A manifold learning based graph attribute prediction system and method

Abstract

This invention discloses a graph attribute prediction system based on manifold learning, relating to the fields of graph neural networks and machine learning technology. It includes: a feature smoothing module, a graph structure feature extraction module, a manifold similarity calculation module, a deep graph representation learning module, a manifold structure preservation loss calculation module, a graph attribute prediction module, and a joint optimization module. The invention also discloses a graph attribute prediction method based on manifold learning, comprising the following steps: S100, system initialization; S200, data input; S300, generating a node embedding matrix; S400, calculating a node similarity matrix; S500, latent space structure feature extraction; S600, manifold learning loss calculation; S700, graph attribute training and prediction; S800, joint optimization; and S900, graph attribute inference and prediction. This invention effectively maintains the topological authenticity of the latent space and significantly improves performance in downstream tasks such as node classification and link prediction.

Description

Technical Field

[0001] This invention relates to the field of graph neural networks and machine learning technology, and in particular to a graph attribute prediction system and method based on manifold learning. Background Technology

[0002] Attribute graphs are prevalent in various fields such as social networks, reference networks, and bioinformatics. Graph embedding technology aims to map nodes in a graph to a low-dimensional vector space while preserving their structural and attribute information, in order to serve downstream tasks such as node classification, link prediction, and graph clustering.

[0003] Existing deep learning-based graph embedding methods, such as graph autoencoders (GAEs) and their variants (VGAEs), typically learn node representations by minimizing the reconstruction loss of the adjacency matrix. However, these methods often focus solely on the reconstruction loss, neglecting the inherent geometric structure (i.e., manifold structure) of the data in high-dimensional space and the topological consistency of the underlying encoding. This results in the learned embedding matrix failing to adequately capture the global and local structural features of the graph, particularly when dealing with complex and noisy real-world graph data, leading to poor generalization ability and robustness, thus impacting the performance of downstream prediction tasks. For example, this problem is more pronounced in specific fields such as protein structure prediction. The inherent biological principles of protein molecules (such as the physicochemical properties of amino acids and spatial constraints) are difficult to capture effectively by traditional deep learning models, resulting in representations lacking biological rationality and performing poorly in tasks with limited samples.

[0004] Manifold learning, as a robust theoretical framework, assumes that high-dimensional observation data actually resides on a low-dimensional manifold, and its goal is to discover and preserve this low-dimensional structure. Although some studies have attempted to combine manifold learning with graph neural networks, the methods used in existing techniques generally fail to systematically establish multi-level (local and global) topology preservation mechanisms between the input space and the latent space, and also lack a similarity metric that can effectively handle complex neighborhood relationships in graph data.

[0005] Therefore, those skilled in the art are dedicated to developing a graph attribute prediction system and method based on manifold learning. Summary of the Invention

[0006] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that existing graph neural networks have problems such as low representation quality, insufficient generalization ability, difficulty in incorporating domain knowledge, and distortion of potential spatial topology in attribute prediction tasks.

[0007] Existing deep learning-based graph embedding methods (such as GAE and VGAE) primarily rely on minimizing the reconstruction loss of the adjacency matrix. Their learning objectives are too singular and fail to adequately consider the inherent geometric structure of high-dimensional graph data within a low-dimensional manifold. This results in the learned node embeddings failing to maintain the topological relationships between nodes in the original data space, affecting the quality and discriminative power of the embedding matrix. This application introduces a manifold learning loss function to explicitly constrain the geometric consistency between the latent space and the input space, ensuring that the learned embedding matrix faithfully reflects the manifold characteristics of the original data.

[0008] Existing technologies typically focus only on local neighborhood relationships, lacking a unified framework to simultaneously capture the detailed local structure and global topological features of a graph. This application constructs a dual perspective—a prior graph (capturing local structure) and a fully connected graph (capturing global relationships)—and simultaneously constrains the preservation of these two structural information in the latent space within the manifold learning loss. This ensures that the learned embedding matrix reflects both the micro-connection patterns between nodes and the overall macro-layout of the graph.

[0009] In graph data, the similarity relationships between nodes often exhibit complex nonlinear characteristics, which traditional Euclidean distance or cosine similarity methods struggle to accurately capture. This application proposes a long-tail-based approach... t The kernel function of the distribution is used for similarity transformation. Its heavy-tailed characteristic can better adapt to the non-uniform distribution and outlier conditions commonly found in graph data, and through the long tail... t Adjustable degrees of freedom parameters in the distribution kernel function ν This method effectively controls the degree of separation between manifolds and provides a more flexible and accurate method for measuring the similarity of graph nodes.

[0010] Existing techniques often suffer from topological distortions in the latent space when learning low-dimensional embedding matrices, such as excessive clustering or unnatural bending and folding. This application effectively avoids these topological distortion problems by maintaining the similarity between the input space and the latent space across multiple scales, enabling the dimensionality-reduced embedding space to better preserve the essential structural features of the original data.

[0011] In one embodiment of the present invention, a graph attribute prediction system based on manifold learning is provided, comprising: The feature smoothing module smooths the original attribute map. G= ( V, E, X Feature smoothing is performed, where V For a set of nodes, E Let be the set of edges. X For the node feature matrix, the node feature matrix X A smooth node feature matrix is ​​obtained by performing a nonlinear transformation using a multilayer perceptron (MLP). X' This enhances the ability to express features; The graph structure feature extraction module is based on the node feature matrix. X Construct prior graphs respectively and fully connected graph Calculate the geodesic distance matrix of the map; The manifold similarity calculation module uses a kernel function to transform the graph geodesic distance matrix according to the distance calculation rules between nodes, thereby obtaining the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space ; The depth graph representation learning module uses an encoder to process the smoothed node feature matrix. X' , converted K Embedding matrices , , ..., , ..., ; The manifold structure preservation loss calculation module, for the embedding matrix ( ), based on edge set in the latent space E Construct a graph structure and compute the similarity matrix of nodes in the latent space. The similarity matrix between the nodes of the prior graph in the input space and the logistic loss function is measured. Similarity matrix of nodes in the fully connected graph of the input space The differences between them are used to construct a manifold learning loss function. L 2; The graph attribute prediction module includes a linear transformation layer and a softmax activation function, which converts the embedding matrix... Convert to graph nodes C The probability of each category, C The categories depend on the dataset used. C Hyperparameters set according to the task; The joint optimization module incorporates the manifold learning loss function. L 2. Task loss function for graph attribute prediction models By weighting and combining the results, the total loss function is obtained. L By jointly optimizing system parameters through gradient descent algorithm, the graph attribute prediction model can maintain the fundamental structure of the data while completing specific tasks. The graph structure feature extraction module, manifold similarity calculation module, manifold structure preservation loss calculation module, and joint optimization module are sequentially connected in communication. The feature smoothing module, deep graph representation learning module, graph attribute prediction module, and joint optimization module are sequentially connected in communication. The deep graph representation learning module and manifold structure preservation loss calculation module are connected in communication.

[0012] Optionally, in the graph attribute prediction system based on manifold learning in the above embodiments, the multilayer perceptron (MLP) in the feature smoothing module is selected to have two layers with feature dimensions of 512 and 1024, respectively.

[0013] Optionally, in the graph attribute prediction system based on manifold learning in any of the above embodiments, the distance calculation rule between nodes is as follows: if the nodes are connected, the cosine distance is used to calculate the distance between the nodes; if the nodes are connected but not connected, the maximum distance between the graph nodes is taken as the distance between the nodes.

[0014] Optionally, in the manifold learning-based graph attribute prediction system of any of the above embodiments, the kernel function is based on a long tail. t distributed.

[0015] Optionally, in a graph attribute prediction system based on manifold learning in any of the above embodiments, the encoder is a variational graph autoencoder (VGAE).

[0016] Furthermore, in a graph attribute prediction system based on manifold learning in the above embodiments, the variational graph autoencoder (VGAE) learns the distribution parameters of the embedding matrix in the latent space, constructs the distribution of the embedding matrix, and then... K Second sampling, obtained K Embedding matrices , , ..., .

[0017] Furthermore, in a graph attribute prediction system based on manifold learning in the above embodiments, when the autoencoder adopts a variational graph autoencoder (VGAE), it is assumed that the latent embedding follows a standard normal distribution. The variational graph autoencoder outputs the distribution parameters (mean and variance) of the embedding matrix to construct the distribution of the embedding matrix.

[0018] Furthermore, in a graph attribute prediction system based on manifold learning in the above embodiments, the distribution parameters include mean and variance.

[0019] Optionally, in the graph attribute prediction system based on manifold learning in any of the above embodiments, the number of sampling times... K The range is [1, 10].

[0020] Preferably, in the manifold learning-based graph attribute prediction system of the above embodiments, the number of sampling times... K =5. Optionally, in the graph attribute prediction system based on manifold learning in any of the above embodiments, the logistic loss function adopts the binary cross-entropy loss function (BCE Loss).

[0021] Optionally, in the manifold learning-based graph attribute prediction system of any of the above embodiments, the system parameters include the prediction loss weight hyperparameter of the graph attribute prediction module. β Global relation weights in manifold loss α A fully connected graph is used to represent global relationships.

[0022] Optionally, in the graph attribute prediction system based on manifold learning in any of the above embodiments, the manifold learning loss... L Formula 2 is as follows: .

[0023] Optionally, in any of the above embodiments of the graph attribute prediction system based on manifold learning, when the dataset used is the Cora dataset, C = 7, C The categories are {case-based reasoning, genetic algorithms, neural networks, probabilistic methods, reinforcement learning, rule learning, and theory}.

[0024] Optionally, in the graph attribute prediction system based on manifold learning in any of the above embodiments, the total loss function L The formula is as follows: ; in L 1 represents the prediction loss of the graph attribute prediction module.

[0025] Based on any of the above embodiments, in another embodiment of the present invention, a graph attribute prediction method based on manifold learning is provided, comprising the following steps: S100, System initialization, graph attribute prediction system initialization, set the graph attribute prediction system state to training state, set the maximum number of training rounds, and set the training rounds to 0; S200, Data Input: Receive the original attribute map. G= ( V, E, X ),in V For a set of nodes, E Let be the set of edges. X The node feature matrix is ​​processed by the feature smoothing module. X A nonlinear transformation is performed to obtain a smooth node feature matrix. X' ; S300, Generate a node embedding matrix, smoothing the node feature matrix. X 'Input the depth map representation learning module, construct the distribution of the embedding matrix, and randomly sample from the distribution of the embedding matrix.' K This yields multiple embedding matrices. ; S400. Calculate the node similarity matrix. If the graph attribute prediction system state is the predicted state, proceed to step S900; otherwise, if the training rounds are equal to 0, construct the prior graphs respectively. and fully connected graph The geodesic distance matrix of the computational graph is converted into the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space Calculate the distance between nodes; when the training round is greater than 0, execute step S500; S500, latent spatial structure feature extraction, for embedding matrix Based on the set of edges in the latent space E Construct a graph structure and calculate the similarity matrix of nodes in the latent space. ; S600. Manifold learning loss calculation: Calculate the similarity matrix of the latent spatial nodes. Similarity matrix of nodes with the prior graph in the input space The input space fully connected graph node similarity matrix The difference between them yields the manifold learning loss. L 2. The formula is as follows: ; in Logical loss function K For the number of samples, The global relation weight in the manifold loss is set to 1. This is the similarity matrix of potential spatial nodes. Given the node similarity matrix of the prior graph in the input space and The input space is the node similarity matrix of the fully connected graph. S700, graph attribute training and prediction, embedding matrix Convert to graph nodes C The probability of each category; S800, joint optimization, manifold learning loss function L 2. Prediction Loss Function L 1. Combining by weights yields the total loss function. L The formula is as follows: ; in, L 1 represents the prediction loss function of the graph attribute prediction module, and β represents the weight hyperparameter of the prediction loss function of the graph attribute prediction module. The learnable parameters are updated through the backpropagation algorithm. When the number of training rounds is less than the maximum number of training rounds, the number of training rounds is incremented by one, and the process returns to step S200. Otherwise, the graph attribute prediction system state is set to the prediction state, and the process returns to step S200. S900, graph attribute reasoning prediction, will embed matrix Transform into graph nodes C The probability of each category is used to complete the graph attribute prediction.

[0026] Preferably, in the graph attribute prediction method based on manifold learning in the above embodiments, the maximum number of training rounds is 200.

[0027] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the encoder employs a variational graph autoencoder (VGAE) to learn the distribution parameters of the embedding matrix in the latent space, construct the distribution of the embedding matrix, and then... K Second sampling, obtained K Embedding matrices , , ..., .

[0028] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the number of sampling times... K The range is 1-10.

[0029] Preferably, in the graph attribute prediction method based on manifold learning in the above embodiments, the number of sampling times... K=5 .

[0030] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, when the dataset used is the Cora dataset, C = 7, C The categories are {case-based reasoning, genetic algorithms, neural networks, probabilistic methods, reinforcement learning, rule learning, and theory}.

[0031] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, step S400 includes: S410. Determine the state of the graph attribute prediction system. If the state of the graph attribute prediction system is the prediction state, execute step S900; otherwise, execute step S420. S420. Determine the node similarity matrix. When the input spatial prior graph node similarity matrix is... Similarity matrix of nodes in the fully connected graph of the input space If the value is not empty, proceed to step S500; otherwise, proceed to step S430. S430. Construct a prior graph. ,if E If not obtained, then use k Construction of nearest neighbor graph E ; S440. Construct a fully connected graph based on the prior graph. Construct a fully connected graph ; S450, Calculate the geodesic distance matrix based on the prior map. and fully connected graph The rule for calculating the distance between nodes in the graph is as follows: if the nodes are connected, the cosine distance is used to calculate the distance between the nodes; if the nodes are connected but not connected, the maximum distance between the nodes is taken as the distance between the nodes. S460. Calculate the node similarity matrix. Using a kernel function, convert the graph geodesic distance matrix into the node similarity matrix of the prior graph in the input space, based on the distance matrix calculation rules between nodes. Similarity matrix of nodes in the fully connected graph of the input space .

[0032] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the distance calculation rule between nodes is: if nodes are connected, then cosine distance is used to calculate the distance between nodes. and Distance between If nodes are not connected, then the maximum distance between nodes in the graph is taken as the distance between nodes. The formula is as follows: ; in, Indicates node-based and Cosine distance between them , , n Indicates the number of nodes. It is a positive integer, with a value of 1.

[0033] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the kernel function is based on a long tail. t distributed.

[0034] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the logistic loss function adopts the binary cross-entropy loss function (BCE Loss).

[0035] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, step S800 includes: S810. Calculate the total loss function, including the manifold learning loss. L 2. Prediction loss of the graph attribute prediction module L 1. By weight βCombining these, we obtain the total loss function. L The formula is as follows: ; in, L 1 represents the prediction loss function of the graph attribute prediction module. β The weight hyperparameters of the prediction loss function for the graph attribute prediction module; S820. Update system parameters by updating the parameters of the feature smoothing module, the deep graph representation learning module, and the graph attribute prediction module through the backpropagation algorithm. S830. Iterative training: When the number of training rounds is less than the maximum number of training rounds, increment the number of training rounds by one and return to step S200; otherwise, set the graph attribute prediction system state to the prediction state and return to step S200.

[0036] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the learnable parameters include the weight matrix and bias vector of each layer of the MLP in the feature smoothing module, the weight matrix and bias vector of the variational graph autoencoder (VGAE) in the depth graph representation learning module, and the weight matrix and bias vector of the linear transformation layer in the graph attribute prediction module.

[0037] Optionally, in any of the above embodiments, the graph attribute prediction method based on manifold learning further includes embedding quality assessment, the steps of which are as follows: S1000, embedding quality assessment, obtaining the manifold learning loss for each round. L 2. As a structural evaluation metric for embedding quality, it measures the similarity matrix of nodes in the latent space. Similarity matrix of nodes with the prior graph in the input space Input space fully connected graph node similarity matrix The differences between them L The closer 2 is to 0, the smaller the difference and the better the embedding quality. S2000 embeds quality visualization feedback, feeding the embedding quality feedback to a dimensionality reduction visualization tool to generate a visual view of the embedding.

[0038] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, the dimensionality reduction visualization tool uses UMAP (Uniform Manifold Approximation and Projection).

[0039] This invention constructs a dual-view system of prior graph and fully connected graph, explicitly forces the latent space using manifold learning loss, and introduces a long-tail-based approach. tThe distributed kernel function handles non-uniform distributions and outliers in the data. By accurately matching the similarity relationship between the original attribute graph space and the latent space at multiple scales, it effectively maintains the topological authenticity of the latent space and avoids unreasonable structural distortions. This invention explicitly preserves the intrinsic geometric structure of graph data at multiple scales by deeply coupling manifold learning theory with graph autoencoders, thereby learning more discriminative, robust, and interpretable node embeddings, significantly improving performance in downstream tasks such as node classification and link prediction.

[0040] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the structure of a graph attribute prediction system based on manifold learning, as an exemplary embodiment. Figure 2 This is a flowchart of a graph attribute prediction method based on manifold learning, which is an exemplary embodiment. Figure 3 This is the original input feature matrix of the Cora dataset in an exemplary embodiment. X UMAP visualization results; Figure 4 This is a UMAP visualization of the embedding matrix of an exemplary embodiment. Detailed Implementation

[0042] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0043] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of components is schematically exaggerated in some places in the drawings.

[0044] This application designs a graph attribute prediction system based on manifold learning, such as... Figure 1 As shown, it includes: The feature smoothing module smooths the original attribute map. G= ( V, E, X Feature smoothing is performed, where V For a set of nodes, E Let be the set of edges. X For the node feature matrix, the node feature matrix XA smooth node feature matrix is ​​obtained by performing a nonlinear transformation using a multilayer perceptron (MLP). X' To enhance the expressive power of features, the Multilayer Perceptron (MLP) is configured with two layers, with feature dimensions of 512 and 1024 respectively. The graph structure feature extraction module is based on the node feature matrix. X Construct prior graphs respectively and fully connected graph Calculate the geodesic distance matrix of the map; The manifold similarity calculation module utilizes a long-tail-based approach. t The kernel function of the distribution is used to transform the graph geodesic distance matrix according to the distance calculation rules between nodes, thus obtaining the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space The rules for calculating the distance between nodes are as follows: if nodes are connected, the cosine distance is used to calculate the distance between nodes; if nodes are connected but not connected, the maximum distance between nodes in the graph is taken as the distance between nodes. The deep graph representation learning module employs a variational graphical autoencoder (VGAE) to learn the distribution parameters of the embedding matrix in the latent space. Assuming the latent embeddings follow a standard normal distribution, the VGAE outputs the distribution parameters of the embedding matrix, including the mean and variance, thus constructing the distribution of the embedding matrix. K Second sampling, obtained K Embedding matrices , , ..., , K =5; The manifold structure preservation loss calculation module calculates the loss for each embedding matrix. ( ), based on edge set in the latent space E Construct a graph structure and compute the similarity matrix of nodes in the latent space. The binary cross-entropy loss function (BCE Loss) is used to measure the similarity matrix between the nodes of the prior graph in the input space and the input graph. Similarity matrix of nodes in the fully connected graph of the input space The difference between them is used to construct the manifold learning loss. L 2. The formula is as follows: ; in, β For manifold loss weights, α This represents the global relation weight; The graph attribute prediction module includes a linear transformation layer and a softmax activation function, which converts the embedding matrix... Convert to graph nodes C The probability of each category, C The categories depend on the dataset used. C To accommodate the hyperparameters set for the task, this embodiment uses the Cora dataset. C = 7, C The categories are {case-based reasoning, genetic algorithms, neural networks, probabilistic methods, reinforcement learning, rule learning, and theory}. The joint optimization module incorporates the manifold learning loss function. L 2. Task loss function for graph attribute prediction models By weighting and combining the results, the total loss function is obtained. L The formula is as follows: ; in, L 1 represents the prediction loss of the graph attribute prediction module; The system parameters, including the prediction loss weight hyperparameters of the graph attribute prediction module, are jointly optimized using the gradient descent algorithm. β Global relation weights in manifold loss α， Using fully connected graphs to represent global relationships ensures that graph attribute prediction models maintain the fundamental structure of the data while performing specific tasks; The graph structure feature extraction module, manifold similarity calculation module, manifold structure preservation loss calculation module, and joint optimization module are sequentially connected in communication. The feature smoothing module, deep graph representation learning module, graph attribute prediction module, and joint optimization module are sequentially connected in communication. The deep graph representation learning module and manifold structure preservation loss calculation module are connected in communication.

[0045] Based on the above embodiments, this application provides a graph attribute prediction method based on manifold learning, such as... Figure 2 As shown, it includes the following steps: S100. System initialization: Initialize the graph attribute prediction system, set the graph attribute prediction system state to training state, and set the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space If empty, set the maximum number of training rounds to 200, or set the number of training rounds to 0.

[0046] S200, Data Input: Receive the original attribute map. G= ( V, E, X ),in V For a set of nodes, E Let be the set of edges. X The node feature matrix is ​​processed by the feature smoothing module. XA nonlinear transformation is performed to obtain a smooth node feature matrix. X' .

[0047] S300, Generate a node embedding matrix, smoothing the node feature matrix. X The input depth map representation learning module uses a variational graph autoencoder (VGAE) to generate parameters for the distribution of the embedding matrix, constructs the distribution of the embedding matrix, and randomly samples from the obtained distribution of the embedding matrix. K This yields multiple embedding matrices. , , ..., , K=5 .

[0048] S400, Calculate the node similarity matrix. When the graph attribute prediction system is in the prediction state, execute step S900; when the graph attribute prediction system is in the training state, calculate the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space When empty, construct prior graphs respectively. and fully connected graph Calculate the map geodesic distance matrix using a long-tail-based approach. t The kernel functions of the distribution are respectively converted into the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space Calculate the distance between nodes; when the input space prior graph node similarity matrix is ​​used... Similarity matrix of nodes in the fully connected graph of the input space If not empty, proceed to step S500; specifically including: S410. Determine the state of the graph attribute prediction system. If the state of the graph attribute prediction system is the prediction state, execute step S900; otherwise, execute step S420. S420. Determine the node similarity matrix. When the input spatial prior graph node similarity matrix is... Similarity matrix of nodes in the fully connected graph of the input space If the value is not empty, proceed to step S500; otherwise, proceed to step S430. S430. Construct a prior graph. ,if E If not obtained, then use k Construction of nearest neighbor graph E ; S440. Construct a fully connected graph based on the prior graph. Construct a fully connected graph ; S450, Calculate the geodesic distance matrix based on the prior map. and fully connected graph The rule for calculating the distance between nodes in the graph is as follows: if the nodes are connected, the cosine distance is used to calculate the distance between the nodes; if the nodes are connected but not connected, the maximum distance between the nodes is taken as the distance between the nodes. S460. Calculate the node similarity matrix. Using a kernel function, convert the graph geodesic distance matrix into the node similarity matrix of the prior graph in the input space, based on the distance matrix calculation rules between nodes. Similarity matrix of nodes in the fully connected graph of the input space .

[0049] S500, latent spatial structure feature extraction, for embedding matrix Based on the edge set in the latent space E Construct a graph structure and calculate the similarity matrix of nodes in the latent space according to the distance calculation rules between nodes. The rule for calculating the distance between nodes is: if nodes are connected, then the cosine distance is used to calculate the distance between them. and Distance between If nodes are not connected, then the maximum distance between nodes in the graph is taken as the distance between nodes. The formula is as follows: ; in, Indicates node-based and Cosine distance between , , n Indicates the number of nodes. It is a positive integer, with a value of 1.

[0050] S600, manifold learning loss calculation, uses the binary cross-entropy loss function (BCE Loss) to calculate the latent space node similarity matrix. Similarity matrix of nodes with the prior graph in the input space Input space fully connected graph node similarity matrix The differences between them are weighted and summed to obtain the manifold learning loss. L 2. The formula is as follows: ; in Logical loss function K For the number of samples, The global relation weight in the manifold loss is set to 1. This is the similarity matrix of potential spatial nodes. Given the node similarity matrix of the prior graph in the input space and The input space is the node similarity matrix of the fully connected graph.

[0051] S700, Graph Attribute Training and Prediction: Using the Graph Attribute Prediction module to embed the matrix... Convert to graph nodes C The probabilities of each category were used from the Cora dataset. C = 7, C The categories are {case-based reasoning, genetic algorithms, neural networks, probabilistic methods, reinforcement learning, rule learning, and theory}.

[0052] S800, joint optimization, manifold learning loss function L 2. Prediction loss function of the graph attribute prediction module L 1. Combining by weights yields the total loss function. L The formula is as follows: ; in, L 1 represents the prediction loss function of the graph attribute prediction module, and β represents the weight hyperparameter of the prediction loss function of the graph attribute prediction module. The learnable parameters of the feature smoothing module, deep graph representation learning module, and graph attribute prediction module are updated using the backpropagation algorithm. This includes the weight matrices and bias vectors of each layer of the MLP in the feature smoothing module, the weight matrix and bias vectors of the Variational Graph Autoencoder (VGAE) in the deep graph representation learning module, and the weight matrix and bias vectors of the linear transformation layer in the graph attribute prediction module. When the number of training epochs is less than the maximum number of training epochs, the number of training epochs is incremented by one, and the process returns to step S200; otherwise, the graph attribute prediction system state is set to the prediction state, and the process returns to step S200. Specifically, this includes: S810. Calculate the total loss function, and then apply the manifold learning loss function. L 2. Prediction loss function of the graph attribute prediction module L 1. By weight β Combining these, we obtain the total loss function. L The formula is as follows: ; in, L 1 represents the prediction loss function of the graph attribute prediction module, and β represents the weight hyperparameter of the prediction loss function of the graph attribute prediction module. S820. Update system parameters by updating the parameters of the feature smoothing module, the deep graph representation learning module, and the graph attribute prediction module through the backpropagation algorithm. S830. Iterative training: When the number of training rounds is less than the maximum number of training rounds, increment the number of training rounds by one and return to step S200; otherwise, set the graph attribute prediction system state to the prediction state and return to step S200.

[0053] Optionally, in the graph attribute prediction method based on manifold learning in any of the above embodiments, learnable parameters may be used.

[0054] S900, Graph Attribute Reasoning and Prediction: Using the graph attribute prediction module to embed the matrix Transform into graph nodes C The probability of each category is used to complete the graph attribute prediction.

[0055] S1000, embedding quality assessment, obtaining the manifold learning loss for each round. L 2. As a structural evaluation metric for embedding quality, it measures the similarity matrix of nodes in the latent space. Similarity matrix of nodes with the prior graph in the input space Input space fully connected graph node similarity matrix The differences between them L The closer 2 is to 0, the smaller the difference and the better the embedding quality. S2000 embeds quality visualization feedback, feeding the embedding quality feedback to the dimensionality reduction visualization tool UMAP (UniformManifold Approximation and Projection) to generate an embedding visualization.

[0056] In order to fully evaluate the technical effects of the above embodiments, this application uses UMAP to visualize the embeddings learned on the Cora dataset in two-dimensional space and compares them with the original input features. Figure 3 This is the original input feature matrix of the Cora dataset. X The UMAP visualization results show that each point in the graph corresponds to a category of a paper in the Cora dataset, with color used to represent the label category. C=7 The categories are: red - case-based reasoning, green - genetic algorithm, blue - neural network, purple - probabilistic method, orange - reinforcement learning, cyan - rule learning, and yellow - theory. Figure 3 Distributed densely and chaotically in a two-dimensional space, dots of different colors almost completely overlap with no obvious clustering trend. The nodes of each category intertwine to form a compact "scattered cluster," making it impossible to visually distinguish the regions corresponding to different labels. This phenomenon indicates that the spatial structure of the original input features is chaotic, the feature similarity of nodes of different categories has not formed an effective distinction, and the prior structure of the input space cannot directly support the recognition of label categories. Figure 4The image shows the UMAP visualization of the embedding matrix. Nodes of different colors (representing paper label categories in the Cora dataset) exhibit a clear clustered distribution: nodes of the same label category cluster into independent clusters, with each cluster maintaining a reasonable dispersion (avoiding overly compact clustering). This demonstrates that the above embodiment possesses representation learning capabilities; the embedding matrix contains the geometric relationships between nodes, enabling different categories to form different clusters.

[0057] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A graph attribute prediction system based on manifold learning, characterized in that, include: The feature smoothing module smooths the original attribute map. G= ( V, E, X Perform feature smoothing on the node feature matrix. X A smooth node feature matrix is ​​obtained by performing a nonlinear transformation using a multilayer perceptron. X' ; The graph structure feature extraction module constructs prior graphs respectively. and fully connected graph Calculate the geodesic distance matrix of the map; The manifold similarity calculation module uses a kernel function to transform the graph geodesic distance matrix according to the distance calculation rules between nodes, thereby obtaining the node similarity matrix of the prior graph in the input space. Similarity matrix of nodes in the fully connected graph of the input space ; The depth graph representation learning module uses an encoder to process the smoothed node feature matrix. X' , converted K Embedding matrices , , ..., , ..., ; The manifold structure preservation loss calculation module, for the embedding matrix ( ), based on edge set in the latent space E Construct a graph structure and a manifold learning loss function. L 2; The graph attribute prediction module converts the embedding matrix into a graph. Convert to graph nodes C The probability of each category, C Hyperparameters set according to the task; The joint optimization module incorporates the manifold learning loss function. L 2. Task loss function for graph attribute prediction models By weighting and combining the results, the total loss function is obtained. L The system parameters are jointly optimized using the gradient descent algorithm; The graph structure feature extraction module, the manifold similarity calculation module, the manifold structure preservation loss calculation module, and the joint optimization module are sequentially connected in communication. The feature smoothing module, the depth graph representation learning module, the graph attribute prediction module, and the joint optimization module are sequentially connected in communication. The depth graph representation learning module and the manifold structure preservation loss calculation module are connected in communication.

2. The graph attribute prediction system based on manifold learning as described in claim 1, characterized in that, The multilayer perceptron in the feature smoothing module has two layers with feature dimensions of 512 and 1024, respectively.

3. The graph attribute prediction system based on manifold learning as described in claim 2, characterized in that, The distance calculation rule between nodes is as follows: if nodes are connected, the cosine distance is used to calculate the distance between nodes; if nodes are connected but not connected, the maximum distance between nodes is taken as the distance between nodes.

4. The graph attribute prediction system based on manifold learning as described in claim 3, characterized in that, The kernel function is based on long tail. t distributed.

5. The graph attribute prediction system based on manifold learning as described in claim 1, characterized in that, The encoder is a variational graph autoencoder.

6. The graph attribute prediction system based on manifold learning as described in claim 1, characterized in that, The manifold structure preservation loss calculation module calculates the similarity matrix of potential spatial nodes. The similarity matrix between the nodes and the prior graph in the input space is measured using a logistic loss function. Similarity matrix of nodes in the fully connected graph of the input space The difference between them is that the logical loss function adopts the binary cross-entropy loss function.

7. A graph attribute prediction method based on manifold learning, using the graph attribute prediction system based on manifold learning as described in any one of claims 1-6, characterized in that, Includes the following steps: S100, System initialization, graph attribute prediction system initialization, set the graph attribute prediction system state to training state, set the maximum number of training rounds, and set the training rounds to 0; S200, Data Input: Receive the original attribute map. G= ( V, E, X ), for the node feature matrix X A nonlinear transformation is performed to obtain a smooth node feature matrix. X' ; S300. Generate a node embedding matrix, construct a distribution of the embedding matrix, and randomly sample from the distribution of the embedding matrix. K This yields multiple embedding matrices. ; S400. Calculate the node similarity matrix. If the graph attribute prediction system is in the prediction state, proceed to step S900; otherwise, proceed to step S500. S500, latent spatial structure feature extraction, for embedding matrix Based on the set of edges in the latent space E Construct a graph structure and calculate the similarity matrix of nodes in the latent space. ; S600, Manifold learning loss calculation, calculating manifold learning loss. L 2. The formula is as follows: ； in, This is the similarity matrix of potential spatial nodes. For the node similarity matrix of the input space prior graph, The input space is the node similarity matrix of the fully connected graph. S700, Graph attribute training and prediction, using the embedding matrix Convert to graph nodes C The probability of each category; S800, Joint optimization: When the number of training rounds is less than the maximum number of training rounds, increment the number of training rounds by one and return to step S200; otherwise, set the graph attribute prediction system state to prediction state and return to step S200. S900, Graph attribute reasoning and prediction, embedding the matrix Transform into graph nodes C The probability of each category is used to complete the graph attribute prediction.

8. The graph attribute prediction method based on manifold learning as described in claim 7, characterized in that, Step S400 includes: S410. Determine the state of the graph attribute prediction system. If the state of the graph attribute prediction system is a prediction state, execute step S900; otherwise, execute step S420. S420. Determine the node similarity matrix. When the node similarity matrix of the input space prior graph... Similarity matrix of nodes in the fully connected graph of the input space If the value is not empty, proceed to step S500; otherwise, proceed to step S430. S430. Construct the prior graph. ,if E If not obtained, then use k Construction of nearest neighbor graph E ; S440. Construct a fully connected graph based on the prior graph. Construct the fully connected graph ; S450, Calculate the geodesic distance matrix based on the prior map. and the fully connected graph The graph geodesic distance matrix is ​​calculated, and the distance between nodes is calculated according to the following rules: if nodes are connected, the cosine distance is used to calculate the distance between nodes; if nodes are not connected, the maximum distance between graph nodes is taken as the distance between nodes. S460. Calculate the node similarity matrix. Using the kernel function, convert the graph geodesic distance matrix into the node similarity matrix of the prior graph in the input space according to the distance matrix calculation rules between the nodes. Similarity matrix of nodes in the fully connected graph of the input space .

9. The graph attribute prediction method based on manifold learning as described in claim 7 or 8, characterized in that, Step S800 includes: S810. Calculate the total loss function, and apply the manifold learning loss function... L 2. The prediction loss function of the graph attribute prediction module L 1. Combining by weights yields the total loss function. L The formula is as follows: ； in, L 1 represents the prediction loss function of the graph attribute prediction module, and β represents the weight hyperparameter of the prediction loss function of the graph attribute prediction module. S820. Update system parameters by updating the parameters of the feature smoothing module, the deep graph representation learning module, and the graph attribute prediction module through the backpropagation algorithm. S830. Iterative training: when the number of training rounds is less than the maximum number of training rounds, increment the number of training rounds by one and return to step S200; otherwise, set the graph attribute prediction system state to prediction state and return to step S200.

10. The graph attribute prediction method based on manifold learning as described in claim 9, characterized in that, It also includes embedded quality assessment, the steps of which are as follows: S1000, embedding quality assessment, obtaining the manifold learning loss for each round. L 2. As a structural evaluation metric for embedding quality, the similarity matrix of the potential spatial nodes is measured. Similarity matrix of nodes with the prior graph in the input space The input space fully connected graph node similarity matrix The differences between them L The closer 2 is to 0, the smaller the difference, and the better the embedding quality. S2000, Embedded quality visualization feedback: The embedded quality is fed back to the dimensionality reduction visualization tool to generate an embedded visualization.

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