A topology-driven attribute missing graph learning method and device

Abstract

This application relates to a topology-driven attribute-missing graph learning method and apparatus. The method includes using TAAP technology for precise attribute pre-population; then injecting credibility and similarity information related to the node topological position into latent variables and using this as weight to update the embedding space; finally, achieving accurate feature reconstruction supervision by considering homogeneity and potential edge errors. This application has the effect of fully utilizing the complex topological information of the graph to improve the accuracy of recovering missing attributes from the graph data.

Description

Technical Field

[0001] The present application relates to the technical field of graph data analysis, and in particular to a topology-driven attribute missing graph learning method and device. Background Art

[0002] Currently, graph data analysis is widely used in social networks, bioinformatics, recommendation systems, financial risk management, the Internet of Things and other fields. However, in the process of graph data analysis, the problem of missing attributes is prevalent, resulting in inaccurate graph data analysis results.

[0003] In the existing technology, to deal with the problem of graph data with missing attributes, feature interpolation, matrix completion, graph neural networks, etc. can be used based on the principles of statistics and linear algebra, or combined with the initial topology of the graph and node neighbor information to estimate missing data points or generate new node representations to capture the complex initial topology in the graph data.

[0004] With respect to the above-mentioned related technologies, the inventors discovered that existing optimization schemes for missing graph data attributes cannot fully utilize the complex topological information of the graph, resulting in inaccurate recovery of missing attributes of the graph data. Summary of the Invention

[0005] In order to make full use of the complex topological information of the graph and improve the accuracy of recovering missing attributes of graph data, the present application provides a topology-driven attribute missing graph learning method and device.

[0006] In a first aspect, the present application provides a topology-driven attribute missing graph learning method.

[0007] This application is achieved through the following technical solutions:

[0008] A topology-driven attribute missing graph learning method includes the following steps:

[0009] Based on the original image data with missing attributes, obtaining the initial topology of the original image data and constructing a reconstructed attribute feature;

[0010] According to the initial topology, a topology-aware attribute propagation mechanism is introduced to perform attribute propagation, and attribute features of nodes in the initial topology are iteratively updated until attribute features that minimize the Dirichlet energy are obtained, thereby obtaining a refined topology of the original graph data;

[0011] Inputting the refined topology into a preset graph autoencoder-decoder model, and designing a refinement loss function based on the mean squared error between real known attribute nodes and refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension;

[0012] When the refined loss function satisfies a preset condition, the current graph autoencoder-decoder model is output as the attribute missing graph learning model;

[0013] The graph data to be learned is input into the attribute-missing graph learning model, the topology and node attributes of the graph data to be learned are reconstructed, and the missing attributes of the graph data to be learned are restored.

[0014] In a preferred example, the present application can be further configured as follows: the learning of the graph autoencoder-decoder model also adopts an embedding space propagation confidence mechanism, including the following steps:

[0015] Calculate the shortest path from unknown attribute nodes to pre-specified known attribute nodes, quantify the position confidence of unknown attribute nodes, and construct the topological position function of unknown attribute nodes in the embedded space propagation;

[0016] Calculate the number of unknown attribute nodes directly connected to known attribute nodes, quantify the position confidence of known attribute nodes, and construct the topological position function of known attribute nodes in the embedded space propagation;

[0017] When the refined topology is input into a preset graph autoencoder-decoder model, the potential impact or context information of the known attribute nodes and unknown attribute nodes in the original graph data is obtained based on the unknown attribute node topology position function and the known attribute node topology position function.

[0018] In a preferred example, the present application may be further configured as follows: when the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential impact or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes:

[0019] According to the preset distance attenuation factor, the unknown attribute node weight function and the known attribute node weight function are designed;

[0020] Based on the weight values ​​corresponding to the row dimension expansion of unknown attribute nodes and the weight values ​​corresponding to the row dimension expansion of known attribute nodes, combined with the transposed matrix, a confidence weight matrix is ​​constructed;

[0021] When the refined topology is input into the preset graph autoencoder-decoder model, the confidence weight matrix is ​​used to balance the local information from neighboring nodes and the global information related to the context information of the known attribute nodes and unknown attribute nodes in the original graph data, thereby generating a dynamic hidden embedding.

[0022] In a preferred example, the present application may be further configured as follows: when the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential impact or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes:

[0023] Based on the latent variables and their feature dimensions in the learning process of the graph autoencoder-decoder model, construct a correlation coefficient matrix of the latent variables;

[0024] Weighting the confidence weight matrix and the correlation coefficient matrix to obtain an embedding space weighted matrix;

[0025] Merging the dynamic embedding with the original embedding according to the embedding space weighting matrix to generate an overall representation of the impact of the latent variable on the entire node;

[0026] When the refined topology is input into the preset graph encoder-decoder model, the overall representation is used to capture the differences in different feature dimensions of the latent variables, the potential relationships between known attribute nodes and unknown attribute nodes, and the impact of the latent variables on the overall nodes.

[0027] In a preferred example, the present application can be further configured as follows: the learning of the graph autoencoder-decoder model also introduces a node homogeneity score for evaluating the consistency between adjacent nodes, including the following steps:

[0028] Based on the embedding features between nodes, the structural similarity of node embeddings in the embedding space is determined;

[0029] Designing a homogeneity score function for each node based on the structural similarity;

[0030] Using the homogeneity score function, constructing a consistency loss function based on the node homogeneity score;

[0031] When the sum of the refinement loss function and the consistency loss function converges, it is determined that the refinement loss function meets the preset condition.

[0032] In a preferred example, the present application can be further configured as follows: the learning of the graph autoencoder-decoder model also introduces a non-link similarity penalty for penalizing misleading similarities between non-link nodes, including the following steps:

[0033] Calculate the embedding similarity between unlinked node pairs, where unlinked node pairs are pairs of nodes in the graph that have similar embedding attributes but no association relationship;

[0034] Comparing the embedding similarity with a preset embedding threshold;

[0035] When the embedding similarity exceeds the embedding threshold, a non-link similarity penalty function for non-link node pairs is designed based on the embedding similarity to penalize the matched non-link node pairs;

[0036] Constructing a non-link similarity penalty loss function according to the non-link similarity penalty function;

[0037] When the sum of the refinement loss function, the consistency loss function and the non-link similarity penalty loss function converges, it is determined that the refinement loss function meets the preset condition.

[0038] In a second aspect, the present application provides a topology-driven attribute missing graph learning device.

[0039] This application is achieved through the following technical solutions:

[0040] A topology-driven attribute missing graph learning device, comprising:

[0041] A topology structure module is used to obtain the initial topology of the original image data based on the original image data with missing attributes, and to construct a reconstructed attribute feature;

[0042] a topology refinement module, configured to introduce a topology-aware attribute propagation mechanism to perform attribute propagation based on the initial topology, iteratively update attribute features of nodes in the initial topology until an attribute feature that minimizes the Dirichlet energy is obtained, thereby obtaining a refined topology of the original graph data;

[0043] a model training module, configured to input the refined topology into a preset graph autoencoder-decoder model, and design a refinement loss function based on the mean squared error between real known attribute nodes and refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension;

[0044] A target model module is configured to output the current graph autoencoder-decoder model as an attribute-missing graph learning model when the refinement loss function satisfies a preset condition;

[0045] The attribute-missing graph learning module is used to input the graph data to be learned into the attribute-missing graph learning model, reconstruct the topology and node attributes of the graph data to be learned, and restore the missing attributes of the graph data to be learned.

[0046] In a third aspect, the present application provides a computer device.

[0047] This application is achieved through the following technical solutions:

[0048] A computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the processor implements the steps of any one of the above-mentioned topology-driven attribute missing graph learning methods.

[0049] In a fourth aspect, the present application provides a computer-readable storage medium.

[0050] This application is achieved through the following technical solutions:

[0051] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of any one of the above-mentioned topology-driven attribute missing graph learning methods.

[0052] In a fifth aspect, the present application provides a computer program product.

[0053] This application is achieved through the following technical solutions:

[0054] A computer program product includes a computer program, which, when executed by a processor, implements the steps of any one of the above-mentioned topology-driven attribute missing graph learning methods.

[0055] In summary, compared with the prior art, the technical solution provided by this application has at least the following beneficial effects:

[0056] Based on the original graph data with missing attributes, the initial topology of the original graph data is obtained, and reconstructed attribute features, such as known attribute nodes, unknown attribute nodes, edge sets, the number of edges and other parameter information, are constructed as data for subsequent model learning; according to the initial topology, a topology-aware attribute propagation mechanism is introduced for attribute propagation, and the optimal solution of the attribute propagation process is solved by minimizing the Dirichlet energy, so as to achieve a smooth correlation between the Dirichlet energy and the attribute features on the graph, so as to consider the influence of the topological structure and the position of adjacent nodes on the attribute-missing nodes, and perform attribute propagation according to the topological structure of the graph to initialize and refine the attributes of the missing nodes, thereby helping the attributes of the nodes to better reflect their positions and relationships in the entire graph, reducing the mismatch between local attributes and the global graph structure, and ensuring the smooth change of graph attributes in the reconstruction process of the subsequent graph autoencoder-decoder. It is conducive to making full use of the complex topological information of the graph; inputting the refined topology into the preset graph autoencoder-decoder model can transform the graph data into meaningful potential representations while maintaining attribute reconstruction, and designing a refined loss function based on the mean squared error between the real known attribute nodes and the refined attribute nodes in the refined topology, which helps to integrate additional loss components related to different tasks, and finally form a cohesive optimization scheme, enhancing the adaptability of TDAR to multi-task learning, and then integrating the intrinsic attributes of the nodes with their graph context, providing a comprehensive perspective for predicting missing attributes, ensuring the authenticity of the nodes, not only focusing on the attributes of a single node, but also having advantages in capturing the interdependence between node attributes in a wider range and how they are affected by the entire graph structure, thereby improving the recovery accuracy of missing attributes of graph data. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram of the main process of a topology-driven attribute missing graph learning method provided as an exemplary embodiment of the present application.

[0058] Figure 2 A model architecture block diagram of a topology-driven attribute missing graph learning method provided as another exemplary embodiment of the present application.

[0059] Figure 3 A schematic diagram of comparative experimental results of attribute reconstruction on four different datasets of a topology-driven attribute missing graph learning method provided in another exemplary embodiment of the present application and existing algorithms such as SAT, SVGA, ITR, and MATE.

[0060] Figure 4 This is a main structural block diagram of a topology-driven attribute missing graph learning device provided by an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0061] This specific embodiment is merely an explanation of the present application and is not a limitation of the present application. After reading this specification, those skilled in the art may make non-creative modifications to the present embodiment as needed, but as long as they are within the scope of the claims of the present application, they are protected by the patent law.

[0062] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0063] In this document, the term "and / or" simply describes a relationship between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document, unless otherwise specified, generally indicates an "or" relationship between the related objects.

[0064] In the field of graph data analysis, the problem of missing attributes is prevalent and can be caused by a variety of factors, including:

[0065] Privacy protection: Especially in areas where personal data is sensitive, such as social networks, users choose not to share all their information for privacy reasons. However, this self-restricted information sharing behavior leads to incomplete attributes in graph data, which poses challenges for graph data analysis.

[0066] Data collection limitations: During the data collection process, some attributes are difficult to fully collect due to technical or cost limitations. For example, in large-scale data collection activities, some key information is missing due to time and resource constraints.

[0067] Naturally missing: In naturally generated datasets, such as bioinformatics networks, some information is inherently unknown. This incompleteness of graph and text data is due to the limitations of current scientific knowledge.

[0068] User behavior: In networks where users are required to actively provide information, users may forget or choose not to fill in certain information, resulting in incomplete image and text data.

[0069] System error: During data storage or transmission, data loss due to system errors can easily affect the integrity of graphic data and the accuracy of analysis results.

[0070] In addition, in order to more accurately process graphs with missing attributes, existing technologies can adopt deep learning methods, such as the SAT method that uses autoencoders to learn node representations, the SVGA method that combines graph structure and node attributes, the ITR method that uses the initial topology of the graph to adaptively repair missing attributes, and the MATE method, a multi-view framework that performs comparative learning on attribute and topology views.

[0071] However, existing methods fail to fully consider the profound impact of missing attributes on topological information mining, often overlooking the importance of contextual information and underlying structure. Secondly, when attribute information is incomplete, existing methods struggle to accurately determine the relationships and similarity weights between nodes in the graph embedding space. Capturing high-order similarities and effectively integrating node attributes have yet to be effectively addressed. Furthermore, most existing methods lack accuracy in handling implicit relationships and similarities in the embedding space, especially when data is incomplete or flawed, which can easily lead to misunderstandings and fail to provide a clear mechanism for distinguishing unconnected pairs of nodes in the graph.

[0072] Therefore, in order to achieve more accurate map data analysis and attribute prediction, this application proposes a topology-driven attribute missing graph learning method and innovatively designs a topology-driven attribute recovery (TDAR) framework, providing a new method and system for the field of graph data analysis. It aims to solve the limitations of existing graph data analysis technology in dealing with missing attributes, especially the technical problems of inaccurate recovery of missing attributes due to insufficient utilization of the complex topological information of the graph and inability to effectively integrate the node relationships and similarities in the embedding space. It can significantly improve the accuracy of missing attribute recovery. The specific technical problems are as follows:

[0073] How to accurately recover missing attributes in graph data through multi-task learning while taking into account the complex topological structure of the graph;

[0074] How to use the Topology-Driven Attribute Recovery (TAAP) mechanism to initialize and refine attributes in graph data analysis, ensuring that the recovered attributes are consistent with the structural characteristics of the graph;

[0075] How to dynamically evaluate the degree of mutual influence between nodes in the embedding space and effectively compensate for the error loss in information propagation through the Embedding Space Propagation Confidence (ESPC) strategy;

[0076] How to accurately capture and integrate the high-order similarity of node attributes in the embedding space, and optimize the information aggregation process through the node homogeneity score (NHS) and non-link similarity penalty (NLSP) strategies.

[0077] In order to solve the above technical problems, this application provides the following technical solutions:

[0078] We designed an end-to-end topology-driven attribute recovery (TDAR) framework. Through a multi-task learning mechanism based on graph topology, the attribute recovery process can accurately reflect the structural characteristics of the graph.

[0079] We propose Topology-Driven Attribute Recovery (TAAP), which combines Dirichlet energy minimization theory to optimize the initialization and recovery of node attributes through the topological structure of the graph.

[0080] We propose an Embedding Space Propagation Confidence (ESPC) strategy based on embedding space, which uses dynamic attention weights to adjust information propagation in the embedding space to compensate for the error loss of traditional methods in attribute recovery.

[0081] Node Homogeneity Score (NHS) and Non-Link Similarity Penalty (NLSP) are proposed to further optimize information aggregation in the embedding space and improve the quality of embedded features.

[0082] The key technical points of this application include:

[0083] 1. Topology-Aware Attribute Propagation (TAAP): This is a novel graph attribute initialization and recovery method that leverages the graph’s topology to guide the recovery of missing attributes.

[0084] 2. Attribute recovery based on Dirichlet energy minimization: As a key step in the attribute recovery process, it ensures a smooth transition of attributes in the graph, reflecting the natural distribution of node attributes;

[0085] 3. Propagated Confidence in Embedding Space (ESPC) strategy: This is a weight adjustment mechanism used to balance local and global information and tailor dynamic weights for the relationships between nodes in the attribute-missing graph;

[0086] 4. Node Homogeneity Score (NHS): NHS is an evaluation mechanism used to measure the homogeneity of nodes in the embedding space, ensuring that nodes with similar attributes are close in the embedding representation, thereby increasing the consistency and accuracy of node attribute similarity during attribute recovery;

[0087] 5. Non-Link Similarity Penalty (NLSP): NLSP is a strategy for strengthening graph embedding representations by identifying and penalizing pairs of nodes that appear similar in the embedding space but are not directly connected in the actual graph structure. It aims to reduce erroneous attribute propagation and enhance discriminability in the embedding representation.

[0088] 6. Relationship weights based on embedding space: Utilize the correlation matrix and confidence weight matrix to refine the potential representation of nodes and optimize information dissemination;

[0089] 7. Construction of dynamic embedding representation: By combining original embedding and dynamic embedding, the richness and expressiveness of node representation are improved.

[0090] The embodiments of the present application are described in further detail below with reference to the accompanying drawings.

[0091] Reference Figure 1 , an embodiment of the present application provides a topology-driven attribute missing graph learning method, and the main steps of the method are described as follows.

[0092] S1: Based on the original image data with missing attributes, obtain the initial topology of the original image data and construct a reconstructed attribute feature;

[0093] S2: Based on the initial topology, a topology-aware attribute propagation mechanism is introduced to perform attribute propagation, and attribute features of nodes in the initial topology are iteratively updated until attribute features that minimize the Dirichlet energy are obtained, thereby obtaining a refined topology of the original graph data;

[0094] S3: Inputting the refined topology into a preset graph autoencoder-decoder model, and designing a refinement loss function based on the mean squared error between real known attribute nodes and refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension;

[0095] S4: When the refined loss function satisfies a preset condition, the current graph autoencoder-decoder model is output as the attribute missing graph learning model;

[0096] S5: Input the graph data to be learned into the attribute-missing graph learning model, reconstruct the topology and node attributes of the graph data to be learned, and restore the missing attributes of the graph data to be learned.

[0097] Specifically, refer to Figure 2 , define an undirected graph G = (V, E) with missing node attributes, V = V u ∪V k Represents a node set, V u and V k Represent nodes with known and unknown attributes respectively. Assume that among the total number of nodes N, only k nodes have attributes, |u|+|k|=N. E represents the edge set, and M represents the number of edges. The node attribute feature matrix is ​​given by Represented as, where F is the number of attribute features. Other relevant information includes the adjacency matrix Diagonal matrix D, symmetric normalized adjacency matrix and the symmetric normalized Laplacian matrix Through the original image data with missing attributes, the initial topology of the original image data is obtained, and the reconstructed attribute features are constructed to obtain the reconstructed attribute features of the attribute missing graph And apply it to downstream classification tasks, with original inputs: A and X. Based on A or X, the known attribute nodes, unknown attribute nodes, edge sets, number of edges and other parameters of the original graph data are obtained.

[0098] Furthermore, we introduce the Graph Autoencoder (GAE) as a learning framework. GAE provides an effective generative approach to transform graph data into meaningful latent representations while preserving attribute reconstruction, making it particularly well-suited for the unique challenges of recovering attribute-missing graphs. The core advantage of GAE lies in its encoder-decoder architecture. The encoder maps the graph data and its attributes to a latent dimension, while the decoder strives to reconstruct the graph topology and node attributes from this dimension. It mainly includes the encoder, decoder, and refinement loss function design.

[0099] (1) Encoder

[0100] The essence of the encoder is to transform the input node attributes into a potential continuum of continuously distributed features. and the symmetric normalized adjacency matrix The encoding action can be described as:

[0101]

[0102] in, represents the node encoded in the latent embedding Z, GNN is a graph neural network supported by a learnable encoding parameter φ, and σ represents the activation function.

[0103] (2) Decoder

[0104] The decoder performs the opposite action of the encoder and strives to recover the original or specified node attributes from the encoded latent field. Mathematically, the expression includes:

[0105]

[0106] in, represents the improved node features, and MLP is a multilayer perceptron injected with decoding learnable parameters θ.

[0107] (3) Refining loss function design

[0108] Refining properties Together with the adjacency matrix Together as input to GAE to calculate the potential representation Z of the node. At the same time, in order to ensure authenticity, by calculating the real known attribute X k and refined properties The mean square error (MSE) between them is used to design the expression of the refined loss function:

[0109]

[0110] In this way, the TAAP method integrates the intrinsic properties of nodes with their graph context, providing a comprehensive perspective for predicting missing properties. The advantage of this method lies in not only focusing on individual node properties, but also capturing the interdependencies between properties in a broader context and how they are affected by the entire graph structure.

[0111] The GAE framework enhances TDAR’s adaptability to multi-task learning, and the inherent flexibility of the refined loss function helps integrate additional loss components related to different tasks, ultimately forming a cohesive optimization scheme.

[0112] Because attribute-missing nodes in a graph do not exist in isolation but are influenced by their topological structure and the positions of neighboring nodes, we introduced the Topology-Aware Attribute Propagation (TAAP) mechanism. TAAP initializes and refines the attributes of missing nodes by propagating attributes based on the graph's topology. This helps the node attributes better reflect their position and relationships within the entire graph, reducing the mismatch between local attributes and the global structure.

[0113] And, in the analytical scenario, the attribute propagation process of TAAP is linked to the concept of minimizing the Dirichlet energy to achieve the optimal solution by minimizing the Dirichlet energy, which is associated with the smoothness of attribute features on the graph.

[0114] Formally, the Dirichlet energy is expressed as:

[0115]

[0116] in, represents the gradient of the attribute feature, and the energy represents the sum of the squares of the gradient over the domain Ω. When this energy is minimized, it represents an attribute that changes smoothly over the domain. To find the attribute feature that minimizes the Dirichlet energy, it can be associated with the Laplacian matrix L of the graph as follows:

[0117]

[0118] TAAP iteratively updates the attribute vector X, gradually approaching the optimal solution and achieving the goal of minimizing the Dirichlet energy. In each iteration, the attribute vector is updated using the Lagrange multiplier method and the KKT condition.

[0119] Specifically, the gradient calculated based on the current attribute vector Update the attribute vector, where the aggregation function of the refined attribute is expressed as follows:

[0120]

[0121]

[0122] in, is the inverse of the Laplacian matrix of the unknown node. The inverse of this matrix allows the system to take into account the connectivity and relationships between nodes when refining properties. uk X k Through the adjacency matrix A uk and the attribute X of the known node k Represents the relationship between known and unknown nodes. This interaction ensures that the properties of neighboring known nodes influence the unknown nodes during attribute recovery. This directly indicates that the refined properties of the known nodes remain unchanged. l represents the number of propagation layers. The property aggregation process can be continuously optimized and corrected through multiple rounds of iterations until the termination condition is met or the predetermined number of iterations is reached.

[0123] By leveraging graph topology, TAAP uses the refined attributes obtained by minimizing the Dirichlet energy as the structural prior for the subsequent encoding-decoding reconstruction process, ensuring smooth changes in graph attributes. The aggregation scheme in this application is based on the attribute-missing graph and implements the optimization process through Dirichlet energy minimization.

[0124] Although GAE provides the necessary flexibility, it still has limitations in ensuring the compactness of missing data representation and the accuracy of reconstruction. To this end, this application proposes a learning method that is adapted to attribute-missing graph datasets and analysis tasks based on a topology-driven perspective.

[0125] In one embodiment, the learning of the graph autoencoder-decoder model further adopts an embedding space propagation confidence mechanism, including the following steps:

[0126] Calculate the shortest path from unknown attribute nodes to pre-specified known attribute nodes, quantify the position confidence of unknown attribute nodes, and construct the topological position function of unknown attribute nodes in the embedded space propagation;

[0127] Calculate the number of unknown attribute nodes directly connected to known attribute nodes, quantify the position confidence of known attribute nodes, and construct the topological position function of known attribute nodes in the embedded space propagation;

[0128] When the refined topology is input into a preset graph autoencoder-decoder model, the potential impact or context information of the known attribute nodes and unknown attribute nodes in the original graph data is obtained based on the unknown attribute node topology position function and the known attribute node topology position function.

[0129] Because one of the core tasks of the GAE framework is to learn an accurate latent embedding Z, defining the dynamic weight relationships between nodes in a low-dimensional space is crucial in the attribute graph embedding task, as it involves effectively learning multi-scale aggregated information in the graph. To this end, we introduce the Embedding Space Propagation Confidence (ESPC) strategy, a powerful mechanism that captures and maintains the accuracy of the relationships between nodes in the embedding space by considering global and local constraints.

[0130] Specifically, in order to summarize the position confidence of each node in the graph in the embedding space propagation, two functions are introduced: f k2u (v) and f u2k (v) represents the bidirectional influence of two types of nodes, namely, nodes with unknown attributes and nodes with known attributes.

[0131] Function f k2u (v) Calculate the unknown v∈V u To the specified known node V k The shortest path to quantify the position confidence of the unknown node:

[0132]

[0133] Here, d(v, w) represents the shortest path (in terms of edges) between nodes v and w, computed using a BFS traversal. Initially, the shortest path to a node's neighbors is set to 0. Subsequently, paths from the unknown node to the neighbors of a known node of varying order are recursively explored, increasing the path length by 1 with each recursion until a known node is encountered. For known nodes, it simply returns 0.

[0134] f u2k(v) Quantify the location confidence of a known node by counting the number of unknown nodes directly connected to the known node. Formally, for a known node v∈V k , f u2k (v) is defined as:

[0135]

[0136] in, Represents the neighborhood of node v. It evaluates the connectivity of a node to unknown nodes. For known nodes, it counts the number of unknown nodes in its neighbors; for unknown nodes, it simply returns 0.

[0137] Based on the above unknown attribute node topology position function and the above known attribute node topology position function, the position confidence is obtained as a proxy for gaining insight into the potential impact or contextual information that can be provided by known and unknown components in the attribute missing graph.

[0138] In one embodiment, when the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential influence or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes:

[0139] According to the preset distance attenuation factor, the unknown attribute node weight function and the known attribute node weight function are designed;

[0140] Based on the weight values ​​corresponding to the row dimension expansion of unknown attribute nodes and the weight values ​​corresponding to the row dimension expansion of known attribute nodes, combined with the transposed matrix, a confidence weight matrix is ​​constructed;

[0141] When the refined topology is input into the preset graph autoencoder-decoder model, the confidence weight matrix is ​​used to balance the local information from neighboring nodes and the global information related to the context information of the known attribute nodes and unknown attribute nodes in the original graph data, thereby generating a dynamic hidden embedding.

[0142] When dealing with node confidence in attribute-missing graphs, adopting the right weighting strategy can more accurately capture the complex relationships between nodes and their influence on neighboring nodes. There are two key types of information: local information from neighboring nodes, and global information related to the broader context. To strike a balance between these two, this application designs a weight adjustment strategy to produce dynamic hidden embeddings.

[0143] Specifically, a distance decay factor α∈(0,1) is used to measure the two-level confidence.

[0144] at first, Used to measure unknown nodes V u The weight of unknown node V u With known node V k The greater the distance, the smaller the attenuation factor. This means that the farther a known node is from an unknown node, the more its attribute characteristics will be attenuated during the transmission process, and therefore the weight will be reduced.

[0145] on the contrary, Used to measure the weight of known nodes, ensuring that the more unknown nodes a known node connects to, the greater the attenuation factor. This means that the more unknown nodes a known node affects, the greater the weight its attribute characteristics should have during the transmission process.

[0146] When these two are combined, the remote effects can be balanced without neglecting the local direct connections. This method not only reflects the global characteristics of the node, but also integrates its local interactions, achieving a balance between the global and local. In this embodiment, the confidence weight matrix It can be expressed as:

[0147]

[0148] in, and Represent f k2u and f u2k The row dimension is expanded.

[0149] In one embodiment, when the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential influence or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes:

[0150] Based on the latent variables and their feature dimensions in the learning process of the graph autoencoder-decoder model, construct a correlation coefficient matrix of the latent variables;

[0151] Weighting the confidence weight matrix and the correlation coefficient matrix to obtain an embedding space weighted matrix;

[0152] Merging the dynamic embedding with the original embedding according to the embedding space weighting matrix to generate an overall representation of the impact of the latent variable on the entire node;

[0153] When the refined topology is input into the preset graph encoder-decoder model, the overall representation is used to capture the differences in different feature dimensions of the latent variables, the potential relationships between known attribute nodes and unknown attribute nodes, and the impact of the latent variables on the overall nodes.

[0154] Specifically, in order to capture the differences in different feature dimensions and the potential relationships between nodes, the correlation coefficient matrix of the latent variable Z is calculated The specific formula is as follows:

[0155]

[0156] Where D is the characteristic dimension of Z, and Z i and Z j The average value of .

[0157] Weight the confidence weight matrix W and the correlation coefficient matrix C to obtain

[0158]

[0159] in, represents decentralization, and × represents matrix element-wise multiplication.

[0160] Finally, the dynamic embedding is merged with the original embedding to generate an overall representation:

[0161] Z=Z+∈B

[0162] Here, ∈ represents a small constant that determines the impact of the dynamic state on the overall node representation.

[0163] A fine-tuning method based on embedding space weighting is adopted to ensure the organic combination of local interactions and global features, which optimally serves the goal of the ESPC strategy.

[0164] In one embodiment, the learning of the graph autoencoder-decoder model further introduces a node homogeneity score for evaluating the consistency between adjacent nodes, including the following steps:

[0165] Based on the embedding features between nodes, the structural similarity of node embeddings in the embedding space is determined;

[0166] Designing a homogeneity score function for each node based on the structural similarity;

[0167] Using the homogeneity score function, constructing a consistency loss function based on the node homogeneity score;

[0168] When the sum of the refinement loss function and the consistency loss function converges, it is determined that the refinement loss function meets the preset condition.

[0169] In one embodiment, the learning of the graph autoencoder-decoder model further introduces a non-link similarity penalty for penalizing misleading similarities between non-link nodes, including the following steps:

[0170] Calculate the embedding similarity between unlinked node pairs, where unlinked node pairs are pairs of nodes in the graph that have similar embedding attributes but no association relationship;

[0171] Comparing the embedding similarity with a preset embedding threshold;

[0172] When the embedding similarity exceeds the embedding threshold, a non-link similarity penalty function for non-link node pairs is designed based on the embedding similarity to penalize the matched non-link node pairs;

[0173] Constructing a non-link similarity penalty loss function according to the non-link similarity penalty function;

[0174] When the sum of the refinement loss function, the consistency loss function and the non-link similarity penalty loss function converges, it is determined that the refinement loss function meets the preset condition.

[0175] In the embedding space, it is necessary to capture the complex relationships between node attributes and their corresponding connections in the graph. Furthermore, the heuristic that nodes with similar attributes in the graph should be close in the embedding space can be misleading, especially when the data is incomplete or corrupted.

[0176] To address the above two problems, two new concepts are introduced: Node Homogeneity Score (NHS) to evaluate the consistency between adjacent nodes, and Non-Link Similarity Penalty (NLSP) to penalize the misleading similarity between non-linked nodes, thereby improving the accuracy of missing attribute recovery and the robustness of graph embedding.

[0177] Specifically, node homogeneity is usually determined by the similarity of node embeddings in the embedding space. If the node embeddings of two nodes are very close, then they may have similar neighbor nodes or similar attributes in the graph and can be considered homogeneous nodes. Therefore, the node homogeneity score is introduced.

[0178] Taking into account the embedding features of the nodes, the structural similarity between nodes i and j is expressed by cosine similarity:

[0179]

[0180] Considering the embedding space and structure space, NHS can be expressed as:

[0181]

[0182] Nodes with higher NHS values ​​indicate that they already have higher homogeneity in their neighborhood; conversely, nodes with lower NHS values ​​should receive more attention when aggregating neighbor information to update the embedding feature Z, in order to improve the homogeneity of all nodes in the neighborhood.

[0183] Therefore, the loss function based on NHS can be expressed as:

[0184]

[0185] NHS provides an effective way to measure the consistency of node neighborhoods, making embedding learning more dynamic and adaptive by considering the homogeneity of neighborhoods.

[0186] Furthermore, since embedding learning changes the spatial distribution of the original attributes, there may be unlinked node pairs in the graph that have similar embedded attributes but are actually not associated, so a non-linked similarity penalty is introduced.

[0187] NLSP is implemented to penalize this misleading behavior to ensure more accurate representation in the embedding, where the similarity between non-linked nodes is expressed as:

[0188]

[0189] In this embodiment, it is defined that when the embedding similarity between node pairs that do not have a connection relationship in the graph exceeds a threshold τ, a penalty is imposed on them. The NLSP is expressed as:

[0190]

[0191] Therefore, the loss function based on NLS can be expressed as:

[0192]

[0193] NLSP allows for a clearer distinction between nodes that are similar only in terms of attributes but may not actually be related. By penalizing misleading similarities, the model becomes more robust to noisy and incomplete data, leading to better generalization in downstream tasks.

[0194] Furthermore, before introducing the non-link similarity penalty mechanism, the topological structure in the graph structure embedding space can be accurately described first, including the embedding space based on the embedding space weighted matrix containing the confidence weight matrix, merging the dynamic embedding with the original embedding, and generating an overall representation of the impact of the latent variable on the overall node, so that the structural description of the node embedding in the embedding space is more accurate, which is conducive to more accurately determining the structural similarity of the node embedding in the embedding space, and thus obtaining a more accurate homogeneity score for each node.

[0195] In one embodiment, the present application combines the loss function terms of the three strategies of TAAP, NHS, and NLSP into an overall loss function as the total loss function. The goal of the total loss function is to simultaneously consider the three strategies of TAAP, NHS, and NLSP in multi-task learning to maximize the accuracy of recovering the missing attribute graph. The total loss function is expressed as:

[0196]

[0197] Where, Used to calculate the mean square error of features before and after reconstruction; and There are two regularization losses used to introduce additional constraints to influence the learning process of GAE; λ1 and λ2 are hyperparameters used to ensure the best balance between different components.

[0198] To validate our proposed topology-driven attribute-missing graph learning method, we selected four publicly available graph datasets: Cora, Citeseer, Amac, and Amap. Each dataset contains essential information such as node, edge, and attribute features. The graph structures and node features in these datasets have been widely used in various tasks, including node classification, clustering, and representation learning. During validation, attribute features were masked to simulate missing features.

[0199] In the experiments on comparative methods, TDAR was benchmarked against various established baseline methods, as detailed below: NeighAgg: utilizes mean pooling to aggregate neighboring node features, focusing on one-hop neighbors. VAE: a generative model that captures latent instance representations, which in context helps reconstruct missing node attributes. GNN*: a top model representing well-known graph neural networks, such as GCN, GraphSAGE, and GAT, which are popular in various fields. GraphRNA&ARWMF: both are contemporary representation learning methods for feature generation. SAT: advocates sharing latent fields to train independent autoencoders, bridge functions, and graph structures. SVGA: a cutting-edge model that puts Gaussian Markov random fields into play to depict feature spaces across attributes and graph composition. ITR: provides an integrated solution that leverages the inherent topology of the graph to facilitate adaptive restoration of missing attributes. MATE: introduces a dual-view framework to support contrastive learning by leveraging attribute and topology view enhancements.

[0200] During the study, the dataset was split according to the SVGA settings, with the number of random seeds fixed at 72. The dataset was also divided and masked into 40% for training, 10% for validation, and 50% for testing. Of these, 40% of the training set consisted of known nodes, and the rest were unknown nodes with attribute masking.

[0201] Furthermore, the Adam optimizer was used for hyperparameter optimization. For the Cora and Citeseer datasets, the learning rate was set to 0.001. Both the encoder and decoder used a single-layer MLP with a dropout rate of 0.8. The latent layer dimension was set to 256, and training was performed for 2000 epochs. For the Amac and Amcp datasets, the learning rate was 0.01, the encoder used a two-layer GCN, and the decoder used a single-layer MLP. The dropout rate was set to 0.2, the latent layer dimension remained at 256, and training was performed for 400 epochs. Unless otherwise verified in specific experiments, hyperparameters were consistently set to λ1 = 0.1, λ2 = 0.1, l = 30, ε = 0.01, and α = 0.9.

[0202] To evaluate the quality of attribute reconstruction, configuration learning is regarded as a self-supervised graph learning task, and Recall@K and nDCG@K are mainly used as downstream metrics for evaluation, with K = {10, 20, 50}.

[0203] In the comparative experiments on feature reconstruction of attribute-missing graphs, a systematic process was adopted to evaluate and compare various cutting-edge techniques, as well as several widely recognized classical methods and some current leading algorithms such as SAT, SVGA, ITR, and MATE. This application and the above-mentioned existing algorithms were tested on four different datasets, and key performance indicators, especially Recall@k and nDCG@k, were reported. The results are as follows: Figure 3 shown.

[0204] Preliminary analysis shows that this application consistently performs well in benchmarks across all considered datasets. In contrast, methods such as NeighAggre and VAE perform poorly, a difference that may stem from their inability to fully mine and represent the key features of the data during the encoding phase. Although GNN*, GraphRNA, and ARWMF show some performance improvements in some aspects, they are still below expectations. Their limitations are mainly due to their graph neural network-based approach to learn the topological features of the data, but show obvious defects in modules specifically designed for graphs lacking attributes.

[0205] On the other hand, state-of-the-art methods such as SVGA, ITR, and MATE have demonstrated outstanding results in multiple experiments. Through in-depth exploration and careful design, these methods focus on addressing core issues and challenges related to missing attribute graphs, effectively mining the intrinsic properties of the data, and thus achieving impressive performance gains. However, it is worth noting that, in a comprehensive comparison of all these techniques, this application stands out due to its comprehensive optimization strategy.

[0206] This application proposes a topology-driven attribute missing graph learning method that is mainly used in the following fields:

[0207] Social network analysis: In social networks, some personal information of users may be incomplete, but this missing information can be predicted through the network structure and known attributes of this application;

[0208] Bioinformatics: For example, in a gene expression network, the functions of some genes may be unknown, but they can be inferred from the known functions of other genes in the network structure of this application;

[0209] Recommender systems: In a user-item interaction network, a user's preference for certain items may be unknown, but can be predicted by other known interactions in the network structure of this application;

[0210] Financial risk management: In a credit network, the credit status of some entities may be unknown, but can be inferred from the known credit status of other entities in the network structure of this application;

[0211] Internet of Things (IoT): In a network of IoT devices, some devices may lack data but can be supplemented by data from other devices in the network structure of this application.

[0212] In summary, a topology-driven attribute-missing graph learning method obtains the initial topology of the original graph data based on the original graph data with missing attributes, and constructs reconstructed attribute features, such as known attribute nodes, unknown attribute nodes, edge sets, the number of edges and other parameter information, as data for subsequent model learning; according to the initial topology, a topology-aware attribute propagation mechanism is introduced to perform attribute propagation, and the optimal solution of the attribute propagation process is solved by minimizing the Dirichlet energy, so as to achieve the smooth correlation between the Dirichlet energy and the attribute features on the graph, so as to consider the influence of the topological structure and the position of the adjacent nodes on the attribute-missing nodes, and perform attribute propagation according to the topological structure of the graph to initialize and refine the attributes of the missing nodes, thereby helping the attributes of the nodes to better reflect their positions and mutual relationships in the entire graph, reducing the mismatch problem between local attributes and the global graph structure, and ensuring that the subsequent graph autoencoder-decoder is smooth in the reconstruction process. The smooth changes of graph attributes in the process are conducive to making full use of the complex topological information of the graph; inputting the refined topology into the preset graph autoencoder-decoder model can transform the graph data into meaningful potential representations while maintaining attribute reconstruction, and designing a refined loss function based on the mean squared error between the real known attribute nodes and the refined attribute nodes in the refined topology, which helps to integrate the additional loss components related to different tasks, and finally form a cohesive optimization scheme, which enhances the adaptability of TDAR to multi-task learning, and then integrates the intrinsic attributes of nodes with their graph context, providing a comprehensive perspective for predicting missing attributes, ensuring the authenticity of nodes, not only focusing on the attributes of a single node, but also having advantages in capturing the interdependence between node attributes in a wider range and how they are affected by the entire graph structure, thereby improving the recovery accuracy of missing attributes of graph data.

[0213] This application first uses TAAP technology for detailed attribute pre-population; then, it injects credibility and similarity information related to node topological positions into latent variables and uses this as weight to update the embedding space; finally, it achieves precise feature reconstruction supervision by considering homogeneity and potential edge errors. Therefore, this application embodies the comprehensive performance improvement embodied by multi-dimensional, multi-task learning.

[0214] Compared with the existing technology, the technical solution of this application has the following significant advantages:

[0215] 1. Topology sensitivity: This application uses the Topology-Aware Attribute Propagation (TAAP) mechanism to prioritize graph topology. It comprehensively considers the interactions between nodes during node attribute recovery, enabling a more accurate depiction and utilization of graph structural information than traditional methods.

[0216] 2. Dynamic weight adjustment: Using the propagation confidence based on embedding space (ESPC) strategy, this application dynamically adjusts the relationship weights between nodes, which can more flexibly capture and maintain the complex and detailed relationships between nodes in the embedding space, thereby improving the accuracy of attribute recovery and feature learning;

[0217] 3. Multi-scale information fusion: This application adjusts weights by considering both local and global characteristics of nodes, effectively integrating information at different scales. The influence of both direct neighbors and remote nodes is balanced and accurately reflected.

[0218] 4. Refined embedding representation: Through a fine-tuning process, the combination of dynamic embeddings and original embeddings produces a comprehensive node representation that more fully reflects the attribute characteristics of the node and its position and role in the graph;

[0219] 5. Finer-grained attribute recovery: NHS simulates the microstructure of the graph in a finer-grained manner by ensuring the proximity of nodes with similar attributes in the embedding space, improving the accuracy of attribute recovery.

[0220] 6. Optimized node impact assessment: NLSP provides a penalty mechanism for non-directly connected node pairs, reducing the noise that these node pairs may cause in the embedding learning process, thereby improving the robustness of the learning model;

[0221] 7. Adaptability and flexibility: This application not only addresses the problem of missing attributes but also flexibly adapts to different graph structures and task requirements, thus possessing good generalization capabilities in a variety of practical applications.

[0222] 8. Enhanced interpretability: By introducing concepts such as Dirichlet energy minimization, this application enhances the interpretability of graph data analysis, making the learned features not only more robust mathematically but also easier to understand physically.

[0223] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0224] Reference Figure 4 The present application also provides a topology-driven attribute missing graph learning device, which corresponds to the topology-driven attribute missing graph learning method in the above embodiment. The topology-driven attribute missing graph learning device includes:

[0225] A topology structure module is used to obtain the initial topology of the original image data based on the original image data with missing attributes, and to construct a reconstructed attribute feature;

[0226] a topology refinement module, configured to introduce a topology-aware attribute propagation mechanism to perform attribute propagation based on the initial topology, iteratively update attribute features of nodes in the initial topology until an attribute feature that minimizes the Dirichlet energy is obtained, thereby obtaining a refined topology of the original graph data;

[0227] a model training module, configured to input the refined topology into a preset graph autoencoder-decoder model, and design a refinement loss function based on the mean squared error between real known attribute nodes and refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension;

[0228] A target model module is configured to output the current graph autoencoder-decoder model as an attribute-missing graph learning model when the refinement loss function satisfies a preset condition;

[0229] The attribute-missing graph learning module is used to input the graph data to be learned into the attribute-missing graph learning model, reconstruct the topology and node attributes of the graph data to be learned, and restore the missing attributes of the graph data to be learned.

[0230] Furthermore, a topology-driven attribute missing graph learning device also includes:

[0231] The NHS module is used to adopt the embedded space propagation confidence mechanism when the graph autoencoder-decoder model is learning, including calculating the shortest path from the unknown attribute node to the pre-specified known attribute node, quantifying the position confidence of the unknown attribute node, and constructing the unknown attribute node topology position function in the embedded space propagation; calculating the number of unknown attribute nodes directly connected to the known attribute node, quantifying the position confidence of the known attribute node, and constructing the known attribute node topology position function in the embedded space propagation; when the refined topology is input into the preset graph autoencoder-decoder model, based on the unknown attribute node topology position function and the known attribute node topology position function, the potential impact or context information of the known attribute nodes and the unknown attribute nodes in the original graph data is obtained.

[0232] The NHS module is also used to design unknown attribute node weight functions and known attribute node weight functions based on a preset distance attenuation factor; based on the weight values ​​corresponding to the row dimension expansion of the unknown attribute nodes and the weight values ​​corresponding to the row dimension expansion of the known attribute nodes, combined with the transposed matrix, a confidence weight matrix is ​​constructed; when the refined topology is input into the preset graph autoencoder-decoder model, the confidence weight matrix is ​​used to evenly capture the local information from the neighboring nodes and the global information related to the context information of the known attribute nodes and the unknown attribute nodes in the original graph data, thereby generating a dynamic hidden embedding.

[0233] The NHS module is also used to construct a correlation coefficient matrix of the latent variables based on the latent variables and their feature dimensions in the learning process of the graph autoencoder-decoder model; weight the confidence weight matrix and the correlation coefficient matrix to obtain an embedding space weighted matrix; merge the dynamic embedding with the original embedding according to the embedding space weighted matrix to generate an overall representation of the impact of the latent variables on the overall node; when the refined topology is input into the preset graph autoencoder-decoder model, the overall representation is used to capture the differences in different feature dimensions of the latent variables, the potential relationship between known attribute nodes and unknown attribute nodes, and the impact of the latent variables on the overall node.

[0234] Furthermore, a topology-driven attribute missing graph learning device also includes:

[0235] The NLSP module is configured to introduce a node homogeneity score to evaluate the consistency between adjacent nodes during learning of the graph autoencoder-decoder model, including determining the structural similarity of node embeddings in an embedding space based on embedding features between nodes; and designing a homogeneity score function for each node based on the structural similarity. The embedding space is based on an embedding space weighting matrix including a confidence weight matrix, merging dynamic embeddings with original embeddings to generate a holistic representation of the impact of latent variables on the entire node, thereby making the structural description of the node embeddings in the embedding space more accurate, facilitating more accurate determination of the structural similarity of the node embeddings in the embedding space, and thereby obtaining a more accurate homogeneity score for each node.

[0236] Using the homogeneity score function, constructing a consistency loss function based on the node homogeneity score;

[0237] When the sum of the refinement loss function and the consistency loss function converges, it is determined that the refinement loss function meets the preset condition.

[0238] The NLSP module is also used to introduce a non-link similarity penalty when learning a graph autoencoder-decoder model to penalize misleading similarities between non-link nodes, including calculating the embedding similarity between non-link node pairs, where non-link node pairs are node pairs in the graph that have similar embedding attributes but do not have an association relationship; comparing the embedding similarity with a preset embedding threshold; when the embedding similarity exceeds the embedding threshold, designing a non-link similarity penalty function for non-link node pairs based on the embedding similarity to penalize the matched non-link node pairs; constructing a non-link similarity penalty loss function based on the non-link similarity penalty function; when the sum of the refinement loss function, the consistency loss function and the non-link similarity penalty loss function converges, it is determined that the refinement loss function meets the preset conditions.

[0239] Regarding the specific limitations of a topology-driven attribute missing graph learning device, please refer to the above limitations of a topology-driven attribute missing graph learning method, which will not be repeated here.

[0240] Each module in the aforementioned topology-driven attribute missing graph learning device can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in hardware form, or can be stored in a memory in the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0241] In one embodiment, a computer device is provided, which may be a server. The computer device includes a processor, memory, a network interface, and a database connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When executed by the processor, the computer program implements any of the above-mentioned topology-driven attribute missing graph learning methods.

[0242] In one embodiment, a computer-readable storage medium is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, any one of the above-mentioned topology-driven attribute missing graph learning methods is implemented.

[0243] In one embodiment, a computer program product is provided, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements any of the above-mentioned topology-driven attribute missing graph learning methods.

[0244] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium, including a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the various embodiments of the present application. When the computer program is executed, it may include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0245] Those skilled in the art will clearly understand that for the sake of convenience and brevity in description, only the division of the above-mentioned functional units and modules is used as an example. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above.

Claims

1. A topology-driven attribute missing graph learning method, characterized in that: The following steps are included: Based on the original image data with missing attributes, obtaining the initial topology of the original image data and constructing a reconstructed attribute feature; According to the initial topology, a topology-aware attribute propagation mechanism is introduced to perform attribute propagation, and attribute features of nodes in the initial topology are iteratively updated until attribute features that minimize the Dirichlet energy are obtained, thereby obtaining a refined topology of the original graph data; The refined topology is input into a preset graph autoencoder-decoder model, and a refined loss function is designed based on the mean square error between the real known attribute nodes and the refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension; wherein the learning of the graph autoencoder-decoder model also adopts an embedded space propagation confidence mechanism to calculate the shortest path from the unknown attribute node to the pre-specified known attribute node, quantify the position confidence of the unknown attribute node, and construct a topological position function of the unknown attribute node in the embedded space propagation; calculate the number of unknown attribute nodes directly connected to the known attribute node, quantify the position confidence of the known attribute node, and construct a topological position function of the known attribute node in the embedded space propagation; when the refined topology is input into the preset graph autoencoder-decoder model, based on the unknown attribute node topological position function and the known attribute node topological position function, the potential influence or context information of the known attribute nodes and the unknown attribute nodes in the original graph data is obtained; When the refined loss function satisfies a preset condition, the current graph autoencoder-decoder model is output as the attribute missing graph learning model; The graph data to be learned is input into the attribute-missing graph learning model, the topology and node attributes of the graph data to be learned are reconstructed, and the missing attributes of the graph data to be learned are restored.

2. The topology-driven attribute missing graph learning method according to claim 1 is characterized in that: When the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential influence or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes: According to the preset distance attenuation factor, the unknown attribute node weight function and the known attribute node weight function are designed; Based on the weight values ​​corresponding to the row dimension expansion of unknown attribute nodes and the weight values ​​corresponding to the row dimension expansion of known attribute nodes, combined with the transposed matrix, a confidence weight matrix is ​​constructed; When the refined topology is input into the preset graph autoencoder-decoder model, the confidence weight matrix is ​​used to balance the local information from neighboring nodes and the global information related to the context information of the known attribute nodes and unknown attribute nodes in the original graph data, thereby generating a dynamic hidden embedding.

3. The topology-driven attribute missing graph learning method according to claim 2 is characterized in that: When the refined topology is input into a preset graph autoencoder-decoder model, the step of obtaining potential influence or context information of known attribute nodes and unknown attribute nodes in the original graph data based on the unknown attribute node topology position function and the known attribute node topology position function further includes: Based on the latent variables and their feature dimensions in the learning process of the graph autoencoder-decoder model, construct a correlation coefficient matrix of the latent variables; Weighting the confidence weight matrix and the correlation coefficient matrix to obtain an embedding space weighted matrix; Merging the dynamic embedding with the original embedding according to the embedding space weighting matrix to generate an overall representation of the impact of the latent variable on the entire node; When the refined topology is input into a preset graph autoencoder-decoder model, the overall representation is used to capture the differences in different feature dimensions of the latent variables, the potential relationships between known attribute nodes and unknown attribute nodes, and the impact of the latent variables on the overall nodes.

4. The topology-driven attribute missing graph learning method according to claim 1, characterized in that: The learning of the graph autoencoder-decoder model also introduces a node homogeneity score to evaluate the consistency between adjacent nodes, including the following steps: Based on the embedding features between nodes, the structural similarity of node embeddings in the embedding space is determined; Designing a homogeneity score function for each node based on the structural similarity; Using the homogeneity score function, constructing a consistency loss function based on the node homogeneity score; When the sum of the refinement loss function and the consistency loss function converges, it is determined that the refinement loss function meets the preset condition.

5. The topology-driven attribute missing graph learning method according to claim 4 is characterized in that: The learning of the graph autoencoder-decoder model also introduces a non-link similarity penalty to penalize misleading similarities between non-link nodes, including the following steps: Calculate the embedding similarity between unlinked node pairs, where unlinked node pairs are pairs of nodes in the graph that have similar embedding attributes but no association relationship; Comparing the embedding similarity with a preset embedding threshold; When the embedding similarity exceeds the embedding threshold, a non-link similarity penalty function for non-link node pairs is designed based on the embedding similarity to penalize the matched non-link node pairs; Constructing a non-link similarity penalty loss function according to the non-link similarity penalty function; When the sum of the refinement loss function, the consistency loss function and the non-link similarity penalty loss function converges, it is determined that the refinement loss function meets the preset condition.

6. A topology-driven attribute missing graph learning device, characterized in that: Used to perform the topology-driven attribute missing graph learning method according to any one of claims 1 to 5, comprising: A topology structure module is used to obtain the initial topology of the original image data based on the original image data with missing attributes, and to construct a reconstructed attribute feature; a topology refinement module, configured to introduce a topology-aware attribute propagation mechanism to perform attribute propagation based on the initial topology, iteratively update attribute features of nodes in the initial topology until an attribute feature that minimizes the Dirichlet energy is obtained, thereby obtaining a refined topology of the original graph data; a model training module, configured to input the refined topology into a preset graph autoencoder-decoder model, and design a refinement loss function based on the mean squared error between real known attribute nodes and refined attribute nodes in the refined topology, wherein the encoder maps the refined topology of the original graph data to a latent dimension, and the decoder reconstructs the topology and node attributes of the original graph data from the latent dimension; A target model module is configured to output the current graph autoencoder-decoder model as an attribute-missing graph learning model when the refinement loss function satisfies a preset condition; The attribute-missing graph learning module is used to input the graph data to be learned into the attribute-missing graph learning model, reconstruct the topology and node attributes of the graph data to be learned, and restore the missing attributes of the graph data to be learned.

7. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

9. A computer program product, characterized in that The invention comprises a computer program, which implements the steps of the method according to any one of claims 1 to 5 when the computer program is executed by a processor.

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