Fair map representation obtaining method for clustering

Abstract

The invention discloses a fair graph representation obtaining method for clustering, and belongs to the technical field of graph neural networks, and the method comprises the steps: S1, carrying out the pre-training of a graph neural network encoder; s2, acquiring a view which has good clustering performance but does not consider fairness; s3, acquiring multiple views with different fair viewing angles; s4, distributing a weight parameter for each view, and integrating the embedding into a uniform expression in a weighted fusion mode; an initial view focusing clustering performance and a multi-dimensional fair enhanced view are constructed, fair clustering guidance, adversarial depolarization and a multi-view mutual information comparison module are combined to realize embedded fair optimization, and the performance of the initial view and the multi-view mutual information comparison module is balanced by using a weighted fusion strategy. The fairness index is obviously improved, and meanwhile the high clustering performance is kept.

Description

Technical Field

[0001] This invention belongs to the field of graph neural network technology, specifically relating to a fair graph representation acquisition method for clustering. Background Technology

[0002] Clustering is an unsupervised learning method that aims to divide samples in a dataset into several clusters, ensuring high similarity among samples within the same cluster and low similarity among samples in different clusters. In the real world, whether in business decisions, social services, or scientific research, the results of cluster analysis can have a profound impact on different groups. For example, fairness is particularly prominent in medical image analysis because the predictive performance of algorithms can vary significantly across different populations (such as gender, age, or identity). Addressing these fairness issues can improve the reliability and trustworthiness of models in clinical applications, ensuring that all patients receive equitable medical services. Furthermore, fairness is also an important component of legal and ethical requirements. Laws and regulations in many countries and regions require the prevention of discrimination, ensuring that everyone enjoys equal rights and opportunities. Ensuring fairness in the clustering process helps enhance the social responsibility of models, strengthens the credibility of results, and promotes social diversity and inclusion. In addition, improving the fairness of clustering algorithms can help relevant organizations and businesses comply with these laws and regulations, avoiding legal risks and reputational damage. As society's demands for algorithmic fairness increase, research on clustering fairness will become an important driving force for technological progress and social development.

[0003] In recent years, Graph Neural Networks (GNNs) have demonstrated significant advantages in clustering tasks due to their powerful graph structure learning and node representation generation capabilities. However, most existing works have not fully considered the impact of sensitive attributes on clustering results, potentially leading to unfair outcomes for certain groups. On the other hand, most existing fair clustering methods typically modify specific clustering algorithms, such as by introducing fairness constraints or adjusting the objective function. While these methods improve fairness to some extent, they suffer from poor generalization and are difficult to adapt to different clustering algorithms and application scenarios. More importantly, most of these methods fail to achieve a good trade-off between clustering performance and fairness, often sacrificing clustering performance for fairness, thus limiting their practical application value. Therefore, fairness has gradually become an important issue in the field of graph representation learning.

[0004] CN120745689A discloses a method and system for improving fairness in graph neural networks based on mutual information difference constraints of sensitive attribute subgroups. The method includes the following steps: parsing graph data to construct a node set and dividing it into sensitive attribute subgroups; using Bayesian smoothing to estimate the probability distribution of the subgroup prediction results; calculating the mutual information difference between the node prediction results and the sensitive subgroups as the node-level bias value, thereby generating a global average bias; integrating the global bias into the loss function, and using a dynamic weighting strategy to balance task loss and fairness constraints, thus optimizing the model parameters. The system includes: a node set construction module, a sensitive attribute subgroup analysis module, a node bias calculation module, a global constraint generation module, and a joint optimization training module. This invention overcomes the limitations of macroscopic statistics, integrates graph structure information to improve fairness optimization efficiency, and achieves accurate localization of node-level bias.

[0005] CN119005306A discloses a counterfactual fairness method for partially observed sensitive attributes based on graph representation learning. Borrowing the principle in graph neural networks that individuals with the same sensitive attributes tend to cluster together, a sensitive attribute estimator is deployed. This estimator accurately predicts the true sensitive attribute value of a node with a missing sensitive attribute, based on the non-sensitive attribute value of the node and the feature attribute values ​​of its neighboring nodes. After completion by the sensitive attribute estimator, the true graph data with the sensitive attributes completed is obtained, thus enabling the learning of counterfactual fairness graph representations for all nodes.

[0006] The aforementioned inventions aim to generate graph representations with fair properties in supervised learning node classification tasks using graph neural networks, but they cannot be adapted to fair clustering tasks in unsupervised learning scenarios. Summary of the Invention

[0007] To address the aforementioned issues, this application proposes a multi-view fair clustering method based on graph neural networks, aiming to generate graph representation embeddings that combine high clustering quality and fair information through a multi-view fusion strategy.

[0008] Specifically, based on the original single-view data, multiple views were designed and constructed in a targeted manner, including an initial view focused on high clustering performance and three views that enhance fairness from the perspectives of edge structure, node features, and a combination of the two.

[0009] Furthermore, this invention introduces a fair clustering guidance module, an adversarial debiasing module, and a multi-view mutual information comparison module, which are used to optimize the fairness of cluster assignment, reduce sensitive attribute information in the embedding, and maintain the consistency of information between views, respectively. Through a weighted fusion strategy, the embedding representations of each view are further integrated, ensuring that the fused embedding achieves the best balance between clustering performance and fairness. Experimental results on multiple benchmark datasets show that the fair graph representation embedding obtained by this method can be adapted to any common traditional clustering algorithm and achieves a good trade-off between fairness and clustering performance.

[0010] This invention discloses a fair graph representation acquisition method for clustering, the method comprising the following steps:

[0011] S1. Pre-train the graph neural network encoder, including learning low-dimensional representations of graph structure and node features by reconstructing the feature matrix and adjacency matrix;

[0012] S2. Based on the pre-trained encoder, a view with good clustering performance but without considering fairness is obtained. The clustering assignment is optimized by optimizing the joint loss function of reconstruction loss and clustering loss.

[0013] S3. Obtain multiple views with different fairness perspectives, including generating fair enhanced views from the perspectives of edge structure fairness, node feature fairness, and the combination of the two through collaborative training of the reconstruction module, fair clustering guidance module, adversarial debiasing module, and multi-view mutual information comparison module, and using a parameter isolation strategy to update specific parameters of the view.

[0014] S4. Assign a weight parameter to each view, and integrate the embeddings of multiple views into a unified graph representation through weighted fusion for clustering tasks. The weight parameter is determined by a performance evaluation optimization strategy.

[0015] Furthermore, S1 includes the following steps:

[0016] S11, Reconstruct the feature matrix;

[0017] The original graph data is fed into a graph neural network encoder to obtain its output prediction feature matrix. The Frobenius norm is used to measure the predicted feature matrix. With the original feature matrix The error between them is given by the following formula for the loss function:

[0018] (1),

[0019] S12, Reconstruct the adjacency matrix;

[0020] The original graph data is fed into a graph neural network encoder to obtain its output predicted adjacency matrix. The adjacency matrix is ​​predicted using binary cross-entropy. With the true adjacency matrix The difference between them is expressed by the following formula for the loss function:

[0021] (2),

[0022] Where n is the number of nodes in the graph data.

[0023] S13. Reconstruct the loss function by minimizing the overall loss function. To optimize model parameters, the model can simultaneously learn low-dimensional representations of graph structure and node features, providing a more discriminative embedding space for subsequent fair clustering tasks, thereby enabling pre-training of the model.

[0024] Furthermore, S2 includes the following steps:

[0025] S21. Further optimize the reconstruction loss of the pre-trained graph neural network encoder, and simultaneously input the encoder output embedding into a self-optimizing clustering module. The core objective of this module is to optimize the clustering assignment by minimizing the Kullback-Leibler (KL) divergence. Its loss function is defined as follows:

[0026] (3),

[0027] in Represents a node Assigned to cluster The soft assignment probability can be obtained using the following formula:

[0028] (4),

[0029] The above formula calculates the node embedding-based... With cluster center The normalized distance between them can then be used to obtain the target distribution using the following formula. :

[0030] (5),

[0031] in, Cluster The frequency of the target distribution. By using soft assignment probability Square normalization and cluster frequency are performed to balance the distribution among clusters and avoid clustering results that are biased towards a few clusters.

[0032] S22. By weighting and combining the reconstruction loss and clustering loss, a joint loss function for the current view is obtained and optimized:

[0033] (6),

[0034] in, It is a hyperparameter used to balance reconstruction loss and clustering loss.

[0035] Furthermore, S3 includes the following steps:

[0036] S31. A reconstruction module was designed, consistent with the goals of the pre-training stage and the high-cluster quality view acquisition stage, aiming to generate high-information-quality node embeddings by minimizing the reconstruction loss.

[0037] S32. A fair clustering guidance module was designed. The core objective is to ensure that the clustering allocation results are more balanced for groups with different sensitive attributes while guaranteeing the quality of clustering.

[0038] S33. An adversarial debiasing module was designed to ensure that the embedding of each view has more equitable information.

[0039] S34. A multi-view mutual information comparison module was designed to promote the similarity of the embedding of the same nodes between different views by using the idea of ​​contrastive learning.

[0040] S35. Train the GNN by combining the modules from three perspectives: considering only edge structure fairness, considering only node feature fairness, and considering both edge structure and node feature fairness.

[0041] Furthermore, in step S31:

[0042] Loss function of the reconstruction module The formula is as follows:

[0043] (7),

[0044] Where n is the number of nodes in the graph data, A and A' are the original adjacency matrix and the predicted adjacency matrix, respectively, and X and X' are the original feature matrix and the predicted feature matrix, respectively.

[0045] Furthermore, in step S32:

[0046] First, the nodes are calculated using the Student t distribution. Assigned to cluster soft assignment probability Its formula is:

[0047] (8),

[0048] in, It is the embedding representation of node $i$. It is a cluster The center vector, This represents the degrees of freedom of the Student t distribution, set to 1.

[0049] To ensure the fairness of the clustering results, the module also calculates the target distribution based on the sensitive attribute subgroups. Its formula is:

[0050] (9),

[0051] in, Represents a node The subgroup of sensitive attributes to which it belongs. For example, if the sensitive attribute is gender, then... This could be a male or female subgroup. Target distribution. By using soft assignment probability Squared normalization and subgroup frequencies are used in the calculation to balance the distribution of different sensitive attribute groups in the clustering results.

[0052] To optimize fair clustering, the results are optimized by minimizing the KL divergence, with the loss function defined as:

[0053] (10)

[0054] By minimizing the fair clustering loss, the module enables the prediction distribution to be optimized. Gradually approaching the target distribution This process enables the learning of more discriminative clustering information and effectively reduces the impact of sensitive attributes on the clustering results.

[0055] Furthermore, in step S33:

[0056] By leveraging the concept of adversarial learning, an adversarial model is introduced into the embedding of each view. Their goal is to maximize the prediction accuracy of sensitive attributes, and to counteract this, the current view will be gradually updated to reduce... and The bias in the adversarial model makes the adversarial model It is difficult to extract sensitive attribute information from this, thus making the embeddings of the current view more equitable. This process can be formally represented by the following optimization objective:

[0057] (11),

[0058] in, Represents a node The true sensitive attribute value, It is an adversarial model For nodes Predicted values ​​of sensitive attributes, The parameters represent the view embedding. This represents the parameters of the adversarial model.

[0059] Furthermore, in step S34:

[0060] This study utilizes contrastive learning to promote similarity in the embeddings of common nodes across views. Specifically, three sets of view pairs are constructed: , and For each pair of views, a GNN encoder with shared parameters is used to generate node embeddings for each view. By sharing parameters, the encoder can capture common information between views while preserving their individual characteristics. To bring the embeddings of the same nodes in different views closer together while pushing the embeddings of different nodes further apart, the contrastive loss is defined as:

[0061] (12)

[0062] in, This represents the temperature parameter.

[0063] In all nodes, the opposite and The overall comparison target is calculated above:

[0064] (13)

[0065] Furthermore, in step S35:

[0066] The process of generating a fair augmented view is achieved through the collaborative training of a reconstruction module, a fair clustering guidance module, an adversarial debiasing module, and a multi-view mutual information comparison module. This process employs a parameter isolation strategy, meaning that only the parameters emphasized by the current view are updated, while other parameters remain fixed. The total loss function for training the current view is:

[0067] (14).

[0068] It is important to emphasize that a parameter isolation strategy is employed during the generation of fairness-enhanced views. This means that only the parameters relevant to the current view are updated, while other parameters remain fixed. For example, when constructing a view with a fair edge structure, only the parameters related to the adjacency matrix A are updated, while the parameters of the node feature matrix X are fixed. Similarly, when constructing a view with fair node features, only the parameters related to X are updated, while the parameters of A are fixed. For views that enhance both edge structure and node features, the parameters related to both A and X are updated simultaneously. In this way, a view with significant fairness improvements is ultimately obtained: a view emphasizing fair graph structure, a view emphasizing fair feature representation, and a view that improves fairness from both perspectives.

[0069] Furthermore, the embedded representation of the original data under different views can be obtained through S3:

[0070] Original view embedding Fair edge structure view embedding Fair node feature view embedding Fair edge structure and node feature view embedding .in, Indicates the number of nodes. Indicates the embedding dimension.

[0071] Furthermore, the specific steps of S4 include:

[0072] S41. Assign a weight parameter to each view, and integrate these embeddings into a unified representation through weighted fusion.

[0073] S42. Finally, a graph representation with good clustering performance and good fairness is obtained.

[0074] Furthermore, in step S41:

[0075] The unified embedding is represented as:

[0076] (15)

[0077] in, These are weight parameters that satisfy... .

[0078] To determine the optimal combination of weight parameters, a performance evaluation-based optimization strategy was adopted. First, a weight parameter space was defined, where each parameter... The range of values ​​is And satisfy For each candidate combination of weight parameters, calculate its corresponding fused embedding representation. The goal is to find the optimal combination of weight parameters for the evaluation indicators.

[0079] Compared to existing technologies, the advantages of this invention are as follows: Addressing the challenges of balancing fairness and clustering performance, as well as insufficient generalization, in unsupervised graph clustering, this invention proposes a fair clustering method leveraging the multi-view approach. It constructs an initial view focused on clustering performance and a multi-dimensional fairness enhancement view, combining fair clustering guidance, adversarial debiasing, and multi-view mutual information comparison modules to achieve embedded fairness optimization. A weighted fusion strategy is then used to balance the performance of both approaches. This significantly improves fairness metrics while maintaining high clustering performance, and demonstrates good generalization and plug-and-play compatibility with common traditional clustering algorithms, thus promoting the practical application of fair graph learning technology. Attached Figure Description

[0080] Figure 1 This is a schematic diagram illustrating the framework and comparative learning process for obtaining multiple views from different fair perspectives in this invention. Detailed Implementation

[0081] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0082] Example: Figure 1 As shown: The fair graph representation acquisition method for clustering proposed in this embodiment specifically includes the following steps:

[0083] S1. Pre-train the graph neural network encoder, including learning low-dimensional representations of graph structure and node features by reconstructing the feature matrix and adjacency matrix;

[0084] S2. Based on the pre-trained encoder, a view with good clustering performance but without considering fairness is obtained. The clustering assignment is optimized by optimizing the joint loss function of reconstruction loss and clustering loss.

[0085] S3. Obtain multiple views with different fairness perspectives, including generating fair enhanced views from the perspectives of edge structure fairness, node feature fairness, and the combination of the two through collaborative training of the reconstruction module, fair clustering guidance module, adversarial debiasing module, and multi-view mutual information comparison module, and using a parameter isolation strategy to update specific parameters of the view.

[0086] S4. Assign a weight parameter to each view, and integrate the embeddings of multiple views into a unified graph representation through weighted fusion for clustering tasks. The weight parameter is determined by a performance evaluation optimization strategy.

[0087] Furthermore, S1 includes the following steps:

[0088] S11, Reconstruct the feature matrix;

[0089] The original graph data is fed into a graph neural network encoder to obtain its output prediction feature matrix. The Frobenius norm is used to measure the predicted feature matrix. With the original feature matrix The error between them is given by the following formula for the loss function:

[0090] (1),

[0091] S12, Reconstruct the adjacency matrix;

[0092] The original graph data is fed into a graph neural network encoder to obtain its output predicted adjacency matrix. The adjacency matrix is ​​predicted using binary cross-entropy. With the true adjacency matrix The difference between them is expressed by the following formula for the loss function:

[0093] (2),

[0094] Where n is the number of nodes in the graph data.

[0095] S13. Reconstruct the loss function by minimizing the overall loss function. To optimize model parameters, the model can simultaneously learn low-dimensional representations of graph structure and node features, providing a more discriminative embedding space for subsequent fair clustering tasks, thereby enabling pre-training of the model.

[0096] Furthermore, the specific steps of S2 include:

[0097] S21. Further optimize the reconstruction loss of the pre-trained graph neural network encoder, and simultaneously input the encoder output embedding into a self-optimizing clustering module. The core objective of this module is to optimize the clustering assignment by minimizing the Kullback-Leibler (KL) divergence. Its loss function is defined as follows:

[0098] (3),

[0099] in Represents a node Assigned to cluster The soft assignment probability can be obtained using the following formula:

[0100] (4),

[0101] The above formula calculates the node embedding-based... With cluster center The normalized distance between them can then be used to obtain the target distribution using the following formula. :

[0102] (5),

[0103] in, Cluster The frequency of the target distribution. By using soft assignment probability Square normalization and cluster frequency are performed to balance the distribution among clusters and avoid clustering results that are biased towards a few clusters.

[0104] S22. By weighting and combining the reconstruction loss and clustering loss, a joint loss function for the current view is obtained and optimized:

[0105] (6),

[0106] in, It is a hyperparameter used to balance reconstruction loss and clustering loss.

[0107] Furthermore, the specific steps of S3 include:

[0108] S31. A reconstruction module was designed, consistent with the goals of the pre-training stage and the high-cluster quality view acquisition stage, aiming to generate high-information-quality node embeddings by minimizing the reconstruction loss; the loss function of the reconstruction module... The formula is as follows:

[0109] (7),

[0110] Where n is the number of nodes in the graph data, A and A' are the original adjacency matrix and the predicted adjacency matrix, respectively, and X and X' are the original feature matrix and the predicted feature matrix, respectively.

[0111] S32. A fair clustering guidance module was designed. The core objective is to ensure that the clustering assignment results are more balanced for groups with different sensitive attributes while guaranteeing clustering quality. First, the nodes are calculated using the Student t-distribution. Assigned to cluster soft assignment probability Its formula is:

[0112] (8),

[0113] in, It is the embedding representation of node $i$. It is a cluster The center vector, This represents the degrees of freedom of the Student t distribution, set to 1.

[0114] To ensure the fairness of the clustering results, the module also calculates the target distribution based on the sensitive attribute subgroups. Its formula is:

[0115] (9),

[0116] in, Represents a node The subgroup of sensitive attributes to which it belongs. For example, if the sensitive attribute is gender, then... This could be a male or female subgroup. Target distribution. By using soft assignment probability Squared normalization and subgroup frequencies are used in the calculation to balance the distribution of different sensitive attribute groups in the clustering results.

[0117] To optimize fair clustering, the results are optimized by minimizing the KL divergence, with the loss function defined as:

[0118] (10)

[0119] By minimizing the fair clustering loss, the module enables the prediction distribution to be optimized. Gradually approaching the target distribution This process enables the learning of more discriminative clustering information and effectively reduces the impact of sensitive attributes on the clustering results.

[0120] S33. An adversarial bias removal module was designed to ensure that the embeddings of each view have more equitable information; adversarial learning was used to introduce an adversarial model into the embedding of each view. Their goal is to maximize the prediction accuracy of sensitive attributes, and to counteract this, the current view will be gradually updated to reduce... and The bias in the adversarial model makes the adversarial model It is difficult to extract sensitive attribute information from this, thus making the embeddings of the current view more equitable. This process can be formally represented by the following optimization objective:

[0121] (11),

[0122] in, Represents a node The true sensitive attribute value, It is an adversarial model For nodes Predicted values ​​of sensitive attributes, The parameters represent the view embedding. This represents the parameters of the adversarial model.

[0123] S34. A multi-view mutual information comparison module was designed, utilizing the idea of ​​contrastive learning to promote the similarity of embeddings of common nodes among views; specifically, three sets of view pairs were constructed: , and For each pair of views, a GNN encoder with shared parameters is used to generate node embeddings for each view. By sharing parameters, the encoder can capture common information between views while preserving their individual characteristics. To bring the embeddings of the same nodes in different views closer together while pushing the embeddings of different nodes further apart, the contrastive loss is defined as:

[0124] (12)

[0125] in, This represents the temperature parameter.

[0126] In all nodes, the opposite and The overall comparison target is calculated above:

[0127] (13)

[0128] S35. The GNN is trained jointly from three perspectives: considering only edge structure fairness, considering only node feature fairness, and considering both edge structure and node feature fairness. The process of generating a fair augmented view is achieved through the collaborative training of the reconstruction module, the fair clustering guidance module, the adversarial debiasing module, and the multi-view mutual information comparison module. A parameter isolation strategy is employed in this process, i.e., only the parameters emphasized by the current view are updated, while other parameters are fixed. The total loss function for training the current view is:

[0129] (14)

[0130] It is important to emphasize that a parameter isolation strategy is employed during the generation of fair augmented views. This means that only the parameters relevant to the current view are updated, while other parameters remain fixed. For example, when constructing a view with a fair edge structure, only the parameters related to the adjacency matrix A are updated, while the parameters of the node feature matrix X are fixed. Similarly, when constructing a view with fair node features, only the parameters related to X are updated, while the parameters of A are fixed. For views that simultaneously augment both edge structure and node features, the parameters related to both A and X are updated simultaneously. In this way, the embedded representations of the original data under different views are ultimately obtained.

[0131] Original view embedding Fair edge structure view embedding Fair node feature view embedding Fair edge structure and node feature view embedding .in, Indicates the number of nodes. Indicates the embedding dimension.

[0132] Furthermore, the specific steps of S4 include:

[0133] S41. Assign a weight parameter to each view, and integrate these embeddings into a unified representation through weighted fusion:

[0134] (15)

[0135] in, These are weight parameters that satisfy... .

[0136] To determine the optimal combination of weight parameters, a performance evaluation-based optimization strategy was adopted. First, a weight parameter space was defined, where each parameter... The range of values ​​is And satisfy For each candidate combination of weight parameters, calculate its corresponding fused embedding representation. The goal is to find the optimal combination of weight parameters for the evaluation indicators.

[0137] S42. Finally, a graph representation with good clustering performance and good fairness is obtained.

[0138] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for obtaining a fair graph representation for clustering, characterized in that, The method includes the following steps: S1. Pre-train the graph neural network encoder, including learning low-dimensional representations of graph structure and node features by reconstructing the feature matrix and adjacency matrix; S2. Based on the pre-trained encoder, a view with good clustering performance but without considering fairness is obtained. The clustering assignment is optimized by optimizing the joint loss function of reconstruction loss and clustering loss. S3. Obtain multiple views with different fairness perspectives, including generating fair enhanced views from the perspectives of edge structure fairness, node feature fairness, and the combination of the two through collaborative training of the reconstruction module, fair clustering guidance module, adversarial debiasing module, and multi-view mutual information comparison module, and using a parameter isolation strategy to update specific parameters of the view. S4. Assign a weight parameter to each view, and integrate the embeddings of multiple views into a unified graph representation through weighted fusion for clustering tasks. The weight parameter is determined by a performance evaluation optimization strategy.

2. The method according to claim 1, characterized in that, S1 includes the following steps: S11, Reconstruct the feature matrix; The original graph data is fed into a graph neural network encoder to obtain its output prediction feature matrix. The Frobenius norm is used to measure the predicted feature matrix. With the original feature matrix The error between them is given by the following formula for the loss function: （1）， S12, Reconstruct the adjacency matrix; The original graph data is fed into a graph neural network encoder to obtain its output predicted adjacency matrix. The adjacency matrix is ​​predicted using binary cross-entropy. With the true adjacency matrix The difference between them is expressed by the following formula for the loss function: （2）， Where n is the number of nodes in the graph data; S13. Reconstruct the loss function by minimizing the overall loss function. By optimizing the model parameters, the model learns low-dimensional representations of graph structure and node features simultaneously, providing a more discriminative embedding space for subsequent fair clustering tasks.

3. The method according to claim 1, characterized in that, S2 includes the following steps: S21. Further optimize the reconstruction loss of the pre-trained graph neural network encoder, and simultaneously input the encoder output embedding into a self-optimizing clustering module. The core objective of this module is to optimize the clustering assignment by minimizing the Kullback-Leibler divergence. Its loss function is defined as follows: （3）， in Represents a node Assigned to cluster The soft assignment probability is obtained using the following formula: （4）， The above formula calculates the node embedding-based... With cluster center The normalized distance between them is used to obtain the target distribution through the following formula. : （5）， in, Cluster Frequency, target distribution By using soft assignment probability Perform square normalization and consider cluster frequencies; S22. By weighting and combining the reconstruction loss and clustering loss, a joint loss function for the current view is obtained and optimized: （6）， in, It is a hyperparameter used to balance reconstruction loss and clustering loss.

4. The method according to claim 1, characterized in that, S3 includes a design reconstruction module, which aligns with the goals of the pre-training phase and the phase of obtaining a high-quality clustering view: Loss function of the reconstruction module The formula is as follows: （7）， Where n is the number of nodes in the graph data, A and A' are the original adjacency matrix and the predicted adjacency matrix, respectively, and X and X' are the original feature matrix and the predicted feature matrix, respectively.

5. The method according to claim 4, characterized in that, Step S3 includes designing a fair clustering guidance module: First, the nodes are calculated using the Student t distribution. Assigned to cluster soft assignment probability Its formula is: （8）， in, It is the embedding representation of node $i$. It is a cluster The center vector, This represents the degrees of freedom of the Student t distribution, set to 1. The module also calculates the target distribution based on sensitive attribute subgroups. Its formula is: （9）， in, Represents a node The sensitive attribute subgroup to which it belongs, target distribution By using soft assignment probability Calculate by performing square normalization and taking into account subgroup frequencies; The results are optimized by minimizing the KL divergence, and the loss function is defined as follows: （10）。 6. The method according to claim 5, characterized in that, Step S3 includes designing an adversarial debiasing module: utilizing the idea of ​​adversarial learning, an adversarial model is introduced into the embedding of each view. This process can be formally represented by the following optimization objective: （11）， in, Represents a node The true sensitive attribute value, It is an adversarial model For nodes Predicted values ​​of sensitive attributes, The parameters represent the view embedding. This represents the parameters of the adversarial model.

7. The method according to claim 6, characterized in that, Step S3 includes designing a multi-view mutual information comparison module: By leveraging the idea of ​​contrastive learning to promote the similarity of embeddings between common nodes in different views, three sets of view pairs were constructed: , and For each pair of views, a GNN encoder with shared parameters is used to generate node embeddings for each view. By sharing parameters, the encoder can capture common information between views while preserving their individual characteristics. The contrastive loss is defined as: （12）， in, Indicates temperature parameter; In all nodes, the opposite and The overall comparison target is calculated above: （13）。 8. The method according to claim 7, characterized in that, Step S3 includes training the GNN by jointly considering each module from three perspectives: fairness considering only edge structure, fairness considering only node features, and fairness considering both edge structure and node features. The process of generating a fair augmented view is achieved through the collaborative training of a reconstruction module, a fair clustering guidance module, an adversarial debiasing module, and a multi-view mutual information comparison module. This process employs a parameter isolation strategy, meaning that only the parameters emphasized by the current view are updated, while other parameters remain fixed. The total loss function for training the current view is: （14）。 9. The method according to claim 8, characterized in that, The embedded representation of the original data under different views can be obtained through S3: Original view embedding Fair edge structure view embedding Fair node feature view embedding Fair edge structure and node feature view embedding ,in, Indicates the number of nodes. Indicates the embedding dimension.

10. The method according to claim 1, characterized in that, The specific steps of S4 include: S41. Assign a weight parameter to each view, and integrate these embeddings into a unified representation through weighted fusion. The unified embedding is represented as: （15）， in, These are weight parameters that satisfy... ; First, a weight parameter space is defined, where each parameter... The range of values ​​is And satisfy For each candidate set of weight parameters, calculate its corresponding fusion embedding representation. To find the optimal combination of weight parameters for the evaluation index; S42. Finally, a graph representation with good clustering performance and good fairness is obtained.

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