Method for constructing lymphedema pathological network based on graph neural network

Abstract

The present invention relates to a method for constructing a lymphedema pathological network based on graph neural networks. First, collect medical imaging data, clinical records, and biomarker data of the lymphatic system of patients, and use image processing techniques to extract key features and structure them into nodes and edges of a graph; then, based on the anatomical structure and physiological functions of the lymphatic system, define the topological structure of the graph, and introduce multi-modal data fusion technology to combine imaging data and biomarker data; then, design a multi-layer graph convolutional network model for learning the patterns of lymph nodes and their connections, and introduce an attention mechanism; then, use the graph convolutional network for deep learning to extract hidden features of nodes and edges, and apply graph embedding technology to transform high-dimensional graph data into a low-dimensional space; finally, develop a graph-based anomaly detection algorithm for identifying pathological changes that are significantly different from common patterns, and combine time series analysis to predict the pathological progression of lymphedema.

Description

Technical Field

[0001] The present invention relates to a method for constructing a lymphedema pathological network, specifically a method for constructing a lymphedema pathological network based on a graph neural network. Background Art

[0002] Although the current methods for constructing lymphedema pathological networks offer various potential advantages, such as enhanced data analysis capabilities and improved pathological recognition accuracy, they also have a series of deficiencies and drawbacks. First, the construction of lymphedema pathological networks relies on highly complex graph neural network (GNN) models that require a large amount of labeled data for training. In the actual medical field, especially when dealing with specific types of lymphedema such as breast cancer-related lymphedema, it is difficult to obtain sufficient clinical data to train these models. The scarcity of data not only limits the training quality of the models but also leads to overfitting, that is, the models perform well on the training data but poorly on unseen new data. In addition, this data usually involves privacy issues and strict compliance with medical data protection regulations, which poses additional challenges in data collection and processing. Second, the computational complexity of graph neural networks is high, especially when dealing with large-scale graph data, requiring a large amount of computational resources. This not only increases the cost of research but also limits the application of these models in resource-constrained environments. In low-resource medical settings, there is a lack of sufficient technology and computational support to run complex graph analysis models. Moreover, the training and inference times of GNN models are very long and are not practical in clinical settings where rapid diagnosis and treatment decisions are required.

[0003] Furthermore, graph neural networks have deficiencies in model interpretability. Although they excel in feature extraction and pattern recognition, due to the complexity of the model structure, it is difficult to explain the specific behaviors and decision-making paths of the model. In the medical field, model interpretability is very important. Doctors and patients usually need to understand the reasoning process of the model to increase trust and acceptance. The lack of transparency will hinder the acceptance and application of graph-based methods in clinical practice. In addition, the current methods for constructing lymphoedema pathological networks are biased among patient groups of different races, ages, or genders, which is caused by the unevenness in the training dataset. If the data used for training does not represent a wide range of people, then the model will perform well in specific subsets but poorly in other subsets. This bias can be alleviated by using more diverse and inclusive datasets, but the construction of such datasets usually requires additional time and resources. Also, although graph neural networks have significant advantages in identifying complex patterns, they are very sensitive to noise and outliers in the data. In actual clinical data, data quality problems caused by various factors (such as different devices, differences in the technical levels of operators, etc.) are often encountered. These problems will affect the performance of graph neural networks, resulting in misdiagnosis and missed diagnosis. Therefore, further research is needed on how to optimize the model to adapt to fluctuations in data quality and develop new robust algorithms to handle imperfect input data. Summary of the Invention

[0004] The object of the present invention is to provide a method for constructing a lymphoedema pathological network based on a graph neural network, so as to solve some of the drawbacks and deficiencies pointed out in the background art.

[0005] The present invention adopts the following technical solutions to solve its above-mentioned technical problems:

[0006] First, collect the lymphatic system medical image data, clinical records, and biomarker data of patients, and use image processing technology to extract key features and structure them into the nodes and edges of a graph, where the nodes represent lymph nodes and the edges represent the paths or interactions of lymphatic flow;

[0007] Next, based on the anatomical structure and physiological functions of the lymphatic system, define the topological structure of the graph, and introduce multi-modal data fusion technology to combine the image data and biomarker data to enhance the information accuracy of the graph network;

[0008] Then, design a multi-layer graph convolutional network model for learning the patterns of lymph nodes and their connections, and introduce an attention mechanism to identify and emphasize the nodes and edges that play a role in the development of lymphoedema;

[0009] Then, use the graph convolutional network for deep learning to extract the hidden features of the nodes and edges, and apply graph embedding technology to transform the high-dimensional graph data into a low-dimensional space for classification or clustering analysis;

[0010] Finally, develop a graph-based anomaly detection algorithm to identify pathological changes that are significantly different from common patterns, and combine time series analysis to predict the pathological progression of lymphedema.

[0011] Furthermore, the extraction of key features using image processing technology includes the following steps:

[0012] S1. First, adopt a unified data processing framework:

[0013]

[0014] Where G and H represent processing functions for different data sources including CT and MRI image data, blood biochemical indicators, and patient symptom records, and are used to synchronously process and integrate various types of data;

[0015] S2. Then apply an image processing algorithm through the function:

[0016]

[0017] Where v n is the value of each pixel in the image, is the average pixel value, and is used to identify and quantify the size, shape, and distribution characteristics of lymph nodes;

[0018] S3. Then, through the graph construction algorithm:

[0019]

[0020] Where E is the set of edges, α ij is the weight of the edge, k i and k j are the eigenvalue of the nodes connecting the edges, and are used to transform the extracted features into nodes in the graph, that is, representing lymph nodes and edges, that is, representing the physiological relationship or signal transmission path between nodes.

[0021] Furthermore, the definition of the topological structure of the graph includes the following steps:

[0022] S1. First, adopt a graph topology generation algorithm:

[0023]

[0024] Where N represents nodes, L represents edges, L i is the connection specified based on the anatomical structure, A i is the corresponding physiological function connection, d is the distance between nodes, and σ is the normalization parameter, and is used to construct the nodes and edges of the graph according to the anatomical location and physiological function of lymph nodes;

[0025] S2. Then, apply a multi-modal deep fusion network through the function:

[0026]

[0027] where x, y, and z respectively represent input data of different modalities, and w k and v j are weights learned from the data and are used to integrate information from different sources including MRI, CT scans, and biochemical markers to enhance the accuracy of the final graph structure data.

[0028] Furthermore, the construction process of the multi-layer graph convolutional network model:

[0029] First, introduce and implement an adaptive layer structure of the multi-layer graph convolutional network GCN through the calculation formula:

[0030]

[0031] where G represents the overall structure of the graph, E represents the set of edges in the graph, x i and x i-1 respectively represent the feature vectors of consecutive nodes, α i is the inter-layer adaptability factor, and ∈ is the smoothing constant, which are used to adjust the structure of the network layer to adapt to the anatomical features and pathological changes of lymph nodes;

[0032] Secondly, introduce a graph-based attention mechanism, and the calculation formula is:

[0033]

[0034] where u and v are nodes in the graph, f(u) and f(v) represent the feature vectors of nodes u and v, β is the learned attention concentration parameter, and δ is the regularization constant, which are used to emphasize the nodes and edges that are critically relevant to the development of lymphedema.

[0035] Furthermore, the method for extracting the hidden features of nodes and edges adopts the steps:

[0036] S1. First, design and implement an adaptive layer structure of the multi-layer graph convolutional network GCN, and adapt to the connectivity and feature diversity of nodes through graph convolutional operations that adjust the convolution kernel parameters. The convolution kernel size and feature extraction method of each layer are dynamically adjusted according to the local structure of the graph to capture biomarker and pathological features between lymph nodes;

[0037] S2. Further integrate the multi-scale feature extraction strategy, capture biomarker features from micro to macro at different levels, and introduce cross-layer connections to enhance information flow and feature reuse to improve the accuracy of classification and clustering;

[0038] S3. Finally, apply a non-linear dimensionality reduction method based on deep learning for graph embedding. Designed for graph data, it constructs a mapping from high dimension to low dimension while maintaining the topological structure of the graph and the relationships between nodes, facilitating subsequent classification or clustering analysis.

[0039] Further, the adaptive layer structure is implemented through a dynamic convolution kernel adjustment function:

[0040]

[0041] where G represents the overall structure of the graph, E represents the edge set, α vu represents the adaptive weight on the edge (v, u), x v and x u represent the feature vectors of nodes v and u respectively, and θ is a parameter adjusted based on the topology of the graph and the diversity of node features, used to adapt to the feature extraction requirements of each layer, especially in terms of lymph nodes and their interacting biomarkers;

[0042] Further, effective capture of lymphoedema-specific biomarkers and pathological features is achieved through multi-scale feature integration technology, using the formula:

[0043]

[0044] where H l represents the output feature matrix of the l-th layer, W k represents the weight matrix from the k-th layer to the l-th layer, and σ is a non-linear activation function, used to integrate information and extract biomarkers at multiple levels of the graph.

[0045] Further, the integrated multi-scale feature extraction strategy includes the following steps:

[0046] S1. First, implement a multi-scale graph convolutional network M-GCN through the function:

[0047]

[0048] where v represents the current node, N k (v) is the set of neighbor nodes of node v at the k-th scale, ω k is the learning weight at the k-th scale, x u is the feature of the neighbor node, and σ is an activation function, designed to capture biomarker features from micro to macro at different levels;

[0049] S2. Then, introduce cross-layer connections to enhance information flow and feature reuse, specifically through the formula:

[0050]

[0051] Implementation, where F l is the output feature of the l-th layer, and H i is the output feature of the i-th layer, and γ li is the cross-layer connection weight from the i-th layer to the l-th layer, which is used to improve the accuracy of classification and clustering.

[0052] Furthermore, the construction of the graph embedding framework by the non-linear dimensionality reduction method includes:

[0053] S1. First, implement the deep learning-driven graph embedding model DLGE, and learn the non-linear embedding of the graph through an autoencoder. Specifically, by minimizing the function:

[0054]

[0055] where V and E respectively represent the node set and edge set in the graph, f(v) represents the low-dimensional embedding of node v, and λ is the regularization coefficient, which is used to adjust the penalty intensity of non-adjacent node pairs to maintain the topological structure of the graph and the relationship between nodes during the high-dimensional to low-dimensional mapping process;

[0056] S2. Then, introduce the graph structure-preserving loss function GSPL, by calculating:

[0057]

[0058] where ω ij is the importance weight of the node pair (i, j) learned based on the graph attention layer, x i and x j are the original feature vectors, and g(i) and g(j) are the corresponding low-dimensional representations.

[0059] Furthermore, the composition of the graph-based anomaly detection algorithm:

[0060] S1. First, implement the dynamic graph convolutional network DGCN, adopt the dynamic graph convolutional layer, and update the node representation through the function:

[0061]

[0062] to update the node representation, where t represents the time step, v is the current node, is the neighbor set of node v, W t and b t are the weight matrix and bias vector at time step t respectively, h t-1 (u) is the embedding representation of node u at time t - 1, and σ is the standard deviation of the Gaussian kernel, which is used to simulate the interaction intensity between nodes;

[0063] S2. Then, apply the graph-based anomaly detection algorithm GAD, by calculating:

[0064]

[0065] to identify anomalies, where f(v) and f(u) are the embedding vectors of node v and its neighbor u respectively, and p is a selected positive real number used to increase the sensitivity and discrimination of anomaly detection;

[0066] S3. Finally, combining time series analysis and prediction models, process the time series graph data through the long short-term memory network LSTM. The specific implementation formula is:

[0067] h t = LSTM(h t-1 , α·h t-1 +(1 - α)·x t )

[0068] where h t is the hidden state at time t, x t is the input feature, and α is a learning rate between 0 and 1, which is used to balance the influence of historical information and current input to predict the pathological progression of lymphedema.

[0069] Advantages of the present invention:

[0070] 1. Using graph neural networks (GNNs) for in-depth analysis of pathological data, by capturing the interactions and patterns between lymph nodes, these networks can more accurately identify various biomarkers and pathological changes of lymphedema. The highly complex data processing ability of GNNs improves the ability to identify early signs of the disease, which is crucial for early diagnosis and timely treatment.

[0071] 2. The graph-based method is particularly suitable for processing non-Euclidean structure data, including medical images and pathological networks. GNNs can learn and extract key features from the data without relying on traditional, manually formulated feature extraction techniques. This not only reduces the dependence on professional knowledge but also improves the efficiency and effectiveness of processing complex data.

[0072] 3. Through the dynamic graph convolutional network, the present invention can process time-varying pathological features, enabling it to track the development and changes of the disease condition. This is particularly useful for disease states that require continuous monitoring and regular evaluation, such as the dynamic changes of lymphedema during treatment.

[0073] 4. By implementing a multi-scale feature integration strategy, biomarker features from micro to macro can be captured at different levels. Such multi-level analysis enhances the understanding of the complexity of the pathological state, thereby improving the accuracy of classification and clustering. Description of the Drawings

[0074] Figure 1This is the flowchart of the method for constructing a lymphedema pathology network based on graph neural networks in the present invention.

[0075] Figure 2 This is the flowchart of the method for extracting the hidden features of nodes and edges in the present invention. Detailed implementation manners

[0076] The following will make a detailed description of the specific implementation manners of the present invention with reference to the accompanying drawings.

[0077] In the first step of this case Figure 1 First, collect data including medical images (such as CT and MRI scans), clinical records, and biomarkers (such as blood test results) from patients. Through advanced image processing techniques, including edge detection and texture analysis, extract key features from medical images, including the size, shape, and distribution location of lymph nodes, and convert these data points into nodes of a graph.

[0078] In the second step of this case Figure 1 Then, define the edges connecting these nodes according to the lymphatic flow path and the physiological interactions between lymph nodes. Further, define the topological structure of the graph using the knowledge of the anatomy and physiology of the lymphatic system, and apply multi-modal data fusion technology to enhance the overall information accuracy and richness of the graph network by integrating information from different data sources.

[0079] In the third step of this case Figure 1 Subsequently, design and implement a multi-layer graph convolutional network (GCN) model to learn and identify the patterns of lymph nodes and their connections by processing graph data layer by layer. Introduce an attention mechanism in this process to identify and emphasize the nodes and edges that play a key role in the development of lymphedema, so as to more accurately capture the development trend of the pathological state.

[0080] In the fourth step of this case Figure 1 Use deep learning of graph convolutional networks to extract the hidden features of nodes and edges, and effectively convert these complex high-dimensional graph data into low-dimensional representations through graph embedding technology for more effective data analysis, including classification and clustering.

[0081] In the fifth step of this case Figure 1 Develop a graph-based anomaly detection algorithm specifically used to identify changes that are significantly different from known and common lymph node pathological patterns, so as to early warn of potential pathological abnormalities. This algorithm is combined with time series analysis technology, which can not only detect the current abnormal state, but also predict the future development trend of lymphedema

[0082] Example 1:

[0083] The embodiment first requires collecting data from the patient, including CT scan, MRI image data, blood biochemical indicators, and the patient's clinical symptom records. These data exist in different data formats and scales, so a unified data processing framework is needed to integrate this information for further analysis. The following mathematical model is used to integrate the data:

[0084]

[0085] Among them, G(x i , y i , z i ) and H(x i , y i , z i ) represent the processing functions for various medical images and biochemical indicators respectively. The G function represents a feature extraction algorithm, including algorithms for extracting the size and shape of lymph nodes from image data, while the H function is a normalization function used to standardize the data to eliminate the influence of dimensions and differences between different devices.

[0086] The G and H functions are defined as:

[0087]

[0088] H(x i , y i , z i ) = x i + y i + z i

[0089] Where x i , y i , z i are the normalized values of the three-dimensional coordinate data extracted from the CT scan respectively. These values vary between 0 and 1, representing the relative position of the lymph nodes in the body.

[0090] It is assumed that the three-dimensional coordinate data extracted from the CT scan has been normalized to the range of 0, 1, and the specific values are x i = 0.5, y i = 0.3, z i = 0.4. Substitute these values into the above functions to first calculate the values of G and H:

[0091] G(0.5, 0.3, 0.4) = 0.5 2 + 0.3 2 + 0.4 2 = 0.25 + 0.09 + 0.16 = 0.50

[0092] H(0.5, 0.3, 0.4) = 0.5 + 0.3 + 0.4 = 1.2

[0093] Further, perform integral calculation:

[0094]

[0095] This value can be regarded as the integrated measure of the single-point estimation based on the given node features in the entire graph, which will be used for setting the weights of the graph nodes and as features input into the graph neural network.

[0096] Further technical implementation schemes include applying this type of processing to all collected data points to create a complete graph representation, where each node represents a specific lymph node, and the attributes of the nodes are obtained from the results of processing similar to the above. The definition of the edges is based on the paths or interactions of lymphatic flow, which can be obtained from clinical records and input through an expert system. Once the graph is created, a multi-layer graph convolutional network model will be trained to identify and learn the patterns and connections between lymph nodes.

[0097] The embodiment then uses an image processing algorithm to identify and quantify the size, shape, and distribution characteristics of lymph nodes, involving using an image processing algorithm to extract features through the following function:

[0098]

[0099] where v n is the value of each pixel point in the image, and is the average value of these pixel values. This function calculates the root mean square difference between the image pixel values and the average pixel value, and this difference can be used to quantify the visual differences of objects in the image, including the size and morphological characteristics of lymph nodes.

[0100] To further specify and verify the feasibility of this scheme, it is set that an image region containing lymph nodes is obtained from a CT scan, and this region contains N = 100 pixel points. The values vn of these pixel points range from 0 to 255 in the grayscale image, and it is set that these pixel values are randomly distributed, and the specific values are as follows (example values):

[0101] v = [30, 45, 60, 120, 150, 170, 180, 190, 200, 210] (note that there will be 100 such values in the actual situation, and only 10 are shown here to simplify the calculation).

[0102] Average pixel value is calculated as follows:

[0103]

[0104] Then substitute each pixel value into the above formula, and the calculation result is:

[0105]

[0106] M(v)=60

[0107] This result provides a quantitative measure indicating a significant difference in pixel values between lymph nodes and the background in the image. Higher values indicate a higher contrast between the lymph nodes and the surrounding tissue, which is an indicator of abnormal lymph node size and shape.

[0108] The last example uses the extracted features to construct a detailed graph representation for the analysis of the lymphedema pathology network, which involves transforming the extracted image features into nodes (representing lymph nodes) and edges (representing the physiological relationships or signal transmission paths between nodes) in the graph, implemented through the following construction algorithm:

[0109]

[0110] where E is the set of edges, α ij is the weight of the edge, k i and k j are the feature values of the nodes connecting the edges.

[0111] It is assumed that in medical imaging, several key lymph nodes have been identified through the aforementioned image processing steps, and their feature values (such as the metrics extracted based on size, shape, and contrast) are k1 = 150, k2 = 180, and k3 = 160 respectively. These feature values represent quantitative indicators of certain physiological characteristics and pathological states of the lymph nodes. Further, it is assumed that the connection relationships between these nodes are based on the physical distance in the body and the similarity of physiological functions, and the corresponding edge weight α ij can be set to be determined according to the importance of these physiological and pathological relationships, with the weight range between 0.1 and 1, and the specific value depending on the physiological significance of the connection and the influence of the pathological state.

[0112] Based on this, the connection between lymph node 1 and lymph node 2 is very important (showing a high correlation in the pathological process), and α 12 is set to 1; while for relatively less important connections (such as between lymph node 1 and lymph node 3), α 13 is set to 0.5. Substituting these values into the above formula, the structural loss value of this graph is calculated:

[0113] L(E)=α 12 (k1 - k2) 2 +α 13 (k1 - k3) 2

[0114] L(E)=1×(150 - 180) 2 +0.5×(150 - 160) 2

[0115] L(E)=1×900 + 0.5×100

[0116] L(E)=900 + 50

[0117] L(E)=950

[0118] The calculation results provide a quantitative index that reflects the overall strength and stability of the relationships between the nodes (lymph nodes) in the figure based on the given features, helping researchers understand which connections between lymph nodes are particularly important and abnormal during the pathological process, and thus guiding the diagnosis and treatment strategies for lymphedema.

[0119] Example 2:

[0120] In this example, the topological structure of the defined graph is constructed, which involves a graph topology generation algorithm and is expressed by the following formula:

[0121]

[0122] To elaborate on the implementation steps and feasibility of this solution, it is assumed that several key lymph nodes have been identified from medical images when constructing the lymphedema pathological network, and these nodes need to be connected to each other according to their anatomical positions and physiological functions. Consider the following specific data and parameter settings:

[0123] N represents the set of nodes. It is assumed that there are three lymph node nodes, namely Node 1, Node 2, and Node 3;

[0124] L represents the set of edges. According to the anatomical positions and physiological functions of the lymph nodes, it is assumed that there are connections between Node 1 and Node 2 and between Node 2 and Node 3;

[0125] d is the distance between nodes. It is assumed that from the analysis of anatomical images, the distance between Node 1 and Node 2 is 2 cm, and the distance between Node 2 and Node 3 is 3 cm;

[0126] A i is the corresponding physiological function connection. It is assumed that according to the analysis of physiological functions, the functional connection strength score between Node 1 and Node 2 is 0.8, and the functional connection strength score between Node 2 and Node 3 is 0.6;

[0127] It is assumed that the value of σ is 1, which is used to balance the scale in distance calculation.

[0128] Based on these settings, the weight of each pair of connections can be calculated:

[0129]

[0130] F(N,L)=exp(-0.72)+exp(-2.88)

[0131] F(N,L) = 0.486 + 0.056

[0132] F(N,L) = 0.542

[0133] The calculation results provide a quantitative metric that shows the overall weight of the edges in the graph constructed based on anatomical and physiological data, ensuring that the graph model not only reflects the physical proximity of the lymph nodes but also takes into account their interactions in physiological functions.

[0134] In the next step of the embodiment, a multi-modal deep fusion network is used to integrate information from different data sources, thereby enhancing the accuracy of the graph-structured data. By extracting and combining information from multiple different data modalities such as MRI, CT scans, and biochemical markers, a more comprehensive and rich feature representation is provided for the graph neural network. The following multi-modal fusion function is used for data integration:

[0135]

[0136] where 1 represents the input data from different modalities, and w k and v j are the weights learned from the data.

[0137] In practical applications, data is extracted from the patient's MRI scans (x data modality), CT scans (y data modality), and blood biochemical markers (z data modality). Assume:

[0138] x = [x1, x2, …, x K represents the feature vector extracted from the MRI scans, including features related to the size of the lymph nodes;

[0139] y = [y1, y2, …, y J represents the feature vector extracted from the CT scans, including features related to the density of the lymph nodes;

[0140] z represents the continuous data extracted from the blood biochemical markers, including the concentration of specific proteins in the blood.

[0141] Assume there are 5 MRI features and 3 CT features, where the weights w k and v j are learned through a data-driven method. The specific weight values can be automatically adjusted according to their importance during the training process, ranging from 0.1 to 1. For simplicity, assume all weights are 0.5.

[0142] Substitute the data and weights into the fusion function and perform the following calculations:

[0143] G(x, y, z) = (0.5×x1 + 0.5×x2 + … + 0.5×x5)·(0.5×y1 + 0.5×y2 + 0.5×y3) + ∫z dz

[0144] Set x i = 100 and y j = 200 as simplified calculation values, and the integral of z is 300:

[0145] G(x, y, z) = (0.5×500)·(0.5×600) + 300

[0146] G(x, y, z) = 250×300 + 300

[0147] G(x, y, z) = 75300

[0148] The calculation result combines the image features and biochemical marker data of MRI and CT, making the final graph structure data more accurate and providing effective input for the lymphoedema pathological network analysis based on graph neural network.

[0149] Example 3:

[0150] An adaptive layer structure of a multi - layer graph convolutional network (GCN) is constructed in the example to capture and analyze the anatomical features and pathological changes of lymph nodes. This process adjusts the network structure according to the feature differences between nodes through calculation formulas, enabling the model to better adapt to complex medical data and pathological conditions, as follows:

[0151]

[0152] Where G represents the overall structure of the graph, E represents the set of edges in the graph, x i and x i-1 represent the feature vectors of consecutive nodes respectively, α i is the inter - layer adaptability factor, and ε is the smoothing constant, which is used to adjust the structure of the network layer.

[0153] Consider a small network with four nodes, each node representing a lymph node, and the feature vectors of the nodes include parameters such as the size, shape, and density of the lymph nodes. The specific values are as follows:

[0154] x1 = [1.0, 0.8]

[0155] x2 = [1.2, 0.9]

[0156] x3 = [1.1, 0.85]

[0157] x4 = [1.3, 0.95]

[0158] Set α iThe value range of α is from 0.1 to 1.0, and the specific value can be automatically adjusted according to the learning importance of each layer. In this example, all α i values are set to 0.5, and ∈ is set to 0.01 to reduce the influence caused by small feature differences.

[0159] Calculate the terms corresponding to the feature differences between each pair of nodes according to the formula:

[0160]

[0161] Substitute these values into the overall formula:

[0162] F(G,E) = 0.5×log(6) + 0.5×log(3.75) + 0.5×log(5.5)

[0163] F(G,E) ≈ 0.5×1.792 + 0.5×1.321 + 0.5×1.704

[0164] F(G,E) ≈ 0.896 + 0.660 + 0.852

[0165] F(G,E) ≈ 2.408

[0166] The calculation result provides a quantitative measure to illustrate how the model adjusts its internal structure according to the differences between feature vectors, optimizing information flow and feature learning.

[0167] In the next step of the embodiment, a graph-based attention mechanism is introduced with the aim of identifying and highlighting the nodes and edges that play a key role in the development of lymphedema, thereby providing in-depth insights into the dynamic changes of the disease, which is achieved through the following calculation formula:

[0168]

[0169] where u and v are nodes in the graph, f(u) and f(v) represent the feature vectors of nodes u and v respectively, β is the learned attention concentration parameter, and δ is the regularization constant.

[0170] Suppose node u and v represent two lymph nodes, and the feature vectors are f(u) = [1.2, 0.8] and f(v) = [1.1, 0.9] respectively. Set the value of β to 2.0, reflecting a stronger focus on the differences between node features in the analysis. Similarly, set the regularization constant δ to 0.5 to adjust the scale of the influence of feature differences.

[0171] Substitute into the formula for calculation. First, solve the square of the difference between the two node feature vectors:

[0172] ||f(u) - f(v)|| 2 = (1.2 - 1.1) 2+(0.8 - 0.9) 2 = 0.01 + 0.01 = 0.02

[0173] Then substitute it into the attention calculation formula:

[0174]

[0175] A(u, v) = exp(-0.08) ≈ 0.923

[0176] This calculation result shows that there is a relatively high attention weight between nodes u and v, indicating that the two lymph nodes interact importantly in the pathological network and play a key role in the pathological development of lymphedema.

[0177] Example 4:

[0178] In the development of a method for constructing a lymphedema pathological network based on graph neural networks, one of the core steps is to design and implement an adaptive layer structure for a multi-layer graph convolutional network (GCN). The dynamic convolution kernel adjustment function is used to adapt to the connectivity and feature diversity between nodes, ensuring that the size of the convolution kernel and the feature extraction method for each layer can be dynamically adjusted according to the local structure of the graph, thereby effectively capturing the biomarkers and pathological features between lymph nodes.

[0179] The key technologies involved in implementing this solution are:

[0180]

[0181] In this formula, G represents the overall structure of the graph, E represents the edge set, α vu represents the adaptive weight on the edge (v, u), x v and x u represent the feature vectors of nodes v and u respectively, and θ is the adjustment parameter used to adapt to the feature extraction requirements of each layer according to the topology of the graph and the feature diversity of nodes.

[0182] To specifically demonstrate the implementation process and feasibility of this solution, considering a specific example, a simplified lymphedema pathological network is set up, including three nodes and two edges. The feature vectors of the nodes are represented as:

[0183] x1 = [1.0, 2.0]

[0184] x2 = [1.5, 1.8]

[0185] x3 = [0.9, 2.1]

[0186] The set of edges and the corresponding adaptive weights (set between 0.1 and 1.0, and the specific values are determined according to the physiological importance of the edges) are:

[0187] E = {(1, 2), (2, 3)}

[0188] α 12 = 0.9, α 23 = 0.7

[0189] Set θ to 0.5 to emphasize the characteristic differences between connections, and apply the above function to calculate the adjusted network structure:

[0190] F(G, θ) = 0.9exp(-0.5||[1.0, 2.0] - [1.5, 1.8]|| 2 ) + 0.7exp(-0.5||[1.5, 1.8] - [0.9, 2.1]|| 2 )

[0191] = 0.9exp(-0.5((1.0 - 1.5) 2 + (2.0 - 1.8) 2 )) + 0.7exp(-0.5((1.5 - 0.9) 2 + (1.8 - 2.1) 2 ))

[0192] = 0.9exp(-0.5(0.25 + 0.04)) + 0.7exp(-0.5(0.36 + 0.09))

[0193] = 0.9exp(-0.5 × 0.29) + 0.7exp(-0.5 × 0.45)

[0194] = 0.9exp(-0.145) + 0.7exp(-0.225)

[0195] = 0.9 × 0.865 + 0.7 × 0.799

[0196] = 0.7785 + 0.5593

[0197] = 1.3378

[0198] The calculation results show that the graph convolutional network with dynamic adjustment can effectively capture and emphasize important biomarkers and pathological changes.

[0199] The embodiment further applies the multi-scale feature integration technology to enable the network to capture and fuse biomarkers and pathological features at different levels, so as to more comprehensively understand the complex interactions between lymph nodes and their changes in the pathological process. Use the following formula to integrate features and promote in-depth learning of information:

[0200]

[0201] H lrepresents the output feature matrix of the l-th layer, and W k is the weight matrix from the k-th layer to the l-th layer. σ is a non-linear activation function used to enhance the non-linear combination and extraction of features.

[0202] Suppose the graph neural network has three layers, and the purpose of each layer is to capture and integrate information from different data sources (such as MRI, CT, biochemical data). The initial representation of the feature vector is directly extracted from the original medical images and biochemical data:

[0203] H 0 The input layer contains primary features, and the specific values are H 0 = [0.2, 0.8, 0.5, 0.9].

[0204] Next, set the weight matrix W k , which is different for each layer to adapt to the learning requirements of a specific layer. Set the weight matrix W k to be randomly initialized and gradually adjusted and optimized through the training process. The initial weight settings are as follows:

[0205] W 0 is the identity matrix I;

[0206] W 1 and 1 are the weights learned during the training process. Set the initial values to be: W 1 = [0.5, 0.4, 0.6, 0.7], W 2 = [0.3, 0.7, 0.5, 0.2].

[0207] Use ReLU as the non-linear activation function σ (the ReLU function is a commonly used non-linear activation that effectively solves the vanishing gradient problem and provides the stability and fast convergence of the model). Apply the formula calculation to each layer to obtain:

[0208] H 1 = ReLU([1, 0.5, 0.6, 0.7] × [0.2, 0.8, 0.5, 0.9] + [0.5, 0.4, 0.6, 0.7] × [0.2, 0.8, 0.5, 0.9])

[0209] H 1 = ReLU(W 1 H 0 ) = ReLU([0.5×0.2 + 0.4×0.8 + 0.6×0.5 + 0.7×0.9])

[0210] H 1 = ReLU([0.1 + 0.32 + 0.3 + 0.63]) = ReLU([1.35]) = [1.35] (here it is assumed that the vector operation is accumulation)

[0211] Calculate H 2 :

[0212] H 2 = ReLU(W 0 H 1 + W 1 H 2 + W 2 H 0 )

[0213] H 2 = ReLU([1×1.35 + 0.5×1.35 + 0.3×0.2 + 0.7×0.8 + 0.5×0.5 + 0.2×0.9])

[0214] H 2 = ReLU([1.35 + 0.675 + 0.06 + 0.56 + 0.25 + 0.18])

[0215] H 2 = ReLU([3.075]) = [3.075]

[0216] This method allows the system to capture pathological change features from local to global at each layer through hierarchical and non - linear integration, thereby improving the accuracy of diagnosis and the depth of disease understanding.

[0217] Example 5:

[0218] The example implements an integrated multi - scale feature extraction strategy, aiming to capture biomarker features from micro - to macro - scale at different levels through a multi - layer graph convolutional network (M - GCN). This method not only enhances the model's feature capture ability but also enhances information flow and feature reuse through cross - layer connections, thus improving the accuracy of classification and clustering. The following function is used for operation:

[0219]

[0220] where v represents the current node, N k (v) is the set of neighbor nodes of node v at the k - th scale, ω k is the learning weight at the k - th scale, x u is the feature of the neighbor nodes, and σ is the activation function, designed to capture biomarker features from micro - to macro - scale at different levels.

[0221] Suppose we are processing a large graph containing hundreds of lymph nodes, and each lymph node is represented by features defined by a series of biomedical images and biochemical marker data. Each node represents a lymph node, and each lymph node node is connected to other lymph nodes that are anatomically adjacent to it.

[0222] Parameter and Data Setting:

[0223] Set that each lymph node v has a set of features x v =[x v1 ,x v2 ,…,x vm ;

[0224] At different scales k, the neighbor set N k (v) includes different numbers of neighbors, representing different spatial resolutions or functional groups;

[0225] Learn the weight ω k In the range from small to large, such as 0.1 to 1.0, and adjust dynamically according to the importance of each scale.

[0226] Implement the calculation process:

[0227] Scale 1: Focus on the most direct physical neighbors, the 5 lymph nodes closest to v;

[0228] Scale 2: Expand to functionally related neighbors, 10 lymph nodes sharing similar biochemical markers with v;

[0229] Scale 3: Further expand to 15 lymph nodes showing similar dynamic changes during the pathological process.

[0230] At each scale, use the following steps to calculate the new feature vector of each node:

[0231]

[0232] Where ω1, ω2, ω3 are the weights of different scales, and σ selects the ReLU function for non-linear transformation to enhance the expression ability of the model.

[0233] In this way, each node not only considers the influence of its most direct neighbors, but also integrates biomarker and pathological information in a wider network, thus providing more comprehensive biological and medical insights at different levels.

[0234] Then, the example introduces cross-layer connections to significantly enhance information flow and feature reuse, thereby improving the classification and clustering accuracy of the entire network model. The implementation of this strategy relies on the following formula to be concretized:

[0235]

[0236] F l is the output feature of the l-th layer, H i is the output feature of the i-th layer, and γ li is the cross-layer connection weight from the i-th layer to the l-th layer.

[0237] It is assumed that there are four layers in the constructed multi-layer graph convolutional network, i.e., l = 0, 1, 2, 3, and each layer generates a set of output features H 0 , H 1 , H 2 , H 3 . To implement cross-layer connections, first define the weights γ li . These weights determine the connection strength from the early layers to the later layers, thus reusing the information of the early layers in the subsequent layers. For practical application, the weights γ li can depend on the relative distance between the layers or the parameters learned during the network training process, and the weight range is set from 0.1 to 1.0.

[0238] Weight setting: Set γ li as follows to simplify the weight calculation. Take decreasing weight values, indicating that the earlier layers contribute less to the later layers:

[0239] γ 10 = 0.9, γ 20 = 0.8, γ 21 = 0.7, γ 30 = 0.6, γ 31 = 0.5, γ 32 = 0.4

[0240] Layer output features: Set the output feature matrix of each layer as follows:

[0241] H 0 = [1.0, 2.0]

[0242] H 1 = [1.5, 2.5]

[0243] H 2 = [2.0, 3.0]

[0244] H 3 = [2.5, 3.5]

[0245] For F 1 :

[0246] F 1 = γ 10 · H 0 = 0.9 × [1.0, 2.0] = [0.9, 1.8]

[0247] For F 2 :

[0248] F 2 = γ 20 · H 0 + γ 21 · H 1= 0.8 × [1.0, 2.0] + 0.7 × [1.5, 2.5] = [0.8 + 1.05, 1.6 + 1.75]

[0249] = [1.85, 3.35]

[0250] For F 3 :

[0251] F 3 = γ 30 ·H 0 + γ 31 ·H 1 + γ 32 ·H 2 = 0.6 × [1.0, 2.0] + 0.5 × [1.5, 2.5] + 0.4 × [2.0, 3.0]

[0252] = [0.6 + 0.75 + 0.8, 1.2 + 1.25 + 1.2] = [2.15, 3.65]

[0253] Through such calculations, it can be seen that each layer effectively integrates the information from the previous layer, enabling features to be not only captured within the current layer but also enhanced by cross-layer connections.

[0254] Example 6:

[0255] The example applies a deep learning-based non-linear dimensionality reduction method for graph embedding, converting complex high-dimensional graph data into a lower-dimensional space while maintaining the topological structure of the original graph and the relationships between nodes, thereby facilitating more accurate classification or clustering analysis. The non-linear dimensionality reduction method is implemented through a deep learning-driven graph embedding model (DLGE), where an autoencoder is used to learn the non-linear embedding of the graph. The specific loss function is defined as follows:

[0256]

[0257] Here, V and E represent the node set and edge set in the graph respectively, f(v) represents the low-dimensional embedding of node v, and λ is a regularization coefficient used to adjust the penalty for non-adjacent node pairs, thereby maintaining the basic structure of the graph during the dimensionality reduction process.

[0258] Suppose the lymphedema network consists of multiple nodes, each node representing a different lymph node, and the connections between nodes reflect the anatomical or functional connections between lymph nodes. Consider a specific small network:

[0259] Nodes and edges: Suppose there are four nodes, and there are edges between each pair of nodes, indicating biological function or anatomical proximity.

[0260] Regularization coefficient λ: Set λ = 0.01 to ensure that the penalty for non - adjacent node pairs is within a reasonable range.

[0261] The eigenvector of a node is represented in a high - dimensional space:

[0262] f(v1) = [1.0, 2.0], f(v2) = [1.1, 1.9], f(v3) = [0.9, 2.1], f(v4) = [1.0, 2.0]

[0263] For each pair of adjacent nodes (i, j), calculate ||f(v i ) - f(v j )|| 2 . For v1 and v2:

[0264] ||f(v1) - f(v2)|| 2 = ||[1.0, 2.0] - [1.1, 1.9]|| 2 = (1.0 - 1.1) 2 + (2.0 - 1.9) 2 = 0.01 + 0.01

[0265] = 0.02

[0266] Calculate the loss for non - adjacent node pairs. For non - adjacent nodes v1 and v3:

[0267]

[0268] By integrating the losses of all node pairs, the final loss value of the entire network can be obtained, and the value of f(v) can be adjusted accordingly to minimize the loss, thereby learning the optimal low - dimensional embedding of each node.

[0269] The embodiment further introduces a graph structure - preserving loss function (GSPL) to ensure that the topological structure of the original graph and the relationships between nodes are maintained during the non - linear dimensionality reduction of graph embedding. The formula is as follows:

[0270]

[0271] Among them, ω ij is the importance weight of the node pair (i, j) learned based on the graph attention layer, x i and x j are the original feature vectors, and g(i) and g(j) are the corresponding low - dimensional representations.

[0272] Suppose we are processing a graph related to lymphedema research, where each node represents a lymph node and has a specific biomarker feature vector. Select several nodes and connections to specifically show how to implement GSPL.

[0273] Node feature vector (x) and low-dimensional representation (g):

[0274] x1 = [1.0, 2.0], x2 = [1.1, 2.1], x3 = [0.9, 1.9]

[0275] Assume that the low-dimensional representation has been calculated through the graph embedding process, and we get g1 = [0.5, 1.0], g2 = [0.6, 1.1], g3 = [0.4, 0.9]

[0276] Weight setting (ω): Assume that all weights are 1.

[0277] Calculate the difference between the original distance and the low-dimensional representation distance between all node pairs in the graph, and then apply the weights:

[0278] For node pair (1, 2):

[0279] Original distance:

[0280] Low-dimensional distance:

[0281] GSPL contribution:

[0282] Similarly, calculate other node pairs 1, 3 and 2, 3, and accumulate these values to obtain the total GSPL value.

[0283] All low-dimensional representations correctly maintain the distance between the original feature vectors, and the total GSPL will be very low, indicating that the embedding effect is good and the structural integrity of the graph is maintained.

[0284] Example 7:

[0285] The example implements a Dynamic Graph Convolutional Network (DGCN) to be able to adaptively process node characteristics that change over time. The network uses dynamic graph convolutional layers to continuously update node representations, so as to effectively detect abnormal changes in the lymphedema pathological network. The update function is defined as:

[0286]

[0287] where: t represents the time step; v is the current node; is the set of neighbors of node v; W t and b t are the weight matrix and bias vector at time step t respectively; h t-1 (u) is the embedding representation of node u at time t - 1; σ is the standard deviation of the Gaussian kernel, which is used to simulate the interaction strength between nodes.

[0288] The setting is processing a dynamic network containing lymph nodes, where each node is connected to other nodes, and the represented interactions affect the development of the pathological state.

[0289] Parameter setting:

[0290] It is set that there are three main lymph node nodes in the network, and each node is connected to the other two;

[0291] It is set that σ = 1.0, which is used to balance the influence of distance;

[0292] The weight W of the time step t t and the bias b t are initialized and learned to be adjusted during the training process.

[0293] Let the initial feature vector of each node be as follows, as well as the embedding representation at time t - 1:

[0294] x1 = [1.0, 2.0], h t-1 (1) = [0.5, 1.0]

[0295] x2 = [1.1, 2.1], h t-1 (2) = [0.6, 1.1]

[0296] x3 = [0.9, 1.9], h t-1 (3) = [0.4, 0.9]

[0297] At time step t, the updated embedding representation is calculated for each node:

[0298] For node v1, calculate:

[0299]

[0300] Set ||x2 - x1|| 2 = 0.02 and ||x3 - x1|| 2 = 0.02.

[0301] This calculation method not only reflects the dynamic relationship between nodes, but also can update its features through time steps to capture its changes in the pathological process, thus playing a key role in the early detection and analysis of the development of lymphedema.

[0302] The embodiment further applies a graph-based anomaly detection algorithm (GAD) to identify those nodes that significantly deviate from the common pattern or the expected biomarker behavior, and such a deviation indicates specific pathological changes or early signs of the disease. The calculation formula for anomaly detection is as follows:

[0303]

[0304] Wherein:

[0305] f(v) and f(u) are the embedding vectors of node v and its neighbor u respectively;

[0306] is the neighbor set of node v;

[0307] p is a positive real number used to adjust the sensitivity and discrimination of anomaly detection. The actually selected value of p can be chosen within the range from 1 to 3 to be adjusted according to the characteristics of the actual data and the required sensitivity.

[0308] A simplified lymph node network is set up, which contains four nodes. Each node represents a different lymph node, and each node has its specific embedding representation. These embedding vectors are obtained through the deep graph embedding method in the previous step.

[0309] Set the embedding vectors as follows:

[0310] f(v1) = [1.2, 0.8]

[0311] f(v2) = [1.1, 0.9]

[0312] f(v3) = [1.3, 0.7]

[0313] f(v4) = [0.9, 1.0]

[0314] Set p = 2 to improve the sensitivity of anomaly detection.

[0315] Taking node v1 as an example, set the neighbor nodes to include v2 and v3:

[0316] Calculate the embedding difference between v1 and its neighbors:

[0317] ||f(v1) - f(v2)|| 2 = (1.2 - 1.1) 2 + (0.8 - 0.9) 2 = 0.01 + 0.01 = 0.02

[0318] ||f(v1) - f(v3)|| 2 = (1.2 - 1.3) 2 + (0.8 - 0.7) 2 = 0.01 + 0.01 = 0.02

[0319] Apply the anomaly detection formula:

[0320]

[0321] In this way, if the value of d(v1) is significantly higher than that of other nodes, it indicates that v1 exhibits abnormal embedding changes, indicating pathological changes related to this node.

[0322] Finally, the example combines time series analysis and a prediction model for processing and predicting the pathological progression of lymphedema. The time series graph data is processed by a long short-term memory network (LSTM), effectively capturing and utilizing dynamic biomarkers and pathological states that change over time, thus providing an accurate analysis tool for the disease management and prognosis of lymphedema. The formula is as follows:

[0323] h t = LSTM(h t-1 , α·h t-1 +(1 - α)·x t )

[0324] Where:

[0325] h t is the hidden state at time t;

[0326] x t is the input feature at time t;

[0327] α is the learning rate between 0 and 1, used to balance the influence of historical information and the current input.

[0328] A time series data set related to the pathological state of lymph nodes is set, and each time point contains biomarker data from different lymph nodes.

[0329] Parameter setting:

[0330] It is set that each time point t in the data set includes the corresponding lymph node feature vector x t , for example:

[0331] x1 = [0.8, 1.2]

[0332] x2 = [0.85, 1.25]

[0333] x3 = [0.9, 1.3]

[0334] α is set to 0.5, which means the model will equally consider the influence of history and the current input.

[0335] The initial hidden state h0 is initialized to a small random value based on previous data.

[0336] For each time point t, the hidden state is updated using the LSTM formula:

[0337] h1 = LSTM(h0, 0.5·h0 + 0.5·x1)

[0338] h2 = LSTM(h1, 0.5·h1 + 0.5·x2)

[0339] h3 = LSTM(h2, 0.5·h2 + 0.5·x3)

[0340] In this process, the LSTM adjusts its response to the historical state and new input through its internal structure (forget gate, input gate, output gate), thereby finely regulating the information flow.

[0341] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a lymphedema pathology network based on a graph neural network, characterized in that It includes the following steps: Firstly, collect the medical imaging data, clinical records, and biomarker data of the patient's lymphatic system, and use image processing techniques to extract key features and structure them into the nodes and edges of a graph, where the nodes represent lymph nodes and the edges represent the paths or interactions of lymph flow; Next, based on the anatomical structure and physiological function of the lymphatic system, define the topological structure of the graph, and introduce multimodal data fusion technology to combine the imaging data and biomarker data to enhance the information accuracy of the graph network; Then, design a multi-layer graph convolutional network model for learning the patterns of lymph nodes and their connections, and introduce an attention mechanism to identify and emphasize the nodes and edges that play a role in the development of lymphedema; Then, use the graph convolutional network for deep learning to extract the hidden features of the nodes and edges, and apply graph embedding technology to transform the high-dimensional graph data into a low-dimensional space for classification or clustering analysis; Finally, develop a graph-based anomaly detection algorithm for identifying pathological changes that are significantly different from common patterns, and combine time series analysis to predict the pathological progression of lymphedema; The extraction of key features using image processing techniques includes the following steps: S1. First, adopt a unified data processing framework: where G and H represent the processing functions of different data sources including CT, MRI imaging data, blood biochemical indicators, and patient symptom records, for synchronously processing and integrating various types of data; S2. Then, apply image processing algorithms through the function: where v n is the value of each pixel in the image, is the average pixel value, which is used to identify and quantify the size, shape, and distribution characteristics of lymph nodes; S3. Next, through the graph construction algorithm: where E is the set of edges, and α ij is the weight of the edge, k i and k j are the eigenvalues of the nodes connecting the edges, which are used to transform the extracted features into nodes and edges in the graph. The nodes represent lymph nodes, and the edges represent the physiological relationships or signal transmission paths between the nodes; The definition of the topological structure of the graph includes the following steps: S1. First, adopt a graph topology generation algorithm: where N represents nodes, L represents edges, and L i is a connection specified based on anatomical structure, and A i is the corresponding physiological functional connection, d is the distance between nodes, and σ is a normalization parameter used to construct the nodes and edges of the graph according to the anatomical location and physiological function of lymph nodes; S2. Then, apply a multimodal deep fusion network through the function: where x, y, z respectively represent input data of different modalities, and w k and v j are weights learned from the data, used to integrate different source information including MRI, CT scans, and blood biochemical indicators, and enhance the accuracy of the final graph structure data; The construction process of the multi-layer graph convolutional network model: First, introduce and implement the adaptive layer structure of the multi-layer graph convolutional network GCN, through the calculation formula: Among them, G represents the overall structure of the graph, E represents the edge set in the graph, x i and x i-1 respectively represent the feature vectors of consecutive nodes, α i is the inter-layer adaptability factor, and ∈ is the smoothing constant, which is used to adjust the structure of the network layer to adapt to the anatomical features and pathological changes of lymph nodes; Secondly, introduce a graph-based attention mechanism, and the calculation formula is: where u and v are the nodes in the graph, f(u) and f(v) represent the feature vectors of nodes u and v, β is the learned attention concentration parameter, and δ is the regularization constant, used to emphasize the nodes and edges that are critically related to the development of lymphedema; The method for extracting the hidden features of the nodes and edges adopts the steps: S1. First, design and implement the adaptive layer structure of the multi-layer graph convolutional network GCN, and adapt to the connectivity and feature diversity of the nodes through graph convolution operations that adjust the convolution kernel parameters. The convolution kernel size and feature extraction method of each layer are dynamically adjusted according to the local structure of the graph to capture the biomarkers and pathological features between lymph nodes; S2. Further integrate the multi-scale feature extraction strategy to capture the biomarker features from micro to macro at different levels, and introduce cross-layer connections to enhance the information flow and feature reuse to improve the accuracy of classification and clustering; S3. Finally, apply a deep learning-based non-linear dimensionality reduction method for graph embedding, designed for graph data, to construct a mapping from high-dimensional to low-dimensional while maintaining the topological structure of the graph and the relationships between nodes, facilitating subsequent classification or clustering analysis; The composition of the graph-based anomaly detection algorithm: S1. First, implement the dynamic graph convolutional network DGCN, adopt the dynamic graph convolutional layer, through the function: to update the node representation, where t represents the time step, v is the current node, is the set of neighbors of node v, W t and b t are the weight matrix and bias vector at time step t, h t-1 (u) is the embedding representation of node u at time t - 1, and σ is the standard deviation of the Gaussian kernel, which is used to simulate the interaction strength between nodes; S2. Then apply the graph-based anomaly detection algorithm GAD by calculating: to identify anomalies, where f(v) and f(u) are the embedding vectors of node v and its neighbor u respectively, and p is a selected positive real number used to increase the sensitivity and discrimination of anomaly detection; S3. Finally, combine the time series analysis and prediction model, and process the time series graph data through the long short-term memory network LSTM. The specific implementation formula is: h t = LSTM(h t-1 , α·h t-1 + (1 - α)·x t ) where h t is the hidden state at time t, x t is the input feature, and α is a learning rate between 0 and 1 that balances the influence of historical information and the current input to predict the pathological progression of lymphedema.

2. The method for constructing a lymphedema pathology network based on a graph neural network according to claim 1, wherein The adaptive layer structure adjusts the function of the dynamic convolution kernel: is implemented, where G represents the overall structure of the graph, E represents the edge set, α vu represents the adaptive weight on the edge (v, u), x v and x u respectively represent the feature vectors of nodes v and u, and θ is a parameter adjusted based on the graph topology and node feature diversity to adapt to the feature extraction requirements of each layer, including aspects of lymph nodes and their interacting biomarkers; Effectively capture lymph edema-specific biomarkers and pathological features through multi-scale feature integration technology, using the formula: where H l represents the output feature matrix of the l-th layer, and W k represents the weight matrix from the k-th layer to the l-th layer. σ is a non-linear activation function, which is used to integrate information at multiple levels of the graph and extract biomarkers.

3. The method for constructing a lymphedema pathological network based on a graph neural network according to claim 1, wherein The integrated multi-scale feature extraction strategy includes the following steps: S1. First, implement the multi-scale graph convolutional network M-GCN through the function: where \(v\) represents the current node, \(N\) k (v) is the set of neighbor nodes of node \(v\) at the \(k\)-th scale, \(\omega\) k is the learning weight at the \(k\)-th scale, \(x\) u is the feature of the neighbor nodes, and \(\sigma\) is the activation function, designed to capture biomarker features from micro to macro at different levels; S2. Then introduce cross-layer connections to enhance information flow and feature reuse, specifically through the formula: Implementation, where F l is the output feature of the l-th layer, H i is the output feature of the i-th layer, γ li is the cross-layer connection weight from the i-th layer to the l-th layer, which is used to improve the accuracy of classification and clustering.

4. The method for constructing a lymphedema pathology network based on a graph neural network according to claim 1, wherein The construction of the graph embedding framework using the non-linear dimensionality reduction method includes: S1. First, implement the deep learning-driven graph embedding model DLGE, and learn the non-linear embedding of the graph through the autoencoder. Specifically, by minimizing the function: where V and E represent the node set and edge set in the graph respectively, f(v) represents the low-dimensional embedding of node v, and λ is the regularization coefficient used to adjust the penalty intensity of non-adjacent node pairs to maintain the topological structure of the graph and the relationship between nodes during the high-dimensional to low-dimensional mapping process; S2. Then introduce the graph structure-preserving loss function GSPL by calculating: where ω ij is the importance weight of the node pair (i, j) learned based on the graph attention layer, x i and x j are the original feature vectors, and g(i) and g(j) are the corresponding low-dimensional representations.

Images