Manifold Learning-Based Multiscale Wavelet Analysis Method, Device, and Medium for Brain Networks

Abstract

This invention discloses a method, apparatus, and medium for multi-scale wavelet analysis of brain networks based on manifold learning. Using T1-weighted MRI and DW-MRI images, combined with Desctrieux mapping and probabilistic fiber tractography based on surface seeds, an initial adjacency matrix is ​​obtained. The average adjacency matrix is ​​calculated. Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, several nodes are selected from the brain network. Masks at different scales are calculated on the nodes. Multi-scale wavelets are initialized. The eigenvectors of the Laplacian matrix of the average adjacency matrix are solved using a power iteration method to obtain the optimal multi-scale wavelet. Protein signals in the brain network are projected onto this wavelet to obtain new biomarker signals from the brain network. Therefore, this embodiment of the invention uses manifold learning to calculate the mean of a brain network group, which better maintains the geometric topology of the network and, considering the hierarchical modularity and centrality of network nodes, better uncovers some potential physiological and pathological mechanisms in brain diseases.

Description

Technical Field

[0001] This invention relates to the field of brain network technology, and in particular to a method, apparatus and medium for multi-scale wavelet analysis of brain networks based on manifold learning. Background Technology

[0002] Constructing the human brain network is an essential foundation for studying the intrinsic mechanisms of human cognitive function and understanding the essence of abnormal physiological functions in neurological diseases. With the development of modern imaging techniques and network analysis methods, diffusion-weighted magnetic resonance imaging (DW-MRI) and tracer imaging techniques provide a non-invasive measurement method for studying human brain characteristics, which is more in line with the anatomical meaning of connectivity. Furthermore, the human connectome has comprehensively characterized the neural network structure of the human brain at various levels, from macroscopic to microscopic, providing a basis for exploring the connectivity patterns of brain structural networks.

[0003] Graph theory analysis of brain networks provides new insights into the analysis of local and global features of brain networks, such as small-world properties and network set properties highly correlated with network modules, and clustering degree and path length highly correlated with topology. Furthermore, these indicators are used in neuroscience to describe the topological properties of brain networks, thereby understanding the working mechanisms of brain cognitive functions and the physiological essence of disease mechanisms, which has significant scientific implications. Currently, network science has achieved some important results in the application of brain diseases. For example, recent developments in the application of network science to diseases such as Alzheimer's disease (AD), multiple sclerosis, traumatic brain injury, and epilepsy have redefined the classic concepts of "local" or "global" neurological diseases, and pointed out that overload and failure of neural hubs may be decisive factors leading to neurological diseases.

[0004] Currently, among existing technologies, network neuroscience has conducted comprehensive research on understanding brain function and the neurobiological basis of cognition and behavior related to the development of neurological diseases. However, due to the complexity of neural network regulation mechanisms, few technologies are combined with existing neurobiological foundations for research. Secondly, as a complex network, the brain network has the small-world properties of a small-world network and the centrality of a scale-free network. Even though the development of network science has made the mathematical representation of complex networks more concise, integrating these characteristics into the framework of brain networks remains a great challenge. Summary of the Invention

[0005] This invention provides a method, device, and medium for multi-scale wavelet analysis of brain networks based on manifold learning, which addresses the shortcomings of existing brain network research technologies. It can combine the hierarchical modularity and centrality of brain networks, and the calculation of the mean of brain network groups based on manifold learning can better maintain the geometric topology of the network.

[0006] To achieve the above objectives, in a first aspect, embodiments of the present invention provide a multi-scale wavelet analysis method for brain networks based on manifold learning, comprising:

[0007] Acquire T1-weighted MRI and DW-MRI images of the human brain;

[0008] Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging techniques, the corresponding initial adjacency matrices are obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix.

[0009] Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, select several nodes from the brain network; calculate the mask at different scales on the selected nodes;

[0010] Several masks at different scales are selected, and multi-scale wavelets are randomly initialized. The objective function of the multi-scale wavelet is constructed based on the eigenvectors of the graph Laplacian matrix. The objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix is ​​solved by the power iteration method to obtain the optimal multi-scale wavelet.

[0011] Using the optimal multi-scale wavelet as a basis, new biomarker signals for the brain network are obtained by projecting protein signals in the brain network onto the optimal multi-scale wavelet.

[0012] As an improvement to the above scheme, the step of obtaining the corresponding initial adjacency matrix by combining the T1-weighted MRI and DW-MRI images with Desctrieux atlas and surface-seed-based probabilistic fiber tract imaging technology, calculating the minimum spanning tree of all initial adjacency matrices to obtain the average adjacency matrix, and thus obtaining the Laplacian matrix of the average adjacency matrix, specifically includes:

[0013] Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging techniques, the corresponding initial adjacency matrices are obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix.

[0014] Wherein, the initial adjacency matrix is ​​{W s |s∈1,…,S}, where s is the s-th brain network sample and S is the total number of samples in all brain networks; the minimum spanning tree is The average adjacency matrix The Laplace matrix is: yes The degree matrix.

[0015] As an improvement to the above scheme, the step of selecting several masks at multiple different scales, randomly initializing multi-scale wavelets, constructing the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix, and solving the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet specifically includes:

[0016] Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix;

[0017] The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method.

[0018] Among them, the multi-scale wavelet is and m is the number of nodes selected from the brain network, (K*Q) represents the Q wavelets selected at K different scales for each node, j is the j-th multi-scale wavelet in the brain network, and I is the identity matrix.

[0019] The objective function is:

[0020]

[0021]

[0022] In the formula, Ψ is The eigenvector matrix, μ1, μ2 are hyperparameters, K represents the number of scales involved in the multi-scale wavelet, k represents the k-th scale of the multi-scale wavelet, u j，k This is the mask at the k-th scale on the j-th node.

[0023]

[0024] As an improvement to the above scheme, the step of solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet specifically includes:

[0025] a: Simplify the objective function into a second objective function.

[0026] b: Solve the multi-scale wavelet Ω by maximizing the second objective function. j , i.e. Ω j =UV T ;

[0027] The optimal multi-scale wavelet can be obtained by repeating steps a and b until the second objective function converges.

[0028] in, α is the multi-scale wavelet Ω j The eigenvalues, U and V, are the eigenvalues ​​of M. j The left and right characteristic matrices of the SVD decomposition.

[0029] As an improvement to the above scheme, the step of selecting several nodes from the brain network based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, and calculating masks at multiple different scales on the selected nodes, specifically involves:

[0030] Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, select m nodes from the brain network; calculate K masks at different scales on the selected m nodes {u j，k |j=1,…,m;k=1,…,K}, where the k-th scale represents the mask u j，k The nodes within k hops of the j-th node in the brain network are covered.

[0031] As an improvement to the above scheme, the optimal multi-scale wavelet is used as a basis to project protein signals in the brain network onto the optimal multi-scale wavelet to obtain new biomarker signals for the brain network, specifically as follows:

[0032] Using the optimal multi-scale wavelet as a basis, protein signals in the brain network are projected onto the optimal multi-scale wavelet to obtain new biomarker signals for the brain network, and l1-SVM is used for brain disease diagnosis.

[0033] Secondly, embodiments of the present invention provide a multi-scale wavelet analysis device for brain networks based on manifold learning, comprising:

[0034] The image acquisition module is used to acquire T1-weighted MRI and DW-MRI images of the human brain;

[0035] The network computing module is used to obtain the corresponding initial adjacency matrix through the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging technology, calculate the minimum spanning tree of all initial adjacency matrices, obtain the average adjacency matrix, and thus obtain the Laplacian matrix of the average adjacency matrix.

[0036] The mask calculation module is used to select a number of nodes from the brain network based on the node degree, betweenness, PageRank and assignment coefficient of the average adjacency matrix; and to calculate the mask at different scales on the selected nodes.

[0037] The optimal wavelet module is used to select several masks at multiple different scales, randomly initialize multi-scale wavelets, construct the objective function of the multi-scale wavelet based on the eigenvectors of the graph Laplacian matrix, and solve the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix by the power iteration method to obtain the optimal multi-scale wavelet.

[0038] The wavelet diagnostic module is used to obtain new biomarker signals about the brain network by projecting protein signals in the brain network onto the optimal multi-scale wavelet as a basis.

[0039] As an improvement to the above scheme, the optimal wavelet module is specifically used for:

[0040] Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix;

[0041] The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method.

[0042] Among them, the multi-scale wavelet is and m is the number of nodes selected from the brain network, (K*Q) represents the Q wavelets selected at K different scales for each node, j is the j-th multi-scale wavelet in the brain network, and I is the identity matrix.

[0043] The objective function is:

[0044]

[0045]

[0046] In the formula, Ψ is The eigenvector matrix, μ1, μ2 are hyperparameters, K represents the number of scales involved in the multi-scale wavelet, k represents the k-th scale of the multi-scale wavelet, u j，k This is the mask at the k-th scale on the j-th node.

[0047]

[0048] Thirdly, the present invention provides a manifold learning-based multi-scale wavelet analysis device for brain networks, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the above-mentioned manifold learning-based multi-scale wavelet analysis method for brain networks.

[0049] Furthermore, embodiments of the present invention also provide a computer-readable storage medium, the computer-readable storage medium including a stored computer program, wherein, when the computer program is running, it controls the device where the computer-readable storage medium is located to execute the above-described manifold learning-based brain network multi-scale wavelet analysis method.

[0050] Compared with existing technologies, this invention discloses a method, apparatus, and medium for multi-scale wavelet analysis of brain networks based on manifold learning. By dividing the surface of the cerebral cortex in structural MRI brain images into several cortical regions, and then applying probabilistic fiber tractography based on surface seeds to process a series of diffusion tensor imaging (DTI) data (DW-MRI images), the strength of cellulose connections between different cortical regions can be obtained, thereby generating a matrix with anatomically connected properties. The brain network data is obtained by combining the division of the cerebral cortex regions with the connectivity properties between different brain regions. Based on this, this invention explores harmonic variations in human brain networks using manifold learning, extracts relevant features by combining the hierarchical modularity and centrality of network nodes, and discovers some physiological and pathological mechanisms in patients with AD and related brain diseases by comparing the propagation patterns of multi-scale wavelets with the information flow patterns in the networks of AD and related brain diseases. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating a multi-scale wavelet analysis method for brain networks based on manifold learning, provided in an embodiment of the present invention.

[0052] Figure 2 This is a schematic diagram of the structure of a multi-scale wavelet analysis device for brain networks based on manifold learning, provided in an embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] It should be noted that the terms "comprising" and "specific" in this invention, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0055] It's worth noting that numerous studies have now applied the Graph Laplacian operator to brain connectivity matrices to infer the underlying mechanisms of neurodegenerative disease progression, brain malformations, and altered neuronal dynamics in concussion patients. Some literature suggests that the eigenvectors of the Graph Laplacian matrix of brain networks contain a series of frequency-based harmonic propagation patterns existing in the cerebral cortex. This provides an effective Fourier harmonic basis for studying the human brain connectome, thereby revealing the brain's communication pathways. Each harmonic is associated with a different frequency, providing frequency-ordered building blocks that can reconstruct any form of brain activity.

[0056] Harmonic-based analysis has been used to study the prediction of changes in brain neural activity by analyzing alterations in harmonic frequencies in neuropsychiatric disorders and functional neural activity. Because harmonics are orthogonal to each other, encoding brain connectivity through the harmonic domain provides great flexibility for analyzing differences between different brain regions.

[0057] Exploring harmonic variations in the human brain has become a new research direction for understanding the factors behind brain development and neurodegenerative diseases. Quantifying individual differences often requires an unbiased reference space for harmonics. However, current research typically uses simple arithmetic averaging of individual harmonics, but such Euclidean operations can disrupt the inherent data geometry of harmonics. Therefore, this invention performs calculations on manifolds. The structural and functional connectivity characteristics of the brain can be well measured by the connections between networks, which is biologically significant. However, existing measurement techniques cannot effectively remove the influence of different measurement techniques. Therefore, this invention develops an unbiased estimation method. Existing research shows that connectivity abnormalities in patients with neurological diseases lead to changes in network topology. Therefore, this invention aims to extract relevant multi-scale wavelets by considering the hierarchical modularity and centrality of network nodes in brain networks. By comparing the propagation patterns of multi-scale wavelets with the information flow patterns in the networks of AD and related brain diseases, this invention seeks to discover some physiological and pathological mechanisms in patients with brain diseases.

[0058] Please see Figure 1 , Figure 1 This is a flowchart illustrating a multi-scale wavelet analysis method for brain networks based on manifold learning, provided in an embodiment of the present invention. The method includes steps S11 to S15:

[0059] S11: Acquire T1-weighted MRI and DW-MRI images of the human brain;

[0060] S12: Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and probabilistic fiber bundle imaging technology based on surface seeds, the corresponding initial adjacency matrix is ​​obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix.

[0061] S13: Select several nodes from the brain network based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix; calculate the mask at different scales on the selected nodes;

[0062] S14: Select several masks at different scales, randomly initialize multi-scale wavelets, construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix, solve the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix by the power iteration method, and obtain the optimal multi-scale wavelet.

[0063] S15: Using the optimal multi-scale wavelet as a basis, new biomarker signals for the brain network are obtained by projecting protein signals in the brain network onto the optimal multi-scale wavelet.

[0064] It should be noted that brain diseases can be diagnosed through the signals of these new biomarkers.

[0065] Specifically, step S12 includes:

[0066] Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging techniques, the corresponding initial adjacency matrices are obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix.

[0067] Wherein, the initial adjacency matrix is ​​{W s |s∈1,…,S}, where s is the s-th brain network sample and S is the total number of samples in all brain networks; the minimum spanning tree is The average adjacency matrix The Laplace matrix is: yes degree matrix

[0068] Specifically, step S14 includes:

[0069] Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix;

[0070] The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method.

[0071] Among them, the multi-scale wavelet is and m is the number of nodes selected from the brain network, (K*Q) represents the Q wavelets selected at K different scales for each node, j is the j-th multi-scale wavelet in the brain network, and I (K*Q)×(K*Q) It is the identity matrix;

[0072] The objective function is:

[0073]

[0074]

[0075] In the formula, Ψ is The eigenvector matrix, μ1, μ2 are hyperparameters, K represents the number of scales involved in the multi-scale wavelet, k represents the k-th scale of the multi-scale wavelet, u j，kThis is the mask at the k-th scale on the j-th node.

[0076]

[0077] The step of solving for the eigenvectors of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet specifically includes:

[0078] a: Simplify the objective function into a second objective function.

[0079] b: Solve the multi-scale wavelet Ω by maximizing the second objective function. j , i.e. Ω j =UV T ;

[0080] The optimal multi-scale wavelet can be obtained by repeating steps a and b until the second objective function converges.

[0081] in, α is the multi-scale wavelet Ω j The eigenvalues, U and V, are the eigenvalues ​​of M. j The left and right characteristic matrices of the SVD decomposition.

[0082] Specifically, step S13 is as follows:

[0083] Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, select m nodes from the brain network; calculate K masks at different scales on the selected m nodes {u j，k |j=1,…,m;k=1,…,K}, where the k-th scale represents the mask u j，k The nodes within k hops of the j-th node in the brain network are covered.

[0084] Specifically, step S16 includes:

[0085] Using the optimal multi-scale wavelet as a basis, protein signals in the brain network are projected onto the optimal multi-scale wavelet to obtain new biomarker signals for the brain network, and l1-SVM is used for brain disease diagnosis.

[0086] Figure 2 This is a schematic diagram of a multi-scale wavelet analysis device for brain networks based on manifold learning, provided in an embodiment of the present invention. The device includes:

[0087] Image acquisition module 21 is used to acquire T1-weighted MRI and DW-MRI images of the human brain;

[0088] The network computing module 22 is used to obtain the corresponding initial adjacency matrix through the T1-weighted MRI and DW-MRI images, combined with the Desctrieux map and the surface seed-based probabilistic fiber bundle imaging technique, calculate the minimum spanning tree of all initial adjacency matrices, obtain the average adjacency matrix, and thus obtain the Laplacian matrix of the average adjacency matrix.

[0089] The mask calculation module 23 is used to select a number of nodes from the brain network based on the node degree, betweenness, PageRank and assignment coefficient of the average adjacency matrix; and calculate the mask at different scales on the selected nodes.

[0090] The optimal wavelet module 24 is used to select several masks at multiple different scales, randomly initialize multi-scale wavelets, construct the objective function of the multi-scale wavelet based on the eigenvectors of the graph Laplacian matrix, and solve the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix by the power iteration method to obtain the optimal multi-scale wavelet.

[0091] Wavelet diagnostic module 25 is used to obtain new biomarker signals about the brain network by projecting protein signals in the brain network onto the optimal multi-scale wavelet as a basis.

[0092] Specifically, the optimal wavelet module 24 is used for:

[0093] Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix;

[0094] The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method.

[0095] Among them, the multi-scale wavelet is and m is the number of nodes selected from the brain network, (K*Q) represents the Q wavelets selected at K different scales for each node, j is the j-th multi-scale wavelet in the brain network, and I (K*Q)×(K*Q) It is the identity matrix;

[0096] The objective function is:

[0097]

[0098]

[0099] In the formula, Ψ is The eigenvector matrix, μ1, μ2 are hyperparameters, K represents the number of scales involved in the multi-scale wavelet, k represents the k-th scale of the multi-scale wavelet, u j，k This is the mask at the k-th scale on the j-th node.

[0100]

[0101] The manifold learning-based multi-scale wavelet analysis device for brain networks provided in this embodiment of the invention can realize all the processes of the manifold learning-based multi-scale wavelet analysis method for brain networks in the above embodiments. The functions and technical effects of each module in the device are the same as those of the manifold learning-based multi-scale wavelet analysis method for brain networks in the above embodiments, and will not be repeated here.

[0102] This invention provides a manifold learning-based multi-scale wavelet analysis device for brain networks. The device includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps described in the embodiments of the manifold learning-based multi-scale wavelet analysis method for brain networks. Alternatively, when the processor executes the computer program, it implements the functions of each module described in the embodiments of the manifold learning-based multi-scale wavelet analysis device for brain networks.

[0103] For example, the computer program may be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the device.

[0104] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the device, connecting various parts of the entire device via various interfaces and lines.

[0105] The memory can be used to store the computer programs and / or modules. The processor implements various functions of the device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, RAM, plug-in hard disk, smart memory card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0106] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0107] This invention also provides a computer-readable storage medium comprising a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform the manifold learning-based multi-scale wavelet analysis method for brain networks as described in the above embodiments.

[0108] In summary, the present invention discloses a method, apparatus, and medium for multi-scale wavelet analysis of brain networks based on manifold learning. This method obtains initial adjacency matrices by combining T1-weighted MRI and DW-MRI images with Desctrieux maps and probabilistic fiber tract imaging based on surface seeds. It calculates the minimum spanning tree of all initial adjacency matrices, averages all calculated minimum spanning trees to obtain the average adjacency matrix, and then obtains the Laplacian matrix of the average adjacency matrix. Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, several nodes are selected from the brain network. Masks at multiple different scales are calculated for the selected nodes. Several masks at different scales are selected, and multi-scale wavelets are randomly initialized. The objective function of the multi-scale wavelets is constructed. The objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix is ​​solved using a power iteration method to obtain the optimal multi-scale wavelet. Using the optimal multi-scale wavelet as a basis, new biomarker signals about the brain network are obtained by projecting protein signals in the brain network onto the optimal multi-scale wavelet. Therefore, the embodiments of the present invention can better maintain the geometric topology of the network by calculating the mean of the brain network group through manifold learning. By combining the consideration of the hierarchical modularity of the brain network and the centrality of the network nodes to calculate multi-scale wavelets, it can better uncover some potential physiological and pathological mechanisms in brain diseases. Furthermore, by removing the influence of different measurement techniques, an unbiased brain network estimation method has been developed.

[0109] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A multi-scale wavelet analysis method for brain networks based on manifold learning, characterized in that, include: Acquire T1-weighted MRI and DW-MRI images of the human brain; Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging techniques, the corresponding initial adjacency matrices are obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix. Based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix, select several nodes from the brain network; calculate the mask at different scales on the selected nodes; Select several masks at different scales, randomly initialize multi-scale wavelets, construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix, and solve the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix by the power iteration method to obtain the optimal multi-scale wavelet. Using the optimal multi-scale wavelet as a basis, new biomarker signals for the brain network are obtained by projecting protein signals in the brain network onto the optimal multi-scale wavelet. Specifically, the process of selecting several masks at different scales, randomly initializing multi-scale wavelets, constructing the objective function of the multi-scale wavelet based on the eigenvectors of the graph Laplacian matrix, and solving the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet includes: Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix; The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method. Among them, the multi-scale wavelet is ,and , The number of nodes selected from the brain network, This indicates the selected node. Selected at different scales A small wave, The first in the brain network Multiscale wavelets, It is the identity matrix; The objective function is: In the formula, yes eigenvector matrix, It's a hyperparameter. This indicates the number of scales involved in the multi-scale wavelet. The multi-scale wavelet represents the first... One scale, For the first The node at the node Mask at various scales; The step of solving for the eigenvectors of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet specifically includes: a: Simplify the objective function into a second objective function. , ; b: Solve the multi-scale wavelet by maximizing the second objective function. ,Right now ; The optimal multi-scale wavelet can be obtained by repeating steps a and b until the second objective function converges. in, , For the multi-scale wavelet eigenvalues, and They are The left and right characteristic matrices of the SVD decomposition.

2. The multi-scale wavelet analysis method for brain networks based on manifold learning as described in claim 1, characterized in that, The process involves obtaining the corresponding initial adjacency matrix using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlases and probabilistic fiber tract imaging techniques based on surface seeds. The minimum spanning tree of all initial adjacency matrices is then calculated to obtain the average adjacency matrix, which in turn yields the Laplacian matrix of the average adjacency matrix. Specifically, this includes: Using the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging techniques, the corresponding initial adjacency matrices are obtained. The minimum spanning tree of all initial adjacency matrices is calculated to obtain the average adjacency matrix, thereby obtaining the Laplacian matrix of the average adjacency matrix. Wherein, the initial adjacency matrix is , For the first A brain network sample, The number of samples in all brain networks; the minimum spanning tree is The average adjacency matrix The Laplace matrix is , yes The degree matrix.

3. The multi-scale wavelet analysis method for brain networks based on manifold learning as described in claim 1, characterized in that, The step involves selecting several nodes from the brain network based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix; and calculating masks at multiple different scales on the selected nodes, specifically: Nodes are selected from the brain network based on the node degree, betweenness, PageRank, and assignment coefficient of the average adjacency matrix. Each node; calculate the selected nodes. On each node Masks at different scales , among which, the Each scale represents a mask. Covering the first in the brain network Nodes Nodes within a jump range.

4. A multi-scale wavelet analysis device for brain networks based on manifold learning, characterized in that, include: The image acquisition module is used to acquire T1-weighted MRI and DW-MRI images of the human brain; The network computing module is used to obtain the corresponding initial adjacency matrix through the T1-weighted MRI and DW-MRI images, combined with Desctrieux atlas and surface seed-based probabilistic fiber bundle imaging technology, calculate the minimum spanning tree of all initial adjacency matrices, obtain the average adjacency matrix, and thus obtain the Laplacian matrix of the average adjacency matrix. The mask calculation module is used to select a number of nodes from the brain network based on the node degree, betweenness, PageRank and assignment coefficient of the average adjacency matrix; and to calculate the mask at different scales on the selected nodes. The optimal wavelet module is used to select several masks at different scales, randomly initialize multi-scale wavelets, construct the objective function of the multi-scale wavelet based on the eigenvectors of the graph Laplacian matrix, and solve the objective function related to the eigenvectors of the Laplacian matrix of the average adjacency matrix by the power iteration method to obtain the optimal multi-scale wavelet. The wavelet diagnostic module is used to use the optimal multi-scale wavelet as a basis to obtain new biomarker signals about the brain network by projecting protein signals in the brain network onto the optimal multi-scale wavelet. The optimal wavelet module is specifically used for: Select several masks at different scales, randomly initialize multi-scale wavelets, and construct the objective function of the multi-scale wavelets based on the eigenvectors of the graph Laplacian matrix; The optimal multi-scale wavelet is obtained by solving the objective function related to the eigenvector of the Laplacian matrix of the average adjacency matrix using the power iteration method. Among them, the multi-scale wavelet is ,and , The number of nodes selected from the brain network, This indicates the selected node. Selected at different scales A small wave, The first in the brain network Multiscale wavelets, It is the identity matrix; The objective function is: In the formula, yes eigenvector matrix, It's a hyperparameter. This indicates the number of scales involved in the multi-scale wavelet. The multi-scale wavelet represents the first... One scale, For the first The node at the node Mask at various scales; The step of solving for the eigenvectors of the Laplacian matrix of the average adjacency matrix using the power iteration method to obtain the optimal multi-scale wavelet specifically includes: a: Simplify the objective function into a second objective function. , ; b: Solve the multi-scale wavelet by maximizing the second objective function. ,Right now ; The optimal multi-scale wavelet can be obtained by repeating steps a and b until the second objective function converges. in, , For the multi-scale wavelet eigenvalues, and They are The left and right characteristic matrices of the SVD decomposition.

5. A multi-scale wavelet analysis device for brain networks based on manifold learning, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements the manifold learning-based multi-scale wavelet analysis method for brain networks as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform the multi-scale wavelet analysis method for brain networks based on manifold learning as described in any one of claims 1-3.

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