Brain function network mental disease auxiliary diagnosis method based on hyperbolic geometry

Abstract

A brain function network mental disease auxiliary diagnosis method based on hyperbolic geometry comprises the steps that a brain region time sequence is extracted to serve as a brain region node, and a brain function network containing homonymous and reverse correlation partition connection is constructed; mapping the brain region nodes to a hyperbolic space of a Minkowski model, and generating geometric update hyperbolic features; calculating attention scores among brain region nodes based on Minkowski inner products, and respectively performing normalization in the same-direction association subset and the reverse-direction association subset to obtain a same-direction association subset attention weight and a reverse-direction association subset attention weight; distinguishing and aggregating the geometric update hyperboloid features by using the same-direction association subset attention weight and the reverse-direction association subset attention weight to generate final update features; and based on the final updated features, realizing graph-level reading in the hyperbolic manifold by adopting the manifold geometric center and completing mental disease classification. According to the method, the fidelity of brain network structure expression is improved, and the disease-related connection mode is accurately identified.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer vision, and particularly relates to a brain function network mental illness auxiliary diagnosis method based on hyperbolic geometry. BACKGROUND

[0002] Neurodevelopmental disorders such as attention deficit hyperactivity disorder (ADHD) and autism spectrum disorder (ASD) have a high incidence rate in the youth population, and their neural basis and mechanism are still under study. For example, data shows that the prevalence of ADHD in Chinese children is about 5.7%, and about 7.6% globally, and both are showing an increasing trend year by year, and patients often show difficulty in maintaining attention, elevated activity level, and limited behavior control. The above diseases cause a great global burden. Existing diagnosis mainly relies on behavior performance and scale evaluation, which is easily affected by differences in evaluation environment and experience. In addition, the symptoms also have certain heterogeneity, and need to be distinguished from similar situations such as emotional disorders and learning difficulties in clinical evaluation.

[0003] With the development of medical imaging technology, functional magnetic resonance imaging (fMRI) is widely used to record brain activity due to its non-invasiveness and high temporal and spatial resolution, and to construct brain function networks to provide data basis for diseases. Based on this, researchers have begun to use deep learning methods based on fMRI data to carry out disease-related difference analysis, so as to realize the auxiliary diagnosis of mental diseases. However, the brain function organization presents a cross-scale hierarchical structure, and the existing methods still have problems of expression bias and insufficient information fidelity when representing the structure relationship.

[0004] Although there have been studies trying to use fMRI for auxiliary diagnosis of mental illness, the existing methods still have many shortcomings in structure representation:

[0005] 1. The geometric hypothesis does not match the brain function structure: the brain function network has a cross-scale hierarchical organizational structure, and most of the mainstream methods are based on the assumption of flat space for modeling, and the default embedding is in a flat geometric space. This assumption is not consistent with the inherent nonlinear topological structure of the brain network. Under this framework, the cross-hierarchical structure relationship expression is limited and prone to distortion, which may weaken or omit the incomplete structure information, and it is difficult to accurately depict the subtle connection patterns, thereby affecting the discrimination performance and generalization performance in the auxiliary diagnosis of mental illness across data scenarios.

[0006] 2. The expression of functional connection directionality information is insufficient: the correlation between brain regions in fMRI has a sign feature, and the same direction association subset and the reverse direction association subset correspond to different functional coordination patterns. Existing methods usually treat both types of connections uniformly when information is fused, ignoring their physiological function differences, which weakens the sign domain information, and further weakens the expression of functional differences related to diseases, resulting in a decrease in the discrimination stability of auxiliary diagnosis.

[0007] 3Graph-level representation exists base point bias leading to insufficient generalization: the existing method adopts a node feature aggregation method based on a fixed reference point when obtaining a whole brain-level representation. This method does not consider the curvature characteristics of the representation space, and is easy to introduce base point bias in the aggregation stage, leading to unstable graph-level representation. This bias will be further amplified in the cross-center or cross-data scene, thereby affecting the generalization ability and discriminant consistency of mental illness recognition. SUMMARY

[0008] In view of the above defects of the prior art, the present application provides a hyperbolic geometry-based brain function network mental disease auxiliary diagnosis method. The method aims to realize low-distortion expression of hierarchical topological relationship, retain the connection difference between co-directional and reverse association partitions, improve the fidelity of brain network structure expression, and accurately identify disease-related connection patterns for auxiliary diagnosis of mental diseases.

[0009] A hyperbolic geometry-based brain function network mental disease auxiliary diagnosis method, comprising the following steps:

[0010] S1, extracting brain region time series as brain region nodes based on fMRI data and calculating co-directional and reverse correlation to construct a brain function network containing co-directional and reverse association partition connections;

[0011] S2, mapping the brain region nodes to the hyperbolic space of the Minkowski model to generate geometric updated hyperboloid features;

[0012] S3, calculating the attention scores between the brain region nodes based on the Minkowski inner product, and normalizing them in the co-directional association subset and the reverse association subset respectively to obtain co-directional association subset attention weights and reverse association subset attention weights;

[0013] S4, using the co-directional association subset attention weights and the reverse association subset attention weights to perform sign-differentiated aggregation processing on the geometric updated hyperboloid features to generate final updated features;

[0014] S5, based on the final updated features, using manifold geometry to realize graph-level reading in the hyperbolic manifold and complete mental disease classification.

[0015] Preferably, S1 comprises:

[0016] S11, extracting the average blood oxygen-dependent fluctuation sequence of each brain region as the brain region node based on the AAL-116 brain region template;

[0017] S12, calculating the correlation between the average blood oxygen-dependent fluctuation sequences of any two brain regions using the Pearson correlation coefficient to generate a correlation matrix;

[0018] S13, generating a feedforward connection weight matrix and a feedback connection weight matrix according to the signs of the correlation matrix;

[0019] S14, reserving the top k connections with the largest weights for each brain region in the feedforward connection weight matrix and the feedback connection weight matrix respectively, and symmetrizing the connection relationship to generate a sparse, undirected and signed brain function network graph.

[0020] As preferred, S2 comprises:

[0021] The reference point of the Minkowski model is selected as the tangent space anchor point; and the flat space feature corresponding to each brain region node is extracted;

[0022] The flat space feature is lifted to a hyperbolic space by a manifold embedding transformation based on a geodesic line to obtain an initial hyperbolic feature;

[0023] A linear transformation consistent with the curvature is performed on the initial hyperbolic feature layer by layer in the hyperbolic space;

[0024] The initial hyperbolic feature after the linear transformation is biased by using a learnable bias vector to obtain a geometric updated hyperbolic feature of each layer.

[0025] As preferred, the initial hyperbolic feature is projected to the tangent space of the tangent space anchor point for calculation before the linear transformation, and then mapped back to the hyperbolic space; the bias transmission is first completed in the tangent space and then mapped back to the hyperbolic space.

[0026] As preferred, S3 comprises:

[0027] For any brain region node, the feedforward association subset is composed of the neighborhood nodes having non-zero connections with the brain region node in the feedforward connection weight matrix; and the feedback association subset is composed of the neighborhood nodes having non-zero connections with the brain region node in the feedback connection weight matrix;

[0028] Under the curvature constraint of the geometric updated hyperbolic feature, the geometric updated hyperbolic feature is mapped to the tangent space and then performs matrix operation with a preset learnable weight matrix to obtain a query vector, a key vector and a value vector;

[0029] An attention score matrix between brain region nodes is constructed based on the Minkowski inner product.

[0030] As preferred, S3 further comprises:

[0031] For each row in the attention score matrix, the softmax operation is performed on the feedforward association subset and the feedback association subset of the brain region node respectively to generate the feedforward association subset attention weight and the feedback association subset attention weight.

[0032] As preferred, S4 comprises:

[0033] A local tangent space is constructed at the hyperbolic space position corresponding to the hyperbolic space feature of the geometric update hyperboloid of any brain region node and any attention head, and the value vectors of each neighborhood node in the forward associated subset and the reverse associated subset under the corresponding attention head are projected and transformed to the local tangent space;

[0034] The tangent space vectors in the forward associated subset and the reverse associated subset are weighted and accumulated with the forward associated subset attention weight and the reverse associated subset attention weight as the weighting coefficients, respectively, to generate the symbolic aggregation quantity of the brain region node under the current layer and the current attention head;

[0035] The symbolic aggregation quantities of multiple attention heads are integrated in the local tangent space of the brain region node and are lifted to the hyperbolic space through manifold embedding transformation to obtain the aggregated hyperbolic feature of the brain region node at the current layer.

[0036] As preferred, S4 further comprises:

[0037] The aggregated hyperbolic feature is projected to the tangent space by tangent space projection transformation, and a nonlinear activation function is applied in the tangent space; based on the curvature parameter set at the current layer, the vector after nonlinear activation is lifted to a new hyperbolic space through manifold embedding transformation to generate the final update feature.

[0038] As preferred, S5 comprises:

[0039] According to the final update features of all brain region nodes output by the last layer, a graph geometric center capable of representing the overall brain network topology is solved with the manifold geometric center in the hyperbolic space as the graph-level reading mode.

[0040] The final update features of all brain region nodes are projected to the tangent space of the graph geometric center by tangent space projection transformation; an average pooling operation is performed on the tangent vectors generated after projection to generate a graph-level feature representation; and the graph-level feature representation is input into a classification module to output a prediction result of a mental class disease.

[0041] As preferred, generating the graph geometric center comprises:

[0042] A candidate center point is found on the hyperbolic manifold, such that the sum of squared geodesic distances from the candidate center point to all final update features is minimized; an iterative update method is adopted, in each iteration, the final update features of all brain region nodes are projected to the tangent space of the candidate center point by using tangent space projection transformation, and a tangent space average update vector is calculated; the tangent space average update vector is used to act on the current center point by using manifold embedding transformation, so as to obtain the center point of the next iteration; and the graph geometric center is generated after the number of iterations reaches a preset number.

[0043] Compared with the prior art, the beneficial effects of the present application are embodied in:

[0044] 1. Hyperbolic geometry embedding and learnable curvature: The present application introduces a Minkowski hyperbolic geometry modeling framework into the graph neural network, embeds the brain function network on a hyper surface with negative curvature, and sets a learnable curvature parameter at each layer, thereby adaptively adjusting the geometric scale of the feature space. This design overcomes the problem of embedding distortion in the hierarchical structure modeling of traditional flat space graph neural networks, enabling the model to more accurately express the 'core-periphery' hierarchical topological relationship in the brain network, and improving the structural representation capability and robustness.

[0045] 2. Symbolic domain Minkowski attention mechanism: The present application constructs a multi-head attention module based on Minkowski inner product, and combines the same-direction and reverse association sub-partition separation aggregation strategy, respectively performs attention normalization and feature aggregation in the same-direction association subset and the reverse association subset. This mechanism can explicitly distinguish between excitatory connections and inhibitory connections, realize geometric consistent message passing, overcome the defect that existing methods based on flat space dot product or unsigned graph structure are difficult to handle signed connection topologies, and help to improve the model's recognition ability of key pathways and the interpretability of feature representation.

[0046] 3. Manifold-in graph-level readout based on manifold geometric center: The present application adopts the manifold geometric center as the intra-manifold geometric center in the graph-level readout stage, obtains the graph-level center representation by minimizing the geodesic distance from the node to the center, and completes feature aggregation and classification input in the tangent space thereof. This readout method effectively avoids the bias problem caused by reading out with a fixed base point, ensures the geometric consistency and stability of the graph-level features on the hyperbolic manifold, and is conducive to improving the classification robustness in cross-subject and cross-site scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The method framework diagram of embodiment 1 of the present application is shown in the figure;

[0048] Figure 2 The method flowchart of embodiment 1 of the present application is shown in the figure. DETAILED DESCRIPTION

[0049] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0050] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0051] Example 1:

[0052] like Figure 1 , Figure 2 The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks, as shown, includes the following steps:

[0053] S1. Construct a brain functional network with co-directional and inverse correlation partition connections based on fMRI (functional magnetic resonance imaging) data.

[0054] S11. Specifically, the functional magnetic resonance imaging sequence of the subject is divided into regions according to the AAL-116 brain region template (Automated Anatomical Labeling 116-region atlas), and the average blood oxygen-dependent fluctuation sequence of each brain region during the entire scanning period is extracted as brain region nodes.

[0055] S12. Subsequently, the correlation between any two brain region time series was calculated using the Pearson correlation coefficient, resulting in a correlation matrix. .

[0056] S13. Based on the sign property of the correlation matrix, construct the same-direction correlation and opposite-direction correlation as same-direction connection weight matrices respectively. With reverse connection weight matrix Its definition is:

[0057]

[0058] Furthermore, to obtain a sparse and representative functional connectivity structure, the same direction connectivity weight matrix is ​​used for... With reverse connection weight matrix The top k connections with the largest weights are reserved for each brain region, and the connection relationship is symmetrized to form a sparse, undirected, and signed brain function network where V represents the brain region set, and E represents the connection set. The obtained brain function network is used as the input of subsequent hyperbolic space feature mapping and signed domain attention aggregation.

[0059] S2, mapping the brain region nodes to the hyperbolic space of the Minkowski model to generate geometric updated hyperbolic surface features;

[0060] The brain region nodes are mapped to the hyperbolic space to maintain the hierarchical topology of the brain network and provide basic support for subsequent geometric consistent attention aggregation.

[0061] S21, extracting the corresponding flat space features of each brain region node in S1 where T represents the time series length. The reference point of the Minkowski model is selected as the tangent space anchor point, where represents the initial curvature.

[0062] S22, secondly, to realize the smooth embedding of the flat space features to the hyperbolic space, a manifold embedding transformation based on geodesic lines is used for space projection, and the core idea is to use the norm of the tangent space vector as the propulsion parameter along the geodesic line under the Minkowski metric, thereby realizing the continuous transition from linear space to negative curvature space. The mapping can be represented as:

[0063]

[0064] is the base point on the Minkowski hyperbolic space, represents the tangent space of the hyperbolic space at the point near the point, which is used to convert the geometric operations on the hyperbolic space to the operations in the tangent space, and returns to the hyperbolic space after calculation through the manifold embedding transformation. is the vector in the tangent space, represents its norm under the Minkowski metric, curvature scale. The mapping is propelled along the geodesic direction passing through the point on the manifold, so that the brain region node features maintain geometric continuity and nonlinear expansion characteristics of hierarchical spacing during the embedding process, thereby avoiding hierarchical compression and structural distortion caused by linear measurement in the flat space.

[0065] The flat space features are promoted to the Minkowski hyperbolic space by using the above manifold embedding transformation to obtain the initial hyperbolic surface features . To ensure that the brain region node representation is in a geometric space with negative curvature, it can accommodate the cross-scale hierarchical topology of brain function network. If the brain region node is directly represented in a flat space, since the flat space adopts flatness measure, its distance expression grows linearly with scale, which is difficult to correspond to the nonlinear distance distribution in brain network caused by hierarchical organization, thereby possibly leading to the compression of cross-hierarchical structure relationship, the weakening of part of the connection mode in feature mapping, and the inaccurate execution of subsequent feature aggregation and relationship modeling process based on structure relationship:

[0066]

[0067] representing the initial hyperbolic surface feature in the Minkowski hyperbolic space, is the manifold embedding transformation under the curvature parameter is the manifold embedding transformation with the reference point as the base point, which is used to define the corresponding tangent space and as the starting point of the mapping.

[0068] S23, further, performing linear transformation consistent with the curvature inside the hyperbolic space, the structure of the brain function network has a hierarchical nature, where the subscript is used to mark the corresponding level. To achieve feature transformation consistent with the hyperbolic geometric structure, the initial hyperbolic surface feature is projected to the reference point tangent space for calculation before linear operation, and then mapped back to the manifold. The geometric consistent linear transformation of this layer is defined as:

[0069]

[0070] is the inter-layer hyperbolic surface feature of the layer transformation, that is, the initial hyperbolic surface feature corresponding to when =1. is the weight matrix of the layer, and the output of the transformation is the updated layer hyperbolic feature. Its scope is the tangent space , represents the tangent space projection transformation in the Minkowski hyperbolic space with the curvature parameter . The transformation result is sent back to the hyperbolic manifold with the curvature . By using this process, the metric structure consistent with the curvature can be maintained at each layer, avoiding the base point dependence and the distortion of the metric direction introduced by directly doing matrix multiplication on the manifold, and overcoming the problem of cross-scale relationship compression caused by the mismatch between the flat space assumption and the hierarchical topology of brain network.

[0071] S24, further, the bias transmission is implemented in a geometric consistent manner in hyperbolic space. Since the tangent space of each point in hyperbolic space does not share the coordinate system, if the bias vector addition is directly performed on the manifold, the curvature constraint will be destroyed and the base point bias will be introduced, resulting in geometric distortion of the representation, which is not conducive to the stable transmission of subsequent layers. Therefore, the bias transmission adopts the method of first completing the operation corresponding to the bias addition in the tangent space, and then returning to the manifold, thereby avoiding the geometric distortion and base point bias caused by directly adding coordinates in the curvature space, ensuring that the cross-layer calculation is consistent with the curvature of the current layer, and improving the stability of the graph-level representation:

[0072]

[0073] For the first layer bias vector, define the tangent space at the origin , representing the parallel transmission of the bias tangent vector from the reference point tangent space to the tangent space at the base point Parallel transport operator, send the transported bias from the tangent space back to the hyperbolic space.

[0074] Therefore, after completing the linear transformation and bias transmission, the geometric update hyperbolic surface feature of the layer can be obtained , and the calculation relationship satisfies:

[0075]

[0076] Through this form, the geometric linear update and bias correction of the brain region node feature can be realized while maintaining the consistency of the curvature of the manifold where the feature of the previous layer is located . At this time, the feature has not performed cross-layer curvature transition, thereby ensuring the continuity and stability of the feature mapping in the hyperbolic space.

[0077] S3, calculate the attention score between brain region nodes based on the Minkowski inner product, and normalize in the same direction associated subset and reverse associated subset respectively to obtain the signed domain attention weight.

[0078] Specifically, in the present embodiment, after completing the aforementioned feature construction and hyperbolic space representation initialization, the query vector, key vector and value vector are generated based on the geometric update hyperbolic surface feature , and the attention score is calculated. To realize the information interaction between brain region nodes, based on the similarity measurement structure defined by the Minkowski model, the geometric relationship of each geometric update hyperbolic surface feature in the current layer is calculated through the multi-head attention mechanism, and the attention weights of the same direction associated subset and the reverse associated subset are generated in combination with the signed graph structure. ​

[0079] S31, the aforementioned step has obtained a same-direction connection weight matrix and a reverse connection weight matrix . For any brain area node, the same-direction association subset is composed of neighborhood nodes in the matrix that have nonzero connections with the node, and the reverse association subset is composed of neighborhood nodes in the matrix that have nonzero connections with the node. The normalization of the subsequent attention weight is performed within the same-direction association subset and the reverse association subset .

[0080] S32, geometric update hyperbolic feature for the current layer , the query vector , the key vector and the value vector are obtained in the tangent space through a learnable linear transformation matrix. Specifically, the geometric update hyperbolic feature is mapped to the tangent space and the preset learnable weight matrix , , of the current layer is used to perform matrix operation, so as to obtain the query vector , the key vector and the value vector . The process is performed under the curvature constraint where the geometric update hyperbolic feature is currently located, so as to ensure the continuity of the geometric transformation and provide input conforming to the current geometric metric for subsequent similarity calculation based on Minkowski inner product.

[0081] S33, for each head After obtaining the hyperbolic space representation of the query vector, the key vector and the value vector, the embodiment constructs the attention score between nodes based on Minkowski inner product. For the brain area node and its neighborhood node , the geometric update hyperbolic feature is the hyperbolic space representation of the first brain area node in the current layer, and the node is its neighborhood brain area node, and the corresponding feature is . Under the curvature parameter of the current layer, the relative relationship between the brain area nodes is quantified by performing inner product operation on the query vector and the key vector, and combining the normalization factor set in the current layer, and the calculation form of the attention score is:

[0082]

[0083] is the feature dimension of a single attention head, is a curvature adaptive scaling coefficient, and ​​is a constant scaling factor. Through the above calculation, the attention score matrix between brain region nodes can be obtained for subsequent sign domain weight normalization processing.

[0084] S34、According to the signed connection relationship constructed in the previous step, the forward connection weight matrix and the reverse connection weight matrix , the neighborhood of the brain region node is divided into a forward associated subset and a reverse associated subset. For each row in the attention score matrix, the forward associated subset and the reverse associated subset of the brain region node are taken as the range, and softmax operation is performed respectively, so that the forward associated subset attention weight and the reverse associated subset attention weight are obtained. The calculation form is as follows:

[0085]

[0086]

[0087] denotes the brain region node The weight distribution in the forward associated subset, denotes the weight distribution in the reverse associated subset. Since the forward associated subset and the reverse associated subset are normalized respectively, the weights of the two types of signed connections do not interfere with each other, so that the signed domain relationship required by the current layer can be expressed independently.

[0088] S4, using the forward associated subset attention weight and the reverse associated subset attention weight to perform sign-differentiated aggregation processing on the geometric update hyperbolic surface feature to generate the final update feature;

[0089] In this embodiment, S3 obtains the forward associated subset attention weight and the reverse associated subset attention weight of each brain region node in the current layer.

[0090] S41, for any node and any attention head in the current layer, the geometric update hyperbolic surface feature corresponding to the brain region node constructs a local tangent space at the hyperbolic space position corresponding to the geometric update hyperbolic surface feature, and transforms the value vectors of each neighborhood node in the forward associated subset and the reverse associated subset under the corresponding attention head to the tangent space by tangent space projection transformation, so that the above vectors have the form of executable linear combination in the space.

[0091] S42, then, respectively, with the same direction associated subset attention weight and reverse associated subset attention weight as the weighting coefficient, the corresponding tangent space vector in the same direction associated subset and reverse associated subset is weighted and accumulated, wherein the same direction associated subset is accumulated in additive form, and the reverse associated subset is accumulated in subtractive form, thereby obtaining the brain region node In the current layer, the symbolic aggregation quantity under the attention head The above aggregation process is sequentially performed on all brain region nodes and all attention heads in the current layer, and its specific calculation form is as follows:

[0092]

[0093] In the formula and are the same direction associated subset and the reverse associated subset, and are the same direction and reverse associated partition attention weight, indicates the tangent space projection transformation operation under the curvature constraint with the current layer geometric update hyperbolic feature as the base point, which is used to map the vector on the hyperbolic space to the tangent space of the base point.

[0094] S43, the aggregation results of multiple attention heads are integrated in the local tangent space of the brain region node, the aggregation quantities of each attention head are combined in the form of mean value, and a consistent cumulative representation is formed in the same tangent space, and then it is lifted to the hyperbolic space through manifold embedding transformation to obtain the aggregated hyperbolic feature of the brain region node in the current layer . Its calculation form is as follows:

[0095]

[0096] After obtaining the above aggregated hyperbolic feature , in order to introduce a nonlinear transformation and update the manifold curvature, first, the tangent space projection transformation is used to project the feature to the origin tangent space. Then, a nonlinear activation function is applied in the tangent space to adjust the feature distribution and capture nonlinear patterns. Finally, based on the newly set curvature parameter of the current layer, the activated vector is lifted to the new hyperbolic manifold through the manifold embedding transformation, thereby completing the geometric space transition across layers, and obtaining the final updated feature of the brain region node in the current layer , which is in the form of:

[0097]

[0098] S5, graph-level reading and disease classification: graph-level reading is realized in hyperbolic space using manifold geometry center, and mental disease classification is completed.

[0099] Utilize the final update features of all N brain region nodes from the last layer output of the completed image. As input, the geometric center representation of the graph is generated by computation within hyperbolic space.

[0100] S51. Using the geometric center of a manifold in hyperbolic space as the graph-level readout method, solve for a graph geometric center that can characterize the overall brain network topology. The process of determining the center point is essentially an optimization problem, namely, finding a candidate center point on a hyperbolic manifold. This makes the candidate center point reach all the final updated features. The sum of squared geodesic distances is minimized, and its form is as follows:

[0101]

[0102] To solve for the geometric center of the above graph, this embodiment adopts an iterative update method (i.e., the geodesic gradient flow algorithm): in each iteration, the final updated features of all brain region nodes are obtained by using tangent space projection transformation. Project onto the current candidate center point The tangent space is calculated, and the average update vector of the tangent space is computed. Then, the manifold embedding transformation is applied to this vector to the current center, thus obtaining the center position for the next iteration. The iteration form is as follows:

[0103]

[0104]

[0105] in, This is the step size coefficient. To update the direction vector, this embodiment obtains the final center point of the graph after a fixed number of iterations. .

[0106] S52. Obtain the geometric center of the diagram. Subsequently, to obtain a tangent space vector form that can be used for conventional linear classification, this embodiment uses the final updated features of all brain region nodes. The tangent space projection transformation is used to project the image onto the geometric center. The tangent space. Since the tangent space has the properties of a vector space, average pooling can be performed on the projected tangent vectors to generate graph-level feature representations. Its form is as follows:

[0107]

[0108] Finally, the graph-level feature representation is input into the classification module, and the prediction results for mental illnesses are output.

[0109] This embodiment uses the ADHD-200 (Attention Deficit Hyperactivity Disorder-200) dataset and the ABIDE (Autism Brain Imaging Data Exchange) dataset as input data sources. Both datasets are publicly available brain imaging resources, containing resting-state fMRI data of the subjects and providing time series data obtained based on AAL (Automatic Anatomical Marking) templates or equivalent brain region segmentation methods, which can be used to construct marked brain functional connectivity maps. These two datasets originate from multiple data collection sites, and the subject population exhibits cross-center and cross-regional diversity, providing a rich and stable input data foundation for the method in this embodiment during the mapping, feature mapping, and model training stages.

[0110] This embodiment of the brain functional network-based auxiliary diagnostic method for mental illness is implemented based on a deep learning framework. This embodiment uses Python and the PyTorch computing framework to build hyperbolic geometry operations, attention calculations, and feature aggregation modules for the model. Both training and inference run on GPU-accelerated computing devices; a typical environment may include NVIDIA GPUs supporting CUDA (Unified Computing Device Architecture).

[0111] During the training phase, this embodiment performs end-to-end optimization of each computational process from S1 to S5. The model consists of a three-layer hypercurvature attention structure, with four attention heads set in each layer, and learnable curvature parameters assigned to each layer. When constructing the functional network, a weighted sparse graph was generated based on fMRI data. For each brain region node, the first k=10 positive edges and the first k=10 negative edges were retained to form a graph structure containing symbolic connections. In the graph-level readout stage, five geodesic gradient flow iterations were performed in hyperbolic space to obtain the geometric center of the manifold, with the step size coefficient set to η=0.1.

[0112] To ensure numerical stability during training, this embodiment uses the AdamW optimizer for parameter updates, with the learning rate set to [value missing]. The weight decay coefficient is set to The batch size was set to 32, and the training rounds were 100. In each training round, the model sequentially performed hyperbolic mapping, Minkowski attention computation, symbolic domain aggregation, and graph readout operations, and updated parameters under the supervision of cross-entropy loss. The above training process can run stably in a conventional deep learning environment.

[0113] After the training is completed, for new subject functional connectivity data, the embodiment sequentially performs hyperbolic mapping of brain region node features, signed domain attention allocation, hyperbolic space aggregation, and manifold geometry center reading, finally generates a graph-level representation and outputs a prediction result of a mental illness. The running environment and training process of the embodiment ensure the executability of the method on actual computing devices.

[0114] As shown in the experimental results of Tables 1 and 2, the performance indicators of the model proposed in the present application on the ADHD-200 and ABIDE public brain image data sets are all better than those of the existing mainstream methods. On the ADHD-200 data set, the present application achieves a classification accuracy of 83.6% and an AUC of 90.7%; on the ABIDE data set, the classification accuracy reaches 88.3% and the AUC reaches 91.4%, which is significantly improved compared with various CNN, Transformer and flat space graph neural network baseline methods, verifying the effectiveness and advancement of the present application in the complex brain function network representation and auxiliary diagnosis task of mental illness.

[0115] Table 1: Performance comparison on ADHD-200 and ABIDE data sets, all results are reported as "mean ± standard deviation" of 10-fold cross-validation

[0116]

[0117] Table 2: Ablation experiments on ADHD-200 and ABIDE data sets. All results are reported as "mean ± standard deviation" of 10-fold cross-validation.

[0118]

Claims

1. A method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks, characterized in that, Includes the following steps: S1. Based on fMRI data, extract brain region time series as brain region nodes and calculate the same-direction and reverse-direction correlation to construct a brain functional network containing the same-direction and reverse-direction correlation partition connections. S2. Map the brain region nodes to the hyperbolic space of the Minkowski model to generate geometrically updated hyperbolic surface features; S3. Calculate the attention scores between the nodes in the brain regions based on the Minkowski inner product, and normalize them in the same-direction association subset and the opposite-direction association subset respectively to obtain the attention weights of the same-direction association subset and the attention weights of the opposite-direction association subset. S4. The geometrically updated hyperboloid features are aggregated using the attention weights of the same-direction correlation subset and the attention weights of the opposite-direction correlation subset to generate the final updated features. S5. Based on the final updated features, the geometric center of the manifold is used to achieve graph-level readout in the hyperbolic manifold and complete the classification of mental illnesses.

2. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 1, characterized in that, S1 includes: S11. The average blood oxygen-dependent fluctuation sequence of each brain region is extracted based on the AAL-116 brain region template as the brain region node; S12. Calculate the correlation between the mean blood oxygen-dependent fluctuation sequences of any two brain regions using the Pearson correlation coefficient, and generate a correlation matrix; S13. Generate the same-direction connection weight matrix and the opposite-direction connection weight matrix according to the sign of the correlation matrix; S14. In the same direction connection weight matrix and the opposite direction connection weight matrix, retain the top k connections with the largest weights for each brain region, and symmetricize the connection relationships to generate the sparse undirected signed brain functional network.

3. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 2, characterized in that, S2 include: The reference point of the Minkowski model is selected as the tangent space anchor point; the flat space features corresponding to each brain region node are extracted; The flat space features are uplifted to hyperbolic space by a geodesic-based manifold embedding transformation to obtain the initial hyperbolic surface features; The initial hyperboloid feature is subjected to a linear transformation consistent with the curvature layer by layer in hyperboloid space; The initial hyperboloid features after linear transformation are biased by a learnable bias vector to obtain the geometrically updated hyperboloid features of each layer.

4. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 3, characterized in that, Before the linear transformation, the initial hyperboloid features are projected onto the tangent space of the tangent space anchor point for calculation, and then mapped back to the hyperboloid space; the bias transfer is first completed in the tangent space, and then mapped back to the hyperboloid space.

5. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 2, characterized in that, S3 include: For any brain region node, the unidirectional association subset consists of neighboring nodes in the unidirectional connection weight matrix that have non-zero connections with the brain region node; the inverse association subset consists of neighboring nodes in the inverse connection weight matrix that have non-zero connections with the brain region node. Under the curvature constraint of the geometrically updated hyperboloid feature, the geometrically updated hyperboloid feature is mapped to the tangent space and then matrix operations are performed with the preset learnable weight matrix to obtain the query vector, key vector and value vector; An attention score matrix between brain region nodes is constructed based on the Minkowski inner product.

6. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 5, characterized in that, S3 also includes: For each row of the attention score matrix, a softmax operation is performed on the same-direction association subset and the opposite-direction association subset of the brain region node to generate the attention weights of the same-direction association subset and the opposite-direction association subset.

7. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 1, characterized in that, S4 include: A local tangent space is constructed at the hyperbolic space location corresponding to the geometrically updated hyperbolic feature of any brain region node and any attention head. The value vectors of each neighboring node in the same-direction and reverse-direction subsets under the corresponding attention head are transformed to the local tangent space through tangent space projection. The attention weights of the same-direction and reverse-direction subsets are used as weighting coefficients to accumulate the corresponding tangent space vectors in the same-direction and reverse-direction subsets to generate the symbolic aggregation amount of the brain region node under the current layer and the current attention head. The symbolic aggregation of multiple attention heads is integrated within the local tangent space of the brain region node, and then elevated to hyperbolic space through manifold embedding transformation to obtain the aggregated hyperbolic feature of the brain region node in the current layer.

8. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 7, characterized in that, S4 also includes: The aggregated hyperbolic features are projected onto the tangent space using a tangent space projection transformation, and a nonlinear activation function is applied within the tangent space. Based on the curvature parameters set in the current layer, the vector of nonlinear activation is raised to the new hyperbolic space through a manifold embedding transformation to generate the final updated features.

9. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 1, characterized in that, S5 include: Based on the final update features of all brain region nodes output from the last layer, a graph geometric center that can characterize the overall brain network topology is solved using the manifold geometric center in hyperbolic space as the graph-level readout method. The final updated features of all brain region nodes are uniformly projected onto the tangent space of the geometric center of the graph using tangent space projection transformation; average pooling is performed on the tangent vectors generated after projection to generate graph-level feature representations; the graph-level feature representations are input into the classification module to output the prediction results of mental illnesses.

10. The method for auxiliary diagnosis of mental illness based on hyperbolic geometry brain functional networks according to claim 9, characterized in that, Generating the geometric center of the graph includes: A candidate center point is found on the hyperbolic manifold such that the sum of squared geodesic distances from the candidate center point to all final updated features is minimized. An iterative update method is adopted. In each iteration, the final updated features of all brain region nodes are projected to the tangent space of the candidate center point using the tangent space projection transformation, and the tangent space average update vector is calculated. The tangent space average update vector is applied to the current center point using the manifold embedding transformation, thereby obtaining the center point for the next iteration. The geometric center of the graph is generated after the number of iterations reaches a preset number.

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