to rewire the bipartite graph generated to approximately retain the hyper-edge-degree related redundancy coefficient of the brain function hyper-network model; The specific process of rewiring at this time is: first randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, and the degree values ​​of hyperedges e and e′ are the same, then replace (v, e) and (v′, e′) with (v, e′) and (v′, e′) if and only if the distance between the original and replaced hyperedge degree-related redundancy coefficients is reduced; Q v =2.5 and Q e ∈{0,1} means in Q v =2 and Q e ∈{0,1} based on the approximately retained bipartite graph generated by the node degree correlation redundancy coefficient of the brain function hypernetwork model; When (Q v ,Q e )=(2.5,0), it is (Q v ,Q e )=(2,0) to rewire the bipartite graph generated to approximately retain the node degree-related redundancy coefficient of the brain function hypernetwork model; When (Q v ,Q e )=(2.5,1), it is (Q v ,Q e )=(2,1) to rewire the bipartite graph generated to approximately retain the node degree correlation redundancy coefficient of the brain function hypernetwork model; The specific process of rewiring at this time is: first randomly select two edges (v, e) and (v′, e′), and satisfy v≠v′, e≠e′, and the degree values ​​of nodes v and v′ are the same, then replace (v, e) and (v′, e′) with (v, e′) and (v′, e′) if and only if the distance between the original and replaced node degree correlation redundancy coefficients is reduced; (Q v ,Q e )=(2,2.5) means that in (Q v ,Q e )=(2,2) to generate a bipartite graph and then rewire it to approximately retain the hyperedge degree correlation redundancy coefficient of the brain function hypernetwork model. The specific process of rewiring is as follows: first, randomly select two edges (v,e) and (v′,e′), and satisfy v≠v′, e≠e′, the degree values ​​of hyperedges e and e′ are the same, and the degree values ​​of nodes v and v′ are the same. Then, replace (v,e) and (v′,e′) with (v,e′) and (v′,e′) if and only if the distance between the hyperedge degree correlation redundancy coefficients of the original and replaced edges is reduced; (Q v ,Q e )=(2.5,2) means that in (Q v ,Q e )=(2,2) to generate a bipartite graph, and then rewiring is performed on the basis of it to approximately retain the node degree correlation redundancy coefficient of the brain function hypernetwork model. The specific process of rewiring is as follows: first, two edges (v,e) and (v′,e′) are randomly selected, and v≠v′, e≠e′, the degree values ​​of hyperedges e and e′ are the same, and the degree values ​​of nodes v and v′ are the same. Then, (v,e′) and (v′,e′) are used to replace (v,e) and (v′,e′) if and only if the distance between the node degree correlation redundancy coefficients of the original and replaced edges is reduced.

9. The method for analyzing and classifying the topological structure of brain function supernetwork based on the zero model according to claim 1, characterized in that: In step S6, it specifically includes: Step S61: Select the hypernetwork topological attributes of interest, including node average degree, hyperedge average degree, node degree, hyperedge degree, node pairwise joint degree distribution, hyperedge pairwise joint degree distribution, node degree correlation redundancy coefficient, hyperedge degree correlation redundancy coefficient, clustering coefficient and shortest path length, and then calculate the topological attributes of the brain function hypernetwork model and the corresponding brain function hypernetwork null model respectively; Step S62: Pearson correlation analysis method is used to calculate the correlation between the topological attributes of the brain function hypernetwork model and the corresponding brain function hypernetwork null model.

10. The method for analyzing and classifying the topological structure of a brain function supernetwork based on a zero model according to claim 1, characterized in that: In step S7, it specifically includes: Step S71: selecting specific topological attributes according to the correlation between topological attributes, and based on the specific topological attributes, using a radial basis function-based SVM classifier, selecting specific topological attributes with significant differences between groups after non-parametric tests as classification features, and constructing a classification model; Step S72: Randomly select 90% of the samples from the sample set as the training set and the remaining 10% of the samples as the test set, perform classification test and calculate the classification accuracy; perform arithmetic averaging on the classification accuracy obtained after repeating the classification test 100 times, and then take the arithmetic mean as the classification accuracy of the classifier.

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