Graph enhancement method and system based on core subgraph retention and structure compression, and storage medium

Abstract

The invention relates to a graph enhancement method and system based on core subgraph retention and structure compression and a storage medium, and relates to the technical field of graph contrast learning. According to the method, a graph augmentation strategy combining core subgraph extraction and information compression is provided for solving the problems that in existing graph contrast learning, random augmentation is prone to damaging a semantic structure, and redundant information is introduced. The method comprises the following steps: encoding an input graph by using a flexible connection GNN, and identifying and retaining a core sub-graph with a stable structure and dense semantics through adaptive frequency spectrum filtering; and an enhanced view is generated on the basis of the core subgraph, semantic consistency is kept by using comparison consistency loss, and compression loss based on an information bottleneck principle is introduced to remove redundant information. According to the method, noise can be effectively suppressed while the semantic core of the graph is reserved, the discrimination and generalization performance of representation are improved, and the method is suitable for various graph representation learning tasks such as molecular modeling, social network analysis and recommendation systems.

Description

Technical Field

[0001] This invention relates to the field of graph comparison learning technology, and in particular to a graph enhancement method, system, and storage medium based on core subgraph preservation and structural compression. Background Technology

[0002] Graph Contrastive Learning (GCL) is a self-supervised learning framework that generates multiple augmented views of unlabeled graph data and maximizes the representational consistency between them to obtain high-quality graph representations. This technique has achieved significant results in tasks such as molecular modeling, social network analysis, and recommender systems.

[0003] In graph data augmentation (GCL), graph data augmentation is a crucial step affecting representation quality. Early methods often employed random perturbation strategies such as node deletion, edge sampling, and feature masking. While simple to implement and easy to deploy, these methods can easily disrupt important substructures in the graph that carry key semantic information. For example, in molecular graphs, ring structures often correspond to important chemical properties; their disruption can lead to semantic drift, causing the model's learned representation to deviate from the original semantics. In recent years, researchers have proposed some learnable graph augmentation strategies, such as subgraph preservation based on saliency selection and structure simplification based on edge pooling. These methods can, to some extent, highlight information-dense regions, thereby generating semantically consistent augmented views. However, these methods generally only focus on maintaining consistency between views, neglecting the suppression of redundant or irrelevant information. This results in the generated augmented views still containing a large number of useless components, reducing the model's generalization ability.

[0004] Therefore, there is an urgent need for a graph augmentation method that can balance semantic core preservation and structural compression during the augmentation process, so as to improve the model's representation ability and generalization performance. Summary of the Invention

[0005] The purpose of this invention is to provide a graph augmentation method based on core subgraph preservation and structural compression, which simultaneously achieves accurate preservation of the graph's core semantics and effective compression of redundant structures, thereby improving the generalization ability and robustness of graph augmentation models in downstream tasks. The core idea of ​​this invention is to combine core subgraph extraction with contrastive compression optimization to form a closed-loop augmentation and optimization mechanism: first, information-dense and robust core subgraphs are dynamically identified based on spectral features and structural similarity; then, compression constraints are introduced through the information bottleneck principle to effectively suppress irrelevant information in the augmented view. This method can generate compact, high-quality graph representations while maintaining semantic consistency, and is suitable for various application scenarios such as molecular modeling and social network analysis.

[0006] A graph augmentation method based on core subgraph preservation and structure compression includes the following steps:

[0007] Step 1: Obtain the original graph, and dynamically adjust the message passing strength of each edge using soft propagation GNN encoding to obtain the spectral representation before graph filtering. ;

[0008] Step 2: Perform adaptive spectral filtering on the spectrum representation before the graph filtering operation. Perform spectral transformation and dynamic denoising to obtain the spectral representation after graph filtering. ;

[0009] Step 3: For each node in the original graph, calculate the consistency of its spectral representation before and after the graph filtering operation to obtain the core score of that node and acquire the core subgraph. ;

[0010] Step 4: In the core subgraph Based on this, a joint training strategy of contrastive learning and information compression is introduced to generate high-quality graphs that combine semantic integrity and structural compactness.

[0011] Further, step 3 specifically involves: for each node in the graph, calculating the consistency of its spectral representation before and after the graph filtering operation to obtain the core score of that node; for each edge in the graph, taking the average of the core scores of the nodes at its two ends as the core score of that edge; performing differentiable sampling on the nodes and edges based on the Gumbel-Sigmoid strategy; and extracting the core subgraph based on the sampling results. .

[0012] Furthermore, in step 1, from the first The GNN layer directs to the first Output of message passing in +1 GNN layer for:

[0013]

[0014] in, Representing node characteristics, It is a learnable weight matrix. For activation function, This is the adjacency matrix of the original graph. This represents element-wise multiplication. Used to assign continuous and differentiable transmission strength to edges. This is the soft connection matrix of the original graph;

[0015] The spectrum representation before the graph filtering operation Embedding nodes using Chebyshev polynomials The node embedding H, obtained by projecting onto the spectral domain, is the output of message passing.

[0016] Furthermore, the spectrum representation after the filtering operation in step 2... for:

[0017]

[0018]

[0019] in, This is the denoised spectrum representation. For the sigmoid function, For temperature parameters, It is random noise. Learnable threshold, learnable spectral filter .

[0020] Furthermore, the core score calculation method for the node in step 3 is as follows:

[0021]

[0022] The core score of the edge is calculated as follows:

[0023]

[0024] in, , They are the edges The core scores of the two endpoints.

[0025] Furthermore, step 4 specifically includes:

[0026] Step 4.1: Given a containing Image For each graph in the dataset, retain its core subgraph. and in Two independent perturbations are applied. and This generates an enhanced view. Get different enhanced views of the same graph , ;

[0027] Step 4.2: Combine different enhanced views of the same graph , Input the encoder to obtain the representation vector. and Calculate the consistency loss. ;

[0028] Step 4.3: Introduce the information bottleneck principle, define the compression loss as the KL divergence between the posterior and prior distributions, and calculate the compression loss. ;

[0029] Step 4.4: Weight and fuse the consistency loss and compression loss to calculate the overall loss. .

[0030] Further, step 4.1: Obtain different enhanced views of the same graph. , Specifically:

[0031]

[0032] Step 4.2: The ratio consistency loss is defined as:

[0033]

[0034] in, This is a temperature coefficient used to adjust the smoothness of the distribution;

[0035] Step 4.3: Compression Loss Defined as:

[0036]

[0037] Among them, the prior distribution posterior distribution , It is the mean vector. The covariance matrix is ​​used for both, and they are encoded using a graph encoder. and readout function The results were obtained through joint modeling;

[0038] The overall loss in step 4.4 Defined as:

[0039]

[0040] in, To balance the contrast consistency loss and compression loss hyperparameters.

[0041] Furthermore, in step 4.3, the covariance matrix The non-negativity is ensured by using a softplus transformation.

[0042] A graph augmentation system based on core subgraph preservation and structure compression includes a soft propagation GNN encoding module, an adaptive spectral filtering module, a core subgraph extraction module, and a contrastive compression optimization module;

[0043] The soft-propagation GNN encoding module is used to dynamically adjust the message passing strength of each edge, obtaining the spectral representation before graph filtering. ;

[0044] The adaptive spectrum filtering module is used to perform spectrum representation before graph filtering. Perform spectral transformation and dynamic denoising to obtain the spectral representation after graph filtering. ;

[0045] The core subgraph extraction module is used to calculate the consistency of the spectral representation of each node in the original graph before and after the graph filtering operation, and obtain the core score of the node to acquire the core subgraph. ;

[0046] The comparison compression optimization module is used in the core subgraph Based on this, a joint training strategy of contrastive learning and information compression is introduced to generate high-quality graphs that combine semantic integrity and structural compactness.

[0047] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a graph enhancement method based on core subgraph preservation and structural compression.

[0048] The beneficial effects of this invention are as follows:

[0049] 1. For the first time, a dual constraint of preserving the core subgraph and compressing the structure is introduced into the graph augmentation strategy, which effectively avoids the problems of semantic drift and retention of redundant information.

[0050] 2. By combining soft-propagation GNN with adaptive spectral filtering, the distinguishability of high and low frequency components is improved, and the ability to express graph structure features is enhanced.

[0051] 3. Compression constraints based on the information bottleneck principle enable the enhanced view to significantly improve the centrality and generalization performance of the representation while maintaining semantic integrity.

[0052] 4. Experimental results on multiple real datasets show that the present invention significantly outperforms existing mainstream methods in both representation quality and downstream task performance, verifying its effectiveness and universality. Attached Figure Description

[0053] Figure 1 This is a comparative diagram of the functions of the present invention compared with existing graph enhancement methods;

[0054] Figure 2 This is a framework diagram of the present invention; Detailed Implementation

[0055] The present invention will now be further described with reference to the accompanying drawings.

[0056] To enable those skilled in the art to better understand the technical direction of the present invention, the present invention is described in detail through specific embodiments. However, it should be understood that the specific embodiments are provided only for a better understanding of the present invention and should not be construed as limiting the present invention. In the description of the present invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0057] Before describing the technical solution of this invention, it is necessary to first explain the technical terms used in this invention: graph information bottleneck and Chebyshev polynomial.

[0058] (1) Information bottleneck of graph

[0059] The goal of the graph information bottleneck is to identify compressed and information-rich subgraphs from an input graph. Specifically, given an input graph... and its labels In this case, its core objective can be summarized as follows:

[0060]

[0061] in, These are Lagrange multipliers used to balance the two objective terms. The first term is the prediction term, which causes... Image Labels The first term is informative; the second term is a compression term, used to minimize... and Mutual information between them.

[0062] (2) Chebyshev polynomial

[0063] In frequency domain modeling of graphs, to avoid the high eigenvalue decomposition overhead of graph Fourier transform, this invention employs Chebyshev polynomials to map node representations from the spatial domain to the frequency domain. Its basic form is:

[0064]

[0065] in, express Chebyshev polynomial of order 1 Represented as nodes, Let be the order of the polynomial. To satisfy the stability requirement of the Chebyshev polynomial recursion, the polynomial should be defined within the numerically stable interval [-1, 1]. Therefore, this invention addresses the graph Laplace matrix. Normalization is performed, specifically in the following form:

[0066]

[0067] in, express The largest eigenvalue, It is the identity matrix. In practical applications, It can be approximated as a constant (e.g., 2), avoiding explicit eigenvalue calculation and further improving computational efficiency.

[0068] The following is in conjunction with the appendix Figure 2 The present invention will be further illustrated by the embodiments.

[0069] Please refer to Figure 2 This invention provides a graph enhancement method based on core subgraph preservation and structure compression, comprising the following steps:

[0070] Step S1: This step aims to identify and preserve the core semantic structure from the input graph while removing noise and redundancy. The input graph consists of a node feature matrix and an adjacency matrix. First, the adjacency matrix is ​​weighted and adjusted to weaken unimportant edge connections and strengthen structural information highly relevant to the task during subsequent message passing. Based on this, a multi-layer graph neural network is used for message aggregation and feature transformation to obtain preliminary embedded representations of the nodes. This process can integrate global contextual information while preserving local structural features, providing basic data for subsequent spectral analysis.

[0071] Step S2: This step introduces a joint training strategy of contrastive learning and information compression based on the core subgraph to simultaneously ensure the consistency and compactness of the representation. The system generates multiple enhanced views of the same input graph, strengthening semantic consistency by maximizing their similarity in the representation space, while using compression constraints to reduce unnecessary information retention, thereby improving the model's generalization ability and robustness.

[0072] Further, step S1 includes the following steps:

[0073] Step S101: Soft-propagation GNN encoding. In the traditional message passing mechanism of GNNs, nodes typically use fixed weights or uniform weighting when aggregating information from neighboring nodes. This can lead to the mixing of different frequency components, weakening the distinguishability of spectral features and potentially spreading noise throughout the entire graph. This step introduces a soft-connection matrix to dynamically adjust the message passing strength of each edge, thereby reducing noise interference during the encoding stage and providing a cleaner structural input for spectral analysis.

[0074] Under this mechanism, in step 1 from the first The GNN layer directs to the first Output of message passing in +1 GNN layer for:

[0075]

[0076] in, Representing node characteristics, It is a learnable weight matrix. For activation function, This is the adjacency matrix of the original graph. This represents element-wise multiplication. Used to assign continuous and differentiable transmission strength to edges. This is the soft connection matrix of the original graph;

[0077] The spectrum before filtering operation is shown in the figure. Embedding nodes using Chebyshev polynomials The node embedding H, obtained by projecting onto the spectral domain, is the output of message passing.

[0078] Step S102: Adaptive Spectral Filtering. In this step, the node embedding is first mapped to the frequency domain using Chebyshev polynomials. The energy distribution of different frequency components is obtained through spectral decomposition, and the importance of each frequency component is evaluated accordingly. The system introduces a selection mechanism based on differentiable threshold control, utilizing the relationship between task-related signals and frequency energy distribution to adaptively retain frequency components beneficial to the task and remove noise components that do not contribute positively to the model performance. This process effectively enhances the signal-to-noise ratio of the representation and reduces redundant information in the frequency domain. After the above operations, the present invention obtains the denoised spectral representation:

[0079]

[0080] in, It is the sigmoid function. For temperature parameters, Indicates random noise. It is a learnable threshold. The threshold is the learnable threshold.

[0081] This invention utilizes a learnable spectral filter. Multiplied by the denoised features This generates the spectral representation after the graph filtering operation. :

[0082]

[0083] Step S103: Core Sampling. Core nodes in the graph typically possess stronger expressive power, with more stable spectral representations and less susceptibility to noise interference, thus playing a crucial role in graph representation learning. In this step, the present invention performs a consistency measurement between the frequency domain representations before and after filtering to obtain the core score for each node:

[0084]

[0085] in, It's the sigmoid function, edge The core score is defined as the average of the endpoints: Nodes with high core scores will be retained, while low-scoring nodes will be discarded, thus forming a semantically dense and structurally compact core subgraph. During the generation of the core subgraph, the edge connections are adjusted accordingly to ensure that the subgraph maintains structural connectivity and stability. The final output core subgraph contains both the key information required for the task and eliminates useless structural parts.

[0086] Furthermore, in step S2, the specific steps are as follows:

[0087] Step S201: Compare and calculate the consistency loss. Using mutual information estimation, the semantic consistency between augmented views is optimized into InfoNCE loss, ensuring that different augmented views of the same graph have highly consistent representations in the semantic space, thereby improving the model's ability to preserve the semantic core.

[0088] First, given a containing Image For each graph in the dataset, this invention preserves its core subgraph. and in Two independent perturbations are applied. and This generates an enhanced view:

[0089]

[0090] These enhanced views are encoded and pooled to obtain a graph-level representation. and The consistency loss is defined as:

[0091]

[0092] in, It is a temperature coefficient used to adjust the smoothness of the distribution.

[0093] Step S202: Compressibility Loss Calculation. Based on the information bottleneck principle, the KL divergence between the core subgraph representation and the prior distribution is minimized. Redundant features and structures irrelevant to the task are removed from the enhanced view, ensuring that the generated representation retains core semantics while possessing structural compactness and high expressiveness. The compression loss is defined as:

[0094]

[0095] Among them, the prior distribution posterior distribution . It is the mean vector. The covariance matrix (this invention uses a softplus transformation to ensure its non-negativity) and the two are encoded by a graph encoder. and readout function The results were obtained through joint modeling.

[0096] Step S203: Joint Optimization. In this step, the consistency loss and compression loss are jointly optimized by balancing coefficients. Adjusting the relative importance of the two:

[0097]

[0098] This optimization process is executed end-to-end, ensuring that core subgraph extraction, frequency domain processing, and representation compression work together in the same training process, ultimately generating a high-quality graph representation that combines semantic integrity and structural compactness.

[0099] A graph augmentation system based on core subgraph preservation and structure compression includes a soft propagation GNN encoding module, an adaptive spectral filtering module, a core subgraph extraction module, and a contrastive compression optimization module;

[0100] The soft-propagation GNN encoding module is used to dynamically adjust the message passing strength of each edge, obtaining the spectral representation before graph filtering. ;

[0101] The adaptive spectrum filtering module is used to perform spectrum representation before graph filtering. Perform spectral transformation and dynamic denoising to obtain the spectral representation after graph filtering. ;

[0102] The core subgraph extraction module is used to calculate the consistency of the spectral representation of each node in the original graph before and after the graph filtering operation, and obtain the core score of the node to acquire the core subgraph. ;

[0103] The comparison compression optimization module is used in the core subgraph Based on this, a joint training strategy of contrastive learning and information compression is introduced to generate high-quality graphs that combine semantic integrity and structural compactness.

[0104] Example:

[0105] This invention evaluates the effectiveness of the proposed self-supervised framework CI-GCL in graph representation learning through empirical research. To verify its performance, CI-GCL is compared with state-of-the-art methods in unsupervised learning scenarios. These experiments aim to highlight CI-GCL's ability to rapidly learn robust and information-rich representations from complex graph structure data. This invention selects eight widely used real-world datasets across three application domains for experiments. Specifically, these include two molecular datasets (MUTAG, NCI1), four social network datasets (COLLAB, RDT-B, RDT-M5K, IMDB-B), and two bioinformatics datasets (PROTEINS, D&D).

[0106] 1.1 Baseline Method

[0107] The following models (including state-of-the-art and closely related models) were used as representative baselines to evaluate the performance of the proposed model.

[0108] • InfoGraph: InfoGraph maximizes the mutual information between graph-level representations and substructure representations at different scales.

[0109] • GraphCL: GraphCL employs various graph augmentation techniques to generate contrastive views for unsupervised representation learning.

[0110] • JOAO: JOAO uses GraphCL as a baseline model and automatically selects enhancements when performing contrastive learning.

[0111] • AD-GCL: AD-GCL adversarially optimizes the augmentation strategy to avoid redundant information. It designs a trainable edge-dropping augmentation algorithm for dynamic adjustment.

[0112] • SimGRACE: SimGRACE eliminates explicit data augmentation by perturbing encoder parameters.

[0113] This reduces computational load while maintaining performance.

[0114] • LG2AR: LG2AR is an end-to-end jointly trained learnable augmentation and encoder. It adjusts the augmentation strength through node dropping.

[0115] • GCS: GCS uses gradient-based saliency to preserve key structures. It assigns a drop probability based on the importance of nodes / edges.

[0116] • DRGCL: DRGCL decomposes features through causal reasoning. It distinguishes between invariant correlations and spurious correlations to obtain a better representation.

[0117] • DGPM: DGPM incorporates order-aware pre-training at the node / graph level. Frequent subgraphs enable regularization of the hierarchical structure learning.

[0118] • DP: DP adopts a spectral perspective to design a dual-view data augmentation strategy, which effectively improves the model's generalization ability in graph classification tasks.

[0119] • S-CGIB: S-CGIB introduces a subgraph conditional information bottleneck mechanism to pre-train molecular graphs, thereby enhancing the representation ability of GNNs in downstream tasks.

[0120] 1.2 Parameter Settings

[0121] This invention follows the standard evaluation protocol used in previous studies to ensure fair and consistent comparison results. All models are evaluated using 10-fold cross-validation, with the primary metric being the average classification accuracy over 10 runs. For supervised baseline models, this invention uses results reported in original papers whenever possible; if citation is not possible, the models are reimplemented based on their publicly available configurations and parameters are adjusted. The classification task is performed using LIBSVM, where the regularization parameter... from The model is selected from the set. The model in this invention uses a 4-layer GIN as the backbone encoder to maintain consistency among baseline models. The hidden layer dimension is set to 128, the batch size is 128, the learning rate is set to 0.001, and the final graph-level embedding dimension is set to 32.

[0122] 1.3 Overall Comparison

[0123] Table 1: Classification accuracy (%) of unsupervised representation learning on the TU dataset

[0124] Bold text indicates best performance, underlined text indicates second-best performance.

[0125]

[0126] Table 1 shows the classification results on multiple benchmark datasets. This invention has revealed several key results:

[0127] Excellent and consistent performance. CI-GCL achieves state-of-the-art results on all datasets, with significant improvements particularly on NCI1 (with high structural noise) and DD (with complex semantic patterns). These results demonstrate the discriminative power of the method presented in this invention, which significantly outperforms existing methods.

[0128] Core subgraph extraction reduces redundancy and noise. While methods such as GCS and DGPM extract key subgraphs based on structural saliency or semantic sensitivity, they lack explicit mechanisms to suppress redundant information, resulting in noisy patterns in the embeddings. CI-GCL addresses this issue with its core subgraph extraction module, which combines adaptive spectral filtering to remove high-frequency noise with a denoising contrastive strategy to identify highly "core" nodes. This enables the accurate extraction of substructures with low redundancy and high semantic density.

[0129] The compression term improves compactness and generalization ability. By introducing an information compression term into the contrastive objective function, CI-GCL suppresses redundant features and encourages attention to structural discriminative patterns. Compared to S-CGIB, which also employs the IB principle, CI-GCL explicitly integrates the compression function into view construction, filtering out irrelevant structures and emphasizing core semantics, thereby enhancing discriminative and generalization capabilities.

[0130] The dual mechanism improves the overall representation quality. CI-GCL jointly utilizes structural denoising and semantic compression to reduce redundancy while maintaining expressive power, thereby obtaining high-quality graph representations.

[0131] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A graph augmentation method based on core subgraph preservation and structural compression, characterized in that: Includes the following steps: Step 1: Obtain the original graph, and dynamically adjust the message passing strength of each edge using soft propagation GNN encoding to obtain the spectral representation before graph filtering. ; Step 2: Perform adaptive spectral filtering on the spectrum representation before the graph filtering operation. Perform spectral transformation and dynamic denoising to obtain the spectral representation after graph filtering. ; Step 3: For each node in the original graph, calculate the consistency of its spectral representation before and after the graph filtering operation to obtain the core score of that node and acquire the core subgraph. ; Step 4: In the core subgraph Based on this, a joint training strategy of contrastive learning and information compression is introduced to generate high-quality graphs that combine semantic integrity and structural compactness.

2. The graph enhancement method based on core subgraph preservation and structural compression according to claim 1, characterized in that: Step 3 specifically involves: for each node in the graph, calculating the consistency of its spectral representation before and after the graph filtering operation to obtain the core score of that node; for each edge in the graph, taking the average of the core scores of the nodes at both ends as the core score of that edge. Based on the Gumbel-Sigmoid strategy, the nodes and edges are sampled in a differentiable manner; Based on the sampling results, extract the core subgraph. .

3. The graph augmentation method based on core subgraph preservation and structural compression according to claim 1, characterized in that: In step 1, from the first The GNN layer directs to the first Output of message passing in +1 GNN layer for: in, Representing node characteristics, It is a learnable weight matrix. For activation function, This is the adjacency matrix of the original graph. This represents element-wise multiplication. Used to assign continuous and differentiable transmission strength to edges. This is the soft connection matrix of the original graph; The spectrum representation before the graph filtering operation Embedding nodes using Chebyshev polynomials The node embedding H, obtained by projecting onto the spectral domain, is the output of message passing.

4. The graph enhancement method based on core subgraph preservation and structural compression according to claim 3, characterized in that: The spectrum representation after filtering in step 2. for: in, This is the denoised spectrum representation. For the sigmoid function, For temperature parameters, It is random noise. Learnable threshold, learnable spectral filter .

5. The graph enhancement method based on core subgraph preservation and structural compression according to claim 4, characterized in that: The core score of the node in step 3 is calculated as follows: The core score of the edge is calculated as follows: in, , They are the edges The core scores of the two endpoints.

6. The graph enhancement method based on core subgraph preservation and structural compression according to claim 1, characterized in that: Step 4 specifically involves: Step 4.1: Given a containing Image For each graph in the dataset, retain its core subgraph. and in Two independent perturbations are applied. and This generates an enhanced view. Get different enhanced views of the same graph , ; Step 4.2: Combine different enhanced views of the same figure , Input to the encoder to obtain the representation vector. and Calculate the consistency loss. ; Step 4.3: Introduce the information bottleneck principle, define the compression loss as the KL divergence between the posterior and prior distributions, and calculate the compression loss. ; Step 4.4: Weight and fuse the consistency loss and compression loss to calculate the overall loss. .

7. The graph enhancement method based on core subgraph preservation and structural compression according to claim 6, characterized in that: Step 4.1: Obtain different enhanced views of the same image. , Specifically: Step 4.2: The ratio consistency loss is defined as: in, This is a temperature coefficient used to adjust the smoothness of the distribution; Step 4.3: Compression Loss Defined as: Among them, the prior distribution posterior distribution , It is the mean vector. The covariance matrix is ​​used for both, and they are encoded using a graph encoder. and readout function The results were obtained through joint modeling; The overall loss in step 4.4 Defined as: in, To balance the contrast consistency loss and compression loss hyperparameters.

8. The graph enhancement method based on core subgraph preservation and structural compression according to claim 7, characterized in that: In step 4.3, the covariance matrix The non-negativity is ensured by using a softplus transformation.

9. A graph enhancement system based on core subgraph preservation and structural compression, implementing the method described in any one of claims 1-8, characterized in that: It includes a soft-propagation GNN encoding module, an adaptive spectral filtering module, a core subgraph extraction module, and a contrastive compression optimization module; The soft-propagation GNN encoding module is used to dynamically adjust the message passing strength of each edge, obtaining the spectral representation before graph filtering. ; The adaptive spectrum filtering module is used to perform spectrum representation before graph filtering. Perform spectral transformation and dynamic denoising to obtain the spectral representation after graph filtering. ; The core subgraph extraction module is used to calculate the consistency of the spectral representation of each node in the original graph before and after the graph filtering operation, and obtain the core score of the node to acquire the core subgraph. ; The comparison compression optimization module is used in the core subgraph Based on this, a joint training strategy of contrastive learning and information compression is introduced to generate high-quality graphs that combine semantic integrity and structural compactness.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When executed by a processor, the computer program implements the steps of the method according to any one of claims 1 to 8.

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