Attribute missing graph clustering asymmetric encoding graph completion method and system

Abstract

The application provides a property missing graph clustering asymmetric encoding graph completion method, belongs to the field of machine learning and graph learning, generates an adjacency graph, a hypergraph embedding; the hypergraph embedding is decomposed into hypergraph unique features and shared features, a propagation loss of the hypergraph to the adjacency graph is calculated, and an alignment loss is calculated; the adjacency graph and the hypergraph embedding are decoded respectively, a reconstructed graph of the adjacency graph and the hypergraph is obtained, and adjacency graph and hypergraph generation losses are calculated; the adjacency graph and the hypergraph embedding are fused, the fused features are decoded to obtain reconstructed features, a generation loss of the reconstructed features and the adjacency graph embedding is calculated, the adjacency graph and hypergraph generation losses and the generation loss of the reconstructed features and the adjacency graph embedding are weightedly fused to obtain a total generation loss; the alignment loss and the total generation loss are summed, and when the total loss is minimum, a trained encoder is obtained; the property missing graph is input into the trained encoder to generate an embedded graph after completion; the application also provides a graph completion system; and the problem of property missing of deep graph clustering is solved.

Description

Technical Field

[0001] This invention relates to the fields of machine learning and graph learning technology, and in particular to a graph completion method and system for asymmetric encoding of graph clustering with missing attributes. Background Technology

[0002] The problem of missing attributes is prevalent in deep graph clustering (DGC), typically manifesting as incomplete node features due to data acquisition limitations, privacy constraints, or sensor malfunctions. This widespread lack of attributes severely hinders the effectiveness of existing DGC methods in real-world applications such as community detection and proteomics analysis, reducing their efficiency and even rendering them unreliable.

[0003] The main methods for handling deep graph clustering with missing attributes include generative learning, contrastive learning, and hybrid methods combining contrastive and generative learning. Several representative methods have been proposed within these paradigms to address the deep graph clustering problem. The paper "Multi-view Contrastive Graph Clustering" (Erlin Pan, Zhao Kang, 35th Conference on Neural Information Processing Systems, NeurIPS 2021, 2021) proposes a deep graph clustering method that uses contrastive learning to learn a consensus graph. The paper "Heterogeneous Graph Neural Network via Attribute Completion" (Di Jin, Cuiying Huo, Chundong Liang, Liang Yang, In Proceedings of the Web Conference 2021 (WWW '21). Association for Computing Machinery, New York, NY, USA, 391-400, 2021) improves the effectiveness of generative learning by integrating multi-view information to complete missing graph attributes. Among them, the mutual view comparison generation framework algorithm proposes a mutual view comparison generation framework, which explicitly utilizes similarity graph representation and achieves significant performance.

[0004] Existing methods primarily construct training views by adding noise to the graph topology. However, this noise-based view construction strategy suffers from a fundamental technical flaw when dealing with the problem of missing attributes:

[0005] (1) The randomness of perturbation significantly affects model performance: During the noise addition process, the model cannot distinguish which nodes or edges in the graph are associated with important attribute information. This indiscriminate perturbation will cause some important attribute information to be destroyed and covered, making it difficult for the model to extract effective features from the incomplete attributes, resulting in a decrease in the quality of the generated node embeddings.

[0006] (2) Deviation from the real missing pattern: The missing node attributes in the real world often have a specific pattern. However, the randomly added noise is seriously inconsistent with the real situation, which can easily lead the model to learn the wrong completion pattern.

[0007] In summary, existing methods based on noisy views fail to effectively utilize graph structures to guide and compensate for missing attributes. Instead, they introduce additional noise due to blind perturbation, resulting in unsatisfactory clustering accuracy and robustness in scenarios with missing attributes. Summary of the Invention

[0008] The technical problem to be solved by this invention is: how to solve the problem of missing attributes in depth map clustering.

[0009] This invention solves the above-mentioned technical problems through the following technical solution: a graph completion method for asymmetric encoding of attribute-missing graph clustering, the method comprising:

[0010] Construct a hypergraph from the adjacency graph, and input the adjacency graph and hypergraph into the encoder to generate adjacency graph embedding and hypergraph embedding respectively;

[0011] The hypergraph embedding is decomposed into hypergraph-specific features and shared features. The adjacent graph embedding is predicted based on the hypergraph-specific features and shared features respectively. The propagation loss from the hypergraph to the adjacent graph is calculated. The alignment loss is calculated based on the propagation loss from the hypergraph to the adjacent graph and the propagation loss from the adjacent graph to the hypergraph.

[0012] The adjacency graph embedding and hypergraph embedding are decoded separately to obtain the reconstructed graphs of the adjacency graph and hypergraph, respectively. The adjacency graph generation loss and hypergraph generation loss are calculated. The adjacency graph embedding and hypergraph embedding are fused to obtain fused features. The fused features are decoded to obtain reconstructed features. The generation loss of the reconstructed features and the adjacency graph embedding are calculated. The adjacency graph generation loss, hypergraph generation loss and the generation loss of the reconstructed features and the adjacency graph embedding are weighted and fused to obtain the total generation loss.

[0013] The alignment loss and the total generation loss are linearly weighted and summed to obtain the total loss. When the total loss is minimized, the trained encoder is obtained.

[0014] Input the attribute-missing graph into the trained encoder to generate the graph-complete embedding.

[0015] This invention constructs a hypergraph from the adjacency graph. The hypergraph encoding effect can reflect the relationship between individuals and the overall structure at the node level, thereby extending the topological semantics of the traditional adjacency graph to the environmental semantics. By decomposing the hypergraph embedding into hypergraph-specific features and shared features, the shared features maintain the high-order associations of the original graph (such as the community to which the node belongs and indirect connection relationships), while the hypergraph-specific features only eliminate the direct influence of the original edges (only retaining the similarity derived from node attributes), which can weaken the excessive interference of sparse edges on clustering in small data. Predicting adjacency graph embeddings based on hypergraph-specific and shared features respectively can effectively improve knowledge complementarity between two views. An asymmetric propagation alignment mechanism is used in the knowledge complementarity part. Compared to other methods limited by topological semantics, the asymmetric propagation alignment mechanism enables the model to learn the overall structure of the graph, thus making the completion results more reflective of the real situation and improving the model's learning effect on the original graph data. A dual embedding generation mechanism is used to fuse adjacency graph embeddings and hypergraph embeddings, capturing both attribute and structural features of the embeddings. By comparing the original graph reconstructed by the model with the real original graph, the model's ability to retain information about graph embeddings and its learning ability from graph data are reflected and optimized.

[0016] Preferably, the process of decomposing hypergraph embeddings into hypergraph-specific features and shared features includes:

[0017] Initialize the learnable matrix Learnable matrices Decompose into orthogonal matrices and upper triangular matrix ;

[0018] orthogonal matrix With hypergraph embedding Multiplication yields shared features Hypergraph embedding Subtract shared features Obtaining hypergraph-specific features .

[0019] This invention embeds hypergraphs by introducing a learnable orthogonal decomposer. Decomposed into hypergraph-specific features Shared features This decomposer will extract hypergraph-specific features. Shared features Isolation and projection components enable cross-view knowledge transfer, while the residual part retains unique characteristics.

[0020] Preferably, the process of calculating the propagation loss from the hypergraph to the adjacency graph includes:

[0021] Supergraph-specific features Shared features Input the lightweight residual predictor separately to generate the embedded data. , ;

[0022] Computational embedding Loss of adjacency graph embedding Embedded Loss of adjacency graph embedding ;

[0023] Punishment hypergraph-specific features Contribution to the loss, based on the loss , Calculate the propagation loss from the hypergraph to the adjacency graph.

[0024] Preferably, the propagation loss from the hypergraph to the adjacency graph. for:

[0025]

[0026] loss for:

[0027]

[0028] in, For the mask matrix, This represents the number of nodes.

[0029] This invention uses the mean square error of a mask to calculate the loss, through a mask matrix. Filter out nodes with missing attributes to ensure reliable learning signals. Used to punish features unique to hypergraphs. Contribution to the loss.

[0030] Preferably, the calculation process for the propagation loss from the adjacency graph to the hypergraph includes: dividing the adjacency graph... Input a lightweight residual predictor to generate an embedding. Computational embedding With hypergraph embedding The alignment loss is used to obtain the propagation loss from the adjacency graph to the hypergraph. for:

[0031]

[0032] in, For the mask matrix, This represents the number of nodes.

[0033] Preferably, alignment loss for:

[0034]

[0035] in, The propagation loss from the supergraph to the adjacency graph. The weight coefficients represent the propagation loss from the adjacency graph to the hypergraph. Greater than the weight coefficient .

[0036] Weighting coefficients in the asymmetric propagation alignment mechanism of this invention Greater than the weight coefficient It places greater emphasis on the prediction task of hypergraph embedding to adjacency graph embedding, enhancing the model's learning of environmental semantics.

[0037] Preferably, the adjacency graph generation loss and the hypergraph generation loss are calculated in the same way, and the adjacency graph generation loss or the hypergraph generation loss is... for:

[0038]

[0039] in, This represents an adjacency graph or hypergraph. and Labels representing sample pairs, For decoder, This is the sigmoid function.

[0040] Preferably, the generation loss of reconstructed features and adjacency graph embeddings for:

[0041]

[0042] in, N The total number of samples, i For sample index, j Indexed by category / feature dimension, X For real labels logits , M For the mask matrix, Indicates the first i Each sample, in the mask M Under the action logits go through softmax After that, the first one obtained j The probability values ​​of each category, For prediction logits .

[0043] Preferably, the total generation loss for:

[0044]

[0045] in, , , These are the adjacency graph generation loss, hypergraph generation loss, and generation loss for reconstructed features and adjacency graph embedding, respectively. , , These are the weighting coefficients.

[0046] This invention also provides a graph completion system for asymmetric encoding of attribute-missing graph clustering, the system comprising:

[0047] The encoding module is used to construct a hypergraph based on the adjacency graph. The adjacency graph and the hypergraph are input into the encoder to generate the adjacency graph embedding and the hypergraph embedding, respectively.

[0048] The asymmetric propagation alignment module is used to decompose the hypergraph embedding into hypergraph-specific features and shared features, predict the adjacent graph embedding based on the hypergraph-specific features and shared features respectively, calculate the propagation loss from the hypergraph to the adjacent graph, and calculate the alignment loss based on the propagation loss from the hypergraph to the adjacent graph and the propagation loss from the adjacent graph to the hypergraph.

[0049] The dual-embedding generation module is used to decode the adjacency graph embedding and the hypergraph embedding respectively to obtain the reconstructed graphs of the adjacency graph and the hypergraph, and to calculate the adjacency graph generation loss and the hypergraph generation loss. The adjacency graph embedding and the hypergraph embedding are fused to obtain the fused feature. The fused feature is decoded to obtain the reconstructed feature. The generation loss of the reconstructed feature and the adjacency graph embedding are calculated. The adjacency graph generation loss, the hypergraph generation loss and the generation loss of the reconstructed feature and the adjacency graph embedding are weighted and fused to obtain the total generation loss.

[0050] The training module is used to linearly weight and sum the alignment loss and the total generation loss to obtain the total loss. When the total loss is minimized, the trained encoder is obtained.

[0051] The inference module is used to input the attribute-missing graph into the trained encoder and generate an embedding with the graph completed.

[0052] The advantages provided by this invention are:

[0053] 1. This invention constructs an algorithmic framework for unsupervised graph representation learning using adjacency matrices and hypergraph matrices. Within this framework, an asymmetric propagation alignment (APA) mechanism based on dual-attribute prediction is designed to decompose effective components from hypergraph embeddings and transfer them to adjacency embeddings. Furthermore, we envision designing a dual embedding generation (DEG) mechanism to independently generate attribute features from heterogeneous views while jointly integrating structural information. Thus, during compression, the algorithm preserves real-world information while enhancing the consistency and effectiveness of dual-view embeddings.

[0054] 2. In this invention, the hypergraph construction is directly based on the combination of different-order neighborhoods of nodes. Essentially, it directly reflects the relationship between individuals and the environment through hyperedges (traditional adjacency graphs focus on the connection relationships of nodes through binary edges). Compared with randomly constructed similar graphs, it can better focus on the key information needed for attribute missing repair. In addition, the heterogeneity of hypergraph modalities compared to ordinary graphs allows hypergraphs to provide stronger contrast differences than views of the same modality, enhancing the effectiveness of contrastive learning. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the graph completion method for asymmetric encoding of attribute-missing graph clustering provided in Embodiment 1 of the present invention;

[0056] Figure 2 This is a flowchart of the graph completion method for asymmetric encoding of attribute-missing graph clustering provided in Embodiment 1 of the present invention;

[0057] Figure 3 This is a schematic diagram of the graph completion system for asymmetric encoding of attribute-missing graph clustering provided in Embodiment 2 of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0059] Example 1

[0060] like Figure 1 and Figure 2 As shown, this embodiment provides a graph completion method for asymmetric encoding of clustered graphs with missing attributes, which can complete missing information in community detection. For community detection data, nodes correspond to each detected community individual, node attribute vectors correspond to the statistical information of the community individual, including gender, age, occupation, address, etc., and edges correspond to whether there are relationships between individuals; a graph with completely missing attributes corresponds to situations where there are gaps in personnel information in community detection. The final result obtained by the graph completion method of this invention displays the completed "non-existent" personnel information in community detection, returning a complete predicted graph of community information. The method includes the following steps:

[0061] Step 1: By using the adjacency graph The association matrix is ​​constructed by combining the adjacent neighbors of each node into hyperedges. Constructing a hypergraph SuperMap A set of hyperedges that can connect multiple nodes Composition, correlation matrix Capture these relationships, among which, Represents a node Belongs to superedge . express A set of nodes Denotes the set of edges. It is a node attribute matrix. It is a node of 3D eigenvectors. Adjacency matrix. Encoding graph topology, Represents a node and There are edges between them. Vectors As a mask matrix, it is used to mark nodes with observed attributes: if the attribute has been observed, then If the attribute is missing, then .

[0062] The training dataset is obtained based on the adjacency graph and hypergraph. The dataset is preprocessed into .npy files, retaining data labels and content to facilitate reading and loading of the graph data structure, and to aid in subsequent graph type conversion and encoding. The preprocessed dual topological information is encoded by inputting the adjacency graph and hypergraph into the encoder to generate adjacency graph embeddings. Hypergraph embedding :

[0063]

[0064]

[0065] The input feature matrix can be obtained by processing the initial node attributes using a perturbation-based interpolation method. Encoder Graph Attention Networks (GATs) and encoders can be used. Hypergraph Attention Network (HGAT) can be used to capture higher-order correlations.

[0066] Step 2: Embed the hypergraph Decomposed into hypergraph-specific features Shared features Based on the unique features of hypergraphs Shared features Embedding of adjacency graphs Perform prediction to obtain the embedding , The propagation loss from the hypergraph to the adjacency graph is calculated. Based on the propagation loss from the hypergraph to the adjacency graph and from the adjacency graph to the hypergraph, the alignment loss is calculated. An asymmetric propagation alignment mechanism is used to align the embeddings of two nodes, aiming to preserve the hypergraph embeddings. The inherent environment-related semantics in hypergraph embeddings. Embedded with Adjacency Graph This enables cross-view knowledge propagation, enhancing relevant features to obtain richer semantic information. It also allows for the comprehensive calculation of loss functions for both traditional graph structures and hypergraph structures.

[0067] Embedding the hypergraph Decomposed into hypergraph-specific features Shared features The process includes:

[0068] Initialize the learnable matrix identity matrix During forward propagation, a learnable matrix can be generated. Decomposed into orthogonal matrices using QR decomposition. and upper triangular matrix ;

[0069] orthogonal matrix With hypergraph embedding Multiplication yields shared features Shared features Features for sharing adjacency graph information; Hypergraph embedding Subtract shared features Obtaining hypergraph-specific features :

[0070]

[0071] This invention embeds hypergraphs by introducing a learnable orthogonal decomposer. Decomposed into hypergraph-specific features Shared features This decomposer will extract hypergraph-specific features. Shared features Isolation and projection components enable cross-view knowledge transfer, while the residual part retains unique characteristics.

[0072] The process of calculating the propagation loss from a hypergraph to an adjacency graph includes:

[0073] Supergraph-specific features Shared features Input the lightweight residual predictor separately to generate the embedded data. , :

[0074]

[0075]

[0076] , Both are lightweight residual predictors.

[0077] Computational embedding Loss of adjacency graph embedding Embedded Loss of adjacency graph embedding ;

[0078] Punishment hypergraph-specific features Contribution to the loss, based on the loss , Calculate the propagation loss from the hypergraph to the adjacency graph.

[0079] This invention uses the mean square error of a mask to calculate the loss, through a mask matrix. Nodes with missing attributes are filtered out to ensure reliable learning signals, while penalizing hypergraph-specific features. Contribution to the loss, i.e. .

[0080] Propagation loss from hypergraph to adjacency graph for:

[0081]

[0082] loss for:

[0083]

[0084] in, For the mask matrix, This represents the number of nodes.

[0085] The propagation loss from the adjacency graph to the hypergraph is calculated using the mask mean square error. The calculation process includes: dividing the adjacency graph... Input lightweight residual predictor Perform cross-view prediction and generate embeddings Promote adjacency graph embedding With hypergraph embedding Effective knowledge transfer between them, lightweight residual predictor It can avoid the overgeneralization of node embedded information.

[0086] Computational embedding With hypergraph embedding The alignment loss is used to obtain the propagation loss from the adjacency graph to the hypergraph. for:

[0087]

[0088] in, For the mask matrix, This represents the number of nodes.

[0089] Alignment loss for:

[0090]

[0091] in, The propagation loss from the supergraph to the adjacency graph. The weight coefficients represent the propagation loss from the adjacency graph to the hypergraph. Greater than the weight coefficient .

[0092] Step 3: For the encoding matrix in Step 1, use the decoding module to convert it into a complete graph, and compare it with the original graph to calculate the loss function: embed the adjacency graph separately. Hypergraph embedding Decoding is performed to obtain the reconstructed graphs of the adjacency graph and the hypergraph, and the adjacency graph generation loss and hypergraph generation loss are calculated; the average fused adjacency graph embedding is then performed. and hypergraph embedding The fused features are obtained and input into the feature decoder, which can be a multilayer perceptron (MLP). The decoder obtains the reconstructed features, and the generation loss of the reconstructed features and the adjacency graph embedding is calculated using KL divergence. Weighted fusion of adjacency graph generation loss, hypergraph generation loss, and generation loss The total generation loss is obtained. .

[0093] To improve generation stability, this invention employs positive and negative sampling during structure generation. For adjacency graphs, adjacency graph embedding... Edges in the graph are positive samples, and random non-edges are negative samples. For hypergraphs, hypergraph embeddings... Hyperedges in the graph are considered positive samples, while negative samples are generated by replacing half of the nodes in each hyperedge with other nodes in the graph. The adjacency graph generation loss and hypergraph generation loss are calculated in the same way. for:

[0094]

[0095] in, This represents an adjacency graph or hypergraph. and Labels representing sample pairs, For decoder, This is the sigmoid function.

[0096] Reconstruction features and the generation loss of adjacency graph embedding for:

[0097]

[0098] in, N The total number of samples, i For sample indexes, from the 1st to the 2nd. N One sample. j Index the category / feature dimensions, from the 1st to the Dth dimension (e.g., the number of categories in a classification task, or the dimension of a vector space).

[0099] for Softmax The function transforms an input vector into a probability distribution. Specifically, for a vector... ,have:

[0100]

[0101] X It is a real label logits , shape is The matrix has one sample per row and one category / dimension per column. M It is a mask matrix. Point to the first element in the matrix i line, number j The elements of the column. Indicates: For the first i Each sample, in the mask M Under the action logits go through softmax Then, the probability value of the j-th category is obtained.

[0102] For model prediction logits (or estimated value), shape and X same.

[0103] Total generation loss for:

[0104]

[0105] in, , , These are the adjacency graph generation loss, hypergraph generation loss, and generation loss for reconstructed features and adjacency graph embedding, respectively. , , These are the weighting coefficients.

[0106] This invention is based on a dual-embedding generation mechanism, which minimizes information loss by capturing attribute and structural features during the embedding process. It is based on dual-embedding adjacency graph embedding. and hypergraph embedding The combined information and dual-embedding generation mechanism reconstruct the original graph within a unified generation framework by preserving and integrating topological structure and node attribute features.

[0107] Step 4: Alignment loss Total generation loss Perform a linear weighted summation to obtain the total loss. When the total loss When the value is minimized, the trained encoder is obtained.

[0108] Total loss for:

[0109]

[0110] Steps 2 and 3 are two loss function calculation modules that run in parallel and independently, and their order can be interchanged. Ultimately, they provide the loss value for step 4, enhancing the training effect.

[0111] Step 5: Input the attribute-missing graph into the trained encoder to generate the graph-completed embeddings. Apply the K-means algorithm to the graph-completed embeddings to infer cluster labels, following... The tags are primarily used for unsupervised performance evaluation during experiments.

[0112] This invention constructs a hypergraph from adjacency graphs. The hypergraph encoding effect can reflect the relationship between individuals and the overall structure at the node level, thus extending the topological semantics of traditional adjacency graphs to environmental semantics. This avoids the bias that the model tends to complete the topological structure task rather than predict the attribute task during training, and also avoids the instability of heterogeneous graph construction caused by random noise. This invention decomposes hypergraph embedding into hypergraph-specific features and shared features. Shared features maintain the high-order associations of the original graph (such as the community to which nodes belong and indirect connection relationships), while hypergraph-specific features only eliminate the direct influence of the original edges (only retaining the similarity derived from node attributes), which can weaken the excessive interference of sparse edges on clustering in small datasets. Predicting adjacency graph embeddings based on hypergraph-specific and shared features respectively can effectively improve knowledge complementarity between two views. The knowledge complementarity part uses the Asymmetric Propagation Alignment Mechanism (APA). APA emphasizes the prediction task of hypergraph embeddings onto adjacency graphs, enhancing the model's learning of environmental semantics. Compared to other methods limited by topological semantics, APA enables the model to learn the overall structure of the graph, making the completion results more reflective of reality and improving the model's learning effect on the original graph data. Based on the Dual-Embedding Generation Mechanism (DEG), adjacency graph embeddings and hypergraph embeddings are fused to capture both attribute and structural features of the embeddings. By comparing the original graph reconstructed by the model with the real original graph, the model's ability to retain information about graph embeddings and its learning ability from graph data are reflected and optimized.

[0113] Furthermore, hypergraph construction is directly based on the combination of different-order neighborhoods of nodes, essentially reflecting the relationship between individuals and the environment directly through hyperedges (traditional adjacency graphs focus on the connectivity of nodes through binary edges). Compared to randomly constructed similar graphs, it can better focus on the key information needed for attribute missing repair. In addition, the heterogeneity of hypergraph modalities compared to ordinary graphs allows hypergraphs to provide stronger contrast differences than views of the same modality, enhancing the effectiveness of contrastive learning.

[0114] Example 2

[0115] like Figure 3 As shown, this embodiment provides a graph completion system for asymmetric encoding of attribute-missing graph clustering, including:

[0116] The encoding module is used to construct a hypergraph based on the adjacency graph. The adjacency graph and the hypergraph are input into the encoder to generate the adjacency graph embedding and the hypergraph embedding, respectively.

[0117] The asymmetric propagation alignment module is used to decompose the hypergraph embedding into hypergraph-specific features and shared features. It predicts the adjacent graph embedding based on the hypergraph-specific features and shared features respectively, calculates the propagation loss from the hypergraph to the adjacent graph, and calculates the alignment loss based on the propagation loss from the hypergraph to the adjacent graph and the propagation loss from the adjacent graph to the hypergraph.

[0118] The process of decomposing hypergraph embeddings into hypergraph-specific features and shared features includes:

[0119] Initialize the learnable matrix Learnable matrices Decompose into orthogonal matrices and upper triangular matrix ;

[0120] orthogonal matrix With hypergraph embedding Multiplication yields shared features Hypergraph embedding Subtract shared features Obtaining hypergraph-specific features .

[0121] The process of calculating the propagation loss from a hypergraph to an adjacency graph includes:

[0122] Supergraph-specific features Shared features Input the lightweight residual predictor separately to generate the embedded data. , ;

[0123] Computational embedding Loss of adjacency graph embedding Embedded Loss of adjacency graph embedding ;

[0124] Punishment hypergraph-specific features Contribution to the loss, based on the loss , Calculate the propagation loss from the hypergraph to the adjacency graph.

[0125] Propagation loss from hypergraph to adjacency graph for:

[0126]

[0127] loss for:

[0128]

[0129] in, For the mask matrix, This represents the number of nodes.

[0130] The calculation process for the propagation loss from an adjacency graph to a hypergraph includes: dividing the adjacency graph... Input a lightweight residual predictor to generate an embedding. Computational embedding With hypergraph embedding The alignment loss is used to obtain the propagation loss from the adjacency graph to the hypergraph. for:

[0131]

[0132] in, For the mask matrix, This represents the number of nodes.

[0133] Alignment loss for:

[0134]

[0135] in, The propagation loss from the supergraph to the adjacency graph. The weight coefficients represent the propagation loss from the adjacency graph to the hypergraph. Greater than the weight coefficient .

[0136] The dual-embedding generation module is used to decode the adjacency graph embedding and the hypergraph embedding respectively to obtain the reconstructed graphs of the adjacency graph and the hypergraph, and to calculate the adjacency graph generation loss and the hypergraph generation loss. The adjacency graph embedding and the hypergraph embedding are fused to obtain the fused feature. The fused feature is decoded to obtain the reconstructed feature. The generation loss of the reconstructed feature and the adjacency graph embedding are calculated. The adjacency graph generation loss, the hypergraph generation loss and the generation loss of the reconstructed feature and the adjacency graph embedding are weighted and fused to obtain the total generation loss.

[0137] The adjacency graph generation loss and the hypergraph generation loss are calculated in the same way. for:

[0138]

[0139] in, This represents an adjacency graph or hypergraph. and Labels representing sample pairs, For decoder, This is the sigmoid function.

[0140] Reconstruction features and the generation loss of adjacency graph embedding for:

[0141]

[0142] in, N The total number of samples, i For sample indexes, from the 1st to the 2nd. N One sample. j Index the category / feature dimensions, from the 1st to the Dth dimension (e.g., the number of categories in a classification task, or the dimension of a vector space).

[0143] for Softmax The function transforms an input vector into a probability distribution. Specifically, for a vector... ,have:

[0144]

[0145] X It is a real label logits , shape is The matrix has one sample per row and one category / dimension per column. M It is a mask matrix. Point to the first element in the matrix i line, number j The elements of the column. Indicates: For the first i Each sample, in the mask M Under the action logits go through softmax After that, the first one obtained j The probability values ​​of each category. For model prediction logits (or estimated value), shape and X same.

[0146] The training module is used to train the alignment loss. Total generation loss Perform a linear weighted summation to obtain the total loss. When the total loss When the value is minimized, the trained encoder is obtained; the purpose of the training module is to minimize the total loss. Total loss For alignment loss Total generation loss linear sum:

[0147]

[0148]

[0149] in, , , These are the adjacency graph generation loss, hypergraph generation loss, and generation loss for reconstructed features and adjacency graph embedding, respectively. , , These are the weighting coefficients.

[0150] The inference module is used to input the attribute-missing graph into the trained encoder and generate an embedding with the graph completed.

[0151] Comparative experiment

[0152] Table 1 shows the percentage of completeness achieved by the method of this invention and existing methods for missing datasets. HyperAEOurs in Table 1 represents the method of this invention. Existing methods include: Hard Sample Aware Network (HSAN), Multi-view graph imputation network (MATE), Alignment and Uniformity Enhanced Graph Masked Autoencoders (AUG-MAE), Text-enhanced Domain Adaptation Recommendation (TDAR) for addressing data sparsity and implicit feedback issues in recommendation systems, Graph Clustering Completion Algorithm MAGI, and Model View Controller Gateway (MVCG).

[0153] Table 1 shows the datasets in the first column. The Cora dataset contains 2708 scientific publications divided into 7 categories, the Citeseer dataset contains 3312 scientific publications divided into 6 categories, the ACM dataset comes from a paper network, and the AMAP dataset is extracted from the Amazon co-purchase graph, where nodes represent products, edges represent whether two products are frequently co-purchased, features represent product reviews encoded with bag-of-words, and labels are predefined product categories. The second column shows the metrics, where ACC represents precision, NMI (Normalized Mutual Information) represents standardized mutual information, used to measure the consistency between two clustering results, ARI (Adjusted Rand Index) represents the adjusted Rand index, used to measure the consistency of sample pair splits in two clustering results, and F1 is a comprehensive metric representing the harmonic mean of precision and recall. Columns three through eight show the comparison results of existing implementation methods. Columns nine and ten show the ablation experiment results. In column nine, "w / o Hyper" indicates that the experimental hypergraph was replaced with a homogeneous adjacency graph, and in column ten, "w / o APA" indicates that the asymmetric propagation alignment module (APA) was removed. The last column shows the experimental results using the method of this invention.

[0154] Table 1. Percentage of completeness of missing datasets achieved by the method of this invention compared to existing methods.

[0155]

[0156] As shown in Table 1, bold data represents the best experimental results, and underlined data represents the second-best results. Compared with other baseline methods, HyperAE demonstrated best performance on all evaluation metrics across the four datasets, proving its significant advantage in graph-independent completion tasks. Specifically, on the Cora dataset, HyperAE achieved an accuracy of 68.95%, a 3.45 percentage point improvement over the second-best method, MVCG (65.50%). On the more challenging Citeseer dataset, this method also maintained its leading position, achieving an accuracy at least 4.7% higher than all baseline methods.

[0157] The second section of the table verifies the effectiveness of the Hypergraph Structure and Attribute Alignment Module (APA) in this technical solution through ablation experiments. As shown in Table 1, the complete model (HyperAE) outperforms the baseline method on all evaluation metrics; when the Attribute Alignment Module (w / o APA) is removed, the model performance drops significantly; and after removing the Hypergraph View (w / o Hyper), the model performance deteriorates further. It should be noted that the removal of the Dynamic Edge Generator (DEG), a core component of constraint structure information, will cause model training to fail, and therefore it was not included in the ablation experiments.

[0158] Experimental results show that both the attribute alignment module and the hypergraph view effectively improve model performance. This demonstrates that the proposed technical solution is an indivisible whole; removing any component will cause performance to degrade to a level comparable to the baseline method, thus verifying the effectiveness of the hypergraph view and the two innovative mechanisms, as well as the necessity of their synergistic effect.

[0159] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A graph completion method based on asymmetric encoding of clustered graphs with missing attributes, characterized in that: The methods include: Construct a hypergraph from the adjacency graph, and input the adjacency graph and hypergraph into the encoder to generate adjacency graph embedding and hypergraph embedding respectively; The hypergraph embedding is decomposed into hypergraph-specific features and shared features. The adjacent graph embedding is predicted based on the hypergraph-specific features and shared features respectively. The propagation loss from the hypergraph to the adjacent graph is calculated. The alignment loss is calculated based on the propagation loss from the hypergraph to the adjacent graph and the propagation loss from the adjacent graph to the hypergraph. Decode the adjacency graph embedding and the hypergraph embedding respectively to obtain the reconstructed graph of the adjacency graph and the reconstructed graph of the hypergraph, and calculate the adjacency graph generation loss and the hypergraph generation loss; The adjacency graph embedding and hypergraph embedding are fused to obtain fused features. The fused features are decoded to obtain reconstructed features. The generation loss of the reconstructed features and the adjacency graph embedding is calculated. The generation loss of the adjacency graph, the hypergraph, and the reconstructed features and the adjacency graph embedding are weighted and fused to obtain the total generation loss. The alignment loss and the total generation loss are linearly weighted and summed to obtain the total loss. When the total loss is minimized, the trained encoder is obtained. Input the attribute-missing graph into the trained encoder to generate the graph-complete embedding.

2. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: The process of decomposing hypergraph embeddings into hypergraph-specific features and shared features includes: Initialize the learnable matrix Learnable matrices Decompose into orthogonal matrices and upper triangular matrix ; orthogonal matrix With hypergraph embedding Multiplication yields shared features Hypergraph embedding Subtract shared features Obtaining hypergraph-specific features .

3. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: The process of calculating the propagation loss from a hypergraph to an adjacency graph includes: Supergraph-specific features Shared features Input the lightweight residual predictor separately to generate the embedded data. , ; Computational embedding Loss of adjacency graph embedding Embedded Loss of adjacency graph embedding ; Punishment hypergraph-specific features Contribution to the loss, based on the loss , Calculate the propagation loss from the hypergraph to the adjacency graph.

4. The graph completion method for asymmetric encoding of clustered graphs with missing attributes according to claim 1, characterized in that: Propagation loss from hypergraph to adjacency graph for: loss for: in, For the mask matrix, This represents the number of nodes.

5. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: The calculation process for the propagation loss from an adjacency graph to a hypergraph includes: dividing the adjacency graph... Input a lightweight residual predictor to generate an embedding. Computational embedding With hypergraph embedding The alignment loss is used to obtain the propagation loss from the adjacency graph to the hypergraph. for: in, For the mask matrix, This represents the number of nodes.

6. The graph completion method for asymmetric encoding of clustered graphs with missing attributes according to claim 1, characterized in that: Alignment loss for: in, The propagation loss from the supergraph to the adjacency graph. The weight coefficients represent the propagation loss from the adjacency graph to the hypergraph. Greater than the weight coefficient .

7. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: The calculation method for adjacency graph generation loss and hypergraph generation loss is the same. for: in, This represents an adjacency graph or hypergraph. and Labels representing sample pairs, For decoder, This is the sigmoid function.

8. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: Reconstruction features and the generation loss of adjacency graph embedding for: in, N The total number of samples, i For sample index, j Indexed by category / feature dimension, X For real labels logits , M For the mask matrix, Indicates the first i Each sample, in the mask M Under the action logits go through softmax After that, the first one obtained j The probability values ​​of each category, For prediction logits .

9. The graph completion method for asymmetric encoding of attribute-missing graph clustering according to claim 1, characterized in that: Total generation loss for: in, , , These are the adjacency graph generation loss, hypergraph generation loss, and generation loss for reconstructed features and adjacency graph embedding, respectively. , , These are the weighting coefficients.

10. A graph completion system based on asymmetric encoding of clustered graphs with missing attributes, characterized in that: The system includes: The encoding module is used to construct a hypergraph based on the adjacency graph. The adjacency graph and the hypergraph are input into the encoder to generate the adjacency graph embedding and the hypergraph embedding, respectively. The asymmetric propagation alignment module is used to decompose the hypergraph embedding into hypergraph-specific features and shared features, predict the adjacent graph embedding based on the hypergraph-specific features and shared features respectively, calculate the propagation loss from the hypergraph to the adjacent graph, and calculate the alignment loss based on the propagation loss from the hypergraph to the adjacent graph and the propagation loss from the adjacent graph to the hypergraph. The dual-embedding generation module is used to decode the adjacency graph embedding and the hypergraph embedding respectively to obtain the reconstructed graph of the adjacency graph and the reconstructed graph of the hypergraph, and to calculate the adjacency graph generation loss and the hypergraph generation loss. The adjacency graph embedding and hypergraph embedding are fused to obtain fused features. The fused features are decoded to obtain reconstructed features. The generation loss of the reconstructed features and the adjacency graph embedding is calculated. The generation loss of the adjacency graph, the hypergraph, and the reconstructed features and the adjacency graph embedding are weighted and fused to obtain the total generation loss. The training module is used to linearly weight and sum the alignment loss and the total generation loss to obtain the total loss. When the total loss is minimized, the trained encoder is obtained. The inference module is used to input the attribute-missing graph into the trained encoder and generate an embedding with the graph completed.

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