Overlapped cluster detection method of graph regularization fuzzy auto-encoder
Through graph regularization fuzzy autoencoder, combined with network topology information and fuzzy clustering, the problem of poor overfitting and generalization ability of training data in the existing technology is solved, and higher detection accuracy and generalization ability are achieved.
Patent Information
- Application Number
- CN202411888716.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-20
- Publication Date
- 2025-04-04
AI Technical Summary
The existing deep learning contig cluster detection method does not fully utilize network topology information, resulting in overfitting the training data and poor generalization ability.
A contiguous cluster detection method for graph regularization fuzzy autoencoder is proposed. The low-dimensional representation of network nodes is obtained through the autoencoder, and the fuzzy boundary of clusters is captured in combination with the fuzzy clustering method, and graph regular terms are introduced to retain network structure information.
This method obtains cluster division with overlapping structures through the soft allocation mechanism of fuzzy cluster center and membership matrix, improves the accuracy of cluster detection and the generalization ability of the model, and reduces overfitting of the training data.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of complex network analysis, and in particular to an overlapping cluster detection method of a graph regularized fuzzy autoencoder. Background Art
[0002] In complex networks, mining overlapping cluster structures is an important research direction. Overlapping clusters are composed of densely connected subgraphs of partially shared nodes, which can help us more comprehensively understand group behavior, information propagation, and functional modules in complex networks. However, traditional cluster detection methods usually assume that each node belongs to only one cluster, which is not applicable in reality because many nodes span multiple clusters, which is called overlapping cluster structure.
[0003] Existing deep learning cluster detection methods are built on statistical probability models as the basic model. They use representations to describe the community structure in the network, but often ignore complex structures in the network such as heterogeneous structures and hierarchical structures. The accuracy of model detection of clusters is affected by these structures. Graph regularization terms can explicitly integrate the topological information of the network and enhance the ability to express cluster structures. Although these methods can learn more expressive low-dimensional representations through deep network structures, their representations are mostly hard assignments, which make it difficult to represent overlapping cluster structures. The soft assignment mechanism of fuzzy clustering can effectively alleviate the problem of inaccurate cluster division caused by hard assignment.
[0004] In order to solve the problem of overlapping cluster detection in complex networks, Tian et al. published an article titled "An Evolutionary Multiobjective Optimization Based Fuzzy Method for Overlapping Community Detection" in the international journal IEEE TRANSACTIONS ON FUZZY SYSTEM in 2020, using fuzzy C-means clustering to discover overlapping clusters. Guo et al. published an article titled "Community Detection Based on Multiobjective Particle Swarm Optimization and Graph Attention Variational Autoencoder" in the international journal IEEE TRANSACTIONS ON BIGDATA in 2024, detecting the low-dimensional representation obtained by the autoencoder to achieve cluster detection. However, these methods often ignore the rich structural information contained in complex networks, such as hierarchical structures and heterogeneous structures. These structures will cause the detected clusters to overfit the training data. Most of the existing deep learning cluster detection models determine cluster allocation through node representation, which makes it difficult to detect overlapping clusters, and their generalization ability needs to be improved. Summary of the invention
[0005] In order to solve the technical problems that the existing deep learning overlapping cluster detection methods do not fully utilize the network topology information and the detection results rely on node representation, resulting in overfitting of training data and poor generalization ability, this paper proposes a graph regularized fuzzy autoencoder overlapping cluster detection method; the uniqueness of this method lies in: obtaining low-dimensional representation of network nodes through autoencoders, combining fuzzy clustering methods to capture the fuzzy boundaries of clusters, and introducing graph regularization terms to retain network structure information. Finally, the soft allocation mechanism of fuzzy cluster centers and membership matrices is used to obtain cluster divisions with overlapping structures.
[0006] The idea of the present invention is: the present invention designs a fuzzy autoencoder based on graph regularization, and models the network overlapping cluster detection problem as a joint optimization problem of embedding learning and fuzzy membership soft assignment. First, the low-dimensional embedding representation of the node is extracted by the autoencoder, and the fuzzy cluster membership of the node is generated by the fuzzy C-means clustering method; then, the graph regularization term is used to ensure that the low-dimensional representation retains the local structural information of the original network. Finally, a soft assignment strategy based on fuzzy membership is used to determine the cluster division of each node, and an accurate and interpretable overlapping cluster structure is constructed. This method fully considers the structural information of the network and the fuzzy characteristics of the cluster, and is suitable for a variety of practical application scenarios of complex networks.
[0007] To achieve the above object, the present invention is implemented by the following technical scheme: a method for detecting overlapping clusters of a graph regularized fuzzy autoencoder, comprising the following steps:
[0008] Step S1: Any complex network can be described as G = (E, P), where P = {p1, p2, ..., p n} represents the set of nodes in the network, E = {e1, e2, ..., e m} represents the set of links in the network, and the modularity matrix is calculated based on the adjacency matrix and the node degree.
[0009] Step S2: Use the autoencoder and fuzzy C-means clustering to form a fuzzy autoencoder and construct the objective function of the fuzzy autoencoder The fuzzy membership matrix H' is obtained by performing fuzzy C-means clustering on the low-dimensional representation H of the autoencoder;
[0010] Step S3: Use the idea of subspace clustering to construct a graph regularization term Ω to reduce the negative impact of the sparsity of network topology on cluster detection, add it to the fuzzy autoencoder, and construct the objective function of the graph regularized fuzzy autoencoder.
[0011] Step S4, training the regularized fuzzy autoencoder to obtain the fuzzy membership matrix H', and selecting the maximum membership of each node to perform initial cluster division;
[0012] Step S5: Select a strong correlation threshold ε and set the node p i Compare all the membership degrees of with ε to obtain candidate overlapping nodes;
[0013] Step S6: Calculate the overlap threshold δ of different clusters jk , using the fuzzy cluster membership h' ji and the cluster membership degree h' ki With δ jk Make a judgment and determine the node p i Whether it is an overlapping node;
[0014] Step S7: Obtain the final overlapping cluster structure to implement overlapping cluster detection of the graph regularized fuzzy autoencoder.
[0015] Preferably, the step S1 specifically comprises the following steps: the topology information is formalized as follows: the network topology information is represented as an adjacency matrix According to formula (1), the modularity matrix is calculated
[0016]
[0017] Among them, aij =1 means there is a link between nodes, a ij = 0 means there is no link between them, m represents the total number of links in the network, d i Represents node p i The degree.
[0018] Preferably, the step S2 specifically comprises the following steps:
[0019] Step S21: The modularity matrix B is used as the input of the autoencoder. The encoding layer of the autoencoder reduces B to a low-dimensional representation matrix The mapping process of the encoder is as shown in formula (2),
[0020] H=f enc (B) = σ(W enc B+l enc ) (2)
[0021] in, is the encoding weight matrix of the encoder, is the encoder bias vector, σ is the activation function Sigmoid function;
[0022] Step S22: perform fuzzy clustering on the low-dimensional representation H of the network nodes. The objective function O of the fuzzy clustering is fcm is formula (3),
[0023]
[0024] Where n is the number of data points, that is, the dimension of H, γ is the number of cluster centers, that is, the number of clusters, μ is the fuzzy factor, and the value of μ is set to 2. ji , i = 1, 2, ..., n is the node p i The low-dimensional representation h i For the jth cluster center The membership degree of is between 0 and 1. is node p i The low-dimensional representation h i The Euclidean distance to the jth cluster center is used to obtain the fuzzy clustering membership matrix after fuzzy C-means clustering.
[0025] Step S23, the autoencoder decoder reconstructs the fuzzy membership H' into a reconstruction matrix The mapping process of the decoder is as shown in formula (4),
[0026]
[0027] in, is the decoding weight matrix of the decoder, is the decoding bias vector of the decoder, σ is the activation function Sigmoid function, minimizing the input matrix B and the reconstruction matrix The mean square error of is used to train the fuzzy autoencoder. The objective function (5) of the fuzzy autoencoder is as follows:
[0028]
[0029] Where θ={W enc , I enc , W dec , I dec} are the parameters that the fuzzy autoencoder needs to learn.
[0030] Preferably, the step S3 specifically comprises the following steps:
[0031] Step S31: Construct graph regularization term Ω and design node structure similarity matrix where z ij Indicates p i With p j The ratio of the number of nodes with common neighbors to the total number of their neighbor nodes reflects the local structure between nodes. The neighborhood structure of a node Δ(p i )={p j ∈P|e(p i ,p j )∈E}∪{p i} Using the node and its neighbor nodes, the element z of Z ij It can be expressed as:
[0032]
[0033] According to formula (6), the Laplace matrix is L = YZ, where is a diagonal matrix, where
[0034] Step S32: Introduce the Laplace matrix L to control the overfitting of the model. The smoothness of the fuzzy membership representation can be expressed as:
[0035]
[0036] The graph regularization term (7) is introduced into formula (5) using the balancing factor λ, and the value of λ is set to 0.1. The objective function of the graph regularized fuzzy autoencoder can be expressed as:
[0037]
[0038] Preferably, the step S4 specifically comprises the following steps: minimizing the objective function (8), training the graph regularized fuzzy autoencoder to obtain the fuzzy membership matrix, selecting the column where the maximum membership of each node is located, and dividing the current node into the cluster.
[0039] Preferably, the step S5 specifically comprises the following steps: according to the fuzzy membership matrix H' and the strong correlation threshold ε, applying formula (9) to obtain candidate overlapping nodes.
[0040]
[0041] Preferably, the step S6 specifically comprises the following steps:
[0042] Step S61: define the group approximation region based on the rough set theory and set a series of overlapping thresholds δ jk The distribution of the community is divided into different approximate areas. Multiple nodes have strong correlation with a certain cluster and can be regarded as a fuzzy set. The adaptive threshold parameter of a certain cluster is used to form a clear division of the cluster. The overlap threshold δ of different clusters is calculated using formula (10): jk ,
[0043]
[0044] h' ji and h' ki They are p i A certain membership degree h' ji and only less than h' ji The fuzzy membership degree h' ki ;
[0045] Step S62: Calculate h' ji and h' ki If the difference is less than δ jk , then it means that node p i Belong to cluster c j and c k , otherwise the node p i Only belongs to cluster c j ;
[0046] Preferably, the step S7 specifically comprises the following steps: combining non-overlapping nodes with overlapping nodes to form a final overlapping cluster structure.
[0047] Compared with the prior art, the present invention has the following beneficial effects:
[0048] 1. The present invention defines a deep learning objective function that integrates structural information. The graph regularization term explicitly integrates the topological information of the network, enhancing the ability of the deep learning model to express cluster structures. The topological structure prior technology helps the model to further distinguish the hierarchical relationship between groups and the similarity between nodes during the training process, thereby improving the detection accuracy of clusters. In traditional deep learning methods, the constraints of network topology are usually ignored, which is prone to problems such as poor model generalization ability or failure to identify accurate clusters in complex networks. After adopting graph regularization, these problems can be effectively reduced, especially when dealing with networks with complex topological characteristics such as social networks and biological networks, showing stronger robustness and flexibility.
[0049] 2. The present invention jointly optimizes fuzzy clustering and deep learning objective functions, and handles the problem of overlapping clusters based on the soft allocation mechanism of fuzzy clustering, further improving the accuracy of overlapping cluster detection and the generalization ability of the model. By introducing fuzzy clustering into the deep learning objective function, the model can flexibly identify nodes that are fuzzy or have partially overlapping features, and improve the ability to carefully identify overlapping nodes and non-overlapping nodes. In particular, fuzzy clustering can further refine the division of nodes through fuzzy set theory, and accurately distinguish those nodes that neither completely belong to a certain cluster nor are completely independent, so that it can maintain high accuracy and stability when facing more complex network data. This feature effectively improves the expressiveness and generalization ability of deep learning models. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.
[0051] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.
[0052] Figure 2 Schematic diagram of a method according to an embodiment of the present invention.
[0053] Figure 3 The schematic diagram of the performance comparison of different methods using Overlapping Normalized Mutual Information (ONMI) as the evaluation index in Example 1 of the present invention; wherein,
[0054] (a) is the recognition accuracy of FAE and the comparison method in the embodiment on networks with different network scales and the same overlapping node ratio. If the overlapping normalized mutual information entropy obtained by the model is high, it means that the model can more accurately identify the overlapping cluster structure;
[0055] (b) is the recognition accuracy of FAE and the comparison method in the embodiment on networks with the same overlapping node ratio and clear cluster structure. If the model calculates the overlapping normalized mutual information entropy on different networks, the model can also recognize different overlapping structures with high accuracy, reflecting the high generalization ability of the model;
[0056] (c) is the recognition accuracy of FAE and the comparison method in the embodiment in network entropy with the same overlapping node ratio and unclear cluster structure. If the model obtains high overlapping normalized mutual information entropy on different networks, the model has high accuracy in identifying overlapping cluster structures, which reflects that the model can identify overlapping cluster structures with complex structural information. DETAILED DESCRIPTION
[0057] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.
[0058] Example 1
[0059] This embodiment provides a method for detecting overlapping clusters of a graph regularized fuzzy autoencoder, comprising the following steps:
[0060] Step S1, obtain data set information: obtain the verification artificial data set Lancichinetti-Fortunato-Radicchi benchmark (LFR), network G = (E, P), where P = {p1, p2, ..., p n} represents the set of nodes in the network, E = {e1, e2, ..., e m} represents the set of links in the network. The experimental data of the autoencoder overlapping cluster detection method based on fuzzy clustering and graph regularization in this embodiment are as follows. In LFR, the characteristics of the network are controlled by adjusting various parameters. The network size is represented by the parameter n, that is, the total number of nodes in the network, and the parameter d avg Represents the average degree of the node, parameter d max represents the maximum degree of the node, the mixing parameter u mix Represents node p i The ratio of the number of links to external nodes in the cluster to which it belongs to the total number of links. The parameter c min and c max Respectively represent the minimum and maximum number of nodes in each cluster, parameter on represents the number of overlapping nodes, and parameter om represents the number of clusters to which each overlapping node can belong at the same time. In this embodiment, we designed three groups of artificial networks with different characteristics, and the parameter settings are shown in Table 1 below:
[0061] Table 1 shows the parameters of the LFR generation network:
[0062]
[0063] The formalization of topological information is as follows: network topological information is represented by the adjacency matrix The modularity matrix is calculated according to the following formula
[0064]
[0065] Among them, a ij =1 means there is a link between nodes, a ij = 0 means there is no link between them, m represents the total number of edges in the network, d i Represents node p i The degree.
[0066] Step S2: Use the autoencoder and fuzzy C-means clustering method to construct a fuzzy autoencoder to characterize the network structure. Its objective function is as follows:
[0067]
[0068] The step S2 is as follows:
[0069] Step S21: The modularity matrix B is used as the input of the autoencoder. The encoding layer of the autoencoder reduces B to a low-dimensional representation matrix The encoder mapping process is as follows:
[0070] H=f enc (B) = σ(W enc B+l enc )
[0071] in, is the encoding weight matrix of the encoder, is the encoder bias vector, σ is the activation function Sigmoid function;
[0072] Step S22: perform fuzzy clustering on the low-dimensional representation H of the network nodes. The objective function O of the fuzzy clustering is fcm for:
[0073]
[0074] Where n is the number of data points, that is, the dimension of H, γ is the number of cluster centers, that is, the number of clusters, μ is the fuzzy factor, and the value of μ is set to 2. ji , i = 1, 2, ..., n is the node p i The low-dimensional representation h i For the jth cluster center The membership degree is between 0 and 1, ||h i -c κ || 2 is node p i The low-dimensional representation h i The Euclidean distance to the jth cluster center is used to obtain the fuzzy clustering membership matrix after fuzzy C-means clustering.
[0075] Step S23: The decoder of the autoencoder reconstructs the fuzzy membership H' into a reconstruction matrix The mapping process of the decoder is as follows:
[0076]
[0077] in, is the decoding weight matrix of the decoder, is the decoding bias vector of the decoder, σ is the activation function Sigmoid function, minimizing the input matrix B and the reconstruction matrix The mean square error is used to train the fuzzy autoencoder. The objective function of the fuzzy autoencoder is as follows:
[0078]
[0079] Where θ={W enc , l enc , W dec , l dec} are the parameters that the fuzzy autoencoder needs to learn.
[0080] Step S3: Using the subspace clustering idea, a graph regularization term that reflects structural information is constructed, and a graph regularized fuzzy autoencoder is formed. Its objective function is as follows:
[0081]
[0082] The step S3 is as follows:
[0083] Step S31: Construct graph regularization term Ω and design node structure similarity matrix where z ij Indicates p i With p j The ratio of the number of nodes with common neighbors to the total number of their neighbor nodes reflects the local structure between nodes. The neighborhood structure of a node Δ(p i )={p j ∈P|e(p i ,p j )∈E}∪{p i} Using the node and its neighbor nodes, the element z of Z ij It can be expressed as:
[0084]
[0085] According to the above formula, the Laplace matrix is L=YZ, where is a diagonal matrix,
[0086] Step S32: Introduce the Laplace matrix L to control the overfitting of the model. The smoothness of the fuzzy membership representation can be expressed as:
[0087]
[0088] The graph regularization term expressed in the above formula is introduced into the objective function of the fuzzy autoencoder by using the balancing factor λ. The value of λ is set to 0.1. The objective function of the graph regularized fuzzy autoencoder can be expressed as:
[0089]
[0090] Step S4: Use the graph regularized fuzzy autoencoder to obtain the fuzzy membership matrix, select the column where the maximum membership of each node is located, and divide the current node into the cluster.
[0091] Step S5: According to the fuzzy membership matrix H′ and the strong correlation threshold ε, the candidate overlapping nodes are obtained using the following formula:
[0092]
[0093] Step S6: Design overlapping thresholds for different clusters and determine overlapping nodes.
[0094] The step S6 is as follows:
[0095] Step S61: define the group approximation region based on the rough set theory and set a series of overlapping thresholds δ jk The distribution of the community is divided into different approximate areas. Multiple nodes have strong correlation with a certain cluster and can be regarded as a fuzzy set. The adaptive threshold parameter of a certain cluster is used to form a clear division of the cluster. The overlap threshold of different clusters δ jk The calculation method is as follows:
[0096]
[0097] h' ji and h' kij They are p i A certain membership degree h' ji The sum is only less than h' ji The fuzzy membership degree h' ki ;
[0098] Step S62: Calculate h'ji and h' ji If the difference is less than δ jk , then it means that node p i Belong to cluster c j and c k , otherwise the node p i Only belongs to cluster c k ;
[0099] Specifically, the step S7 includes the following steps: combining non-overlapping nodes with overlapping nodes to form a final overlapping cluster structure.
[0100] The effectiveness of this example can be further illustrated by the following comparative experiment. It should be noted that the change of the parameters λ and μ used in the experiment does not affect the generality of this embodiment.
[0101] This experiment aims to evaluate the model of this embodiment. The model is based on graph regularization to describe the structural information of the network, constructs a fuzzy autoencoder to obtain the fuzzy membership of the node, and performs overlapping cluster detection on a network with a complex structure. The experimental results are shown in Figure 3 As shown in the figure, the model FAE is tested on three sets of network data sets containing overlapping nodes, and the performance is evaluated by Overlapping Normalized Mutual Information (ONMI). The experimental results show that the model FAE of this embodiment performs better than the comparison model GNN on the three types of data sets A, B, and C, and has a significant advantage in the accuracy of overlapping cluster detection as a whole.
[0102] The overlapping cluster detection method based on graph fuzzy autoencoder provided in this embodiment is applicable to networks with complex structures and can more naturally discover overlapping clusters in the network. Based on the autoencoder framework and combined with the idea of fuzzy clustering, this embodiment designs an objective function for overlapping cluster detection of fuzzy autoencoder integrating graph regularization, which can not only obtain the deep structure mining of the autoencoder to more strongly express the community structure and contain low-dimensional representations of complex structures, but also obtain the fuzzy membership of nodes through fuzzy clustering, and the fuzzy theory decision process to more effectively characterize the overlapping relationship between clusters, which is applicable to a variety of complex network applications.
[0103] Example 2
[0104] This embodiment provides an overlapping cluster detection method for a graph regularized fuzzy autoencoder, and compares the performance on real datasets Facebook 1684, Cora, and Citeseer. The Facebook 1684 dataset is a social network dataset that contains 792 users in 17 groups and 28,048 social relationships between these users; the Cora dataset is a widely used academic network dataset that contains papers from the field of computer science, which form a citation network through citation relationships. A total of 2,708 papers in the dataset belong to 7 categories, such as "neural networks" and "machine learning", and 5,429 citation relationships between papers; the Citeseer dataset is also an academic network dataset that contains papers in the field of computer science and citation relationships between them, 3,312 articles from 6 categories and 4,731 citation edges between them. The experimental results are shown in Table 2. The model FAE is tested on three real network datasets containing overlapping nodes, and its performance is evaluated using ONMI. Experimental results show that the model FAE of this embodiment performs better than the comparison model GNN on the Facebook1684, Cora, and Citeseer datasets, and its accuracy in detecting overlapping clusters in real scenarios is also competitive.
[0105] Table 2
[0106]
[0107] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims
1. A method for detecting overlapping clusters using a graph regularized fuzzy autoencoder, characterized in that: The following steps are involved: Step S1: any complex network is described as G = (E, P), where P = {p1, p2, ..., p n } represents the set of nodes in the network, E = {e1, e2, ..., e m } represents the set of links in the network, and the modularity matrix is calculated based on the adjacency matrix and the node degree. Step S2: Use the autoencoder and fuzzy C-means clustering to form a fuzzy autoencoder and construct the objective function of the fuzzy autoencoder Among them, the fuzzy membership matrix H' is obtained by fuzzy C-means clustering of the low-dimensional representation H of the autoencoder; Step S3: Use the idea of subspace clustering to construct the graph regularization term Ω, add it to the fuzzy autoencoder, and construct the objective function of the graph regularized fuzzy autoencoder Step S4, training the graph regularized fuzzy autoencoder to obtain the fuzzy membership matrix H', and selecting the maximum membership of each node to perform initial clustering; Step S5: Select a strong correlation threshold ε and set the node p i Compare all the membership degrees of with ε to obtain candidate overlapping nodes; Step S6: Calculate the overlap threshold δ of different clusters jk , using the fuzzy cluster membership h' ji and the cluster membership degree h' ki With δ jk Make a judgment and determine the node p i Whether it is an overlapping node; Step S7: Obtain the final overlapping cluster structure to implement graph regularized fuzzy autoencoder overlapping cluster detection.
2. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The step S1 includes the following steps. The topology information is formalized as follows: the network topology information is represented as an adjacency matrix According to formula (1), the modularity matrix is calculated Among them, a ij =1 means there is a link between nodes, a ij = 0 means there is no link between them, m represents the total number of links in the network, d i Represents node p i The degree.
3. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The step S2 comprises the following steps: Step S21: The modularity matrix B is used as the input of the autoencoder. The encoding layer of the autoencoder reduces B to a low-dimensional representation matrix The mapping process of the encoder is as shown in formula (2), H=f enc (B)=σ(W enc B+l enc ) (2) in, is the encoding weight matrix of the encoder, is the encoder bias vector, σ is the activation function Sigmoid function; Step S22: perform fuzzy clustering on the low-dimensional representation H of the network nodes. The objective function O of the fuzzy clustering is fcm is formula (3), Where n is the number of data points, that is, the dimension of H, γ is the number of cluster centers, that is, the number of clusters, μ is the fuzzy factor, and the value of μ is set to 2. ji , i = 1, 2, ..., n is the node p i The low-dimensional representation h i For the jth cluster center The membership degree of is between 0 and 1. is node p i The low-dimensional representation of h i The Euclidean distance to the jth cluster center is used to obtain the fuzzy clustering membership matrix after fuzzy C-means clustering. Step S23, the autoencoder decoder reconstructs the fuzzy membership H' into a reconstruction matrix The mapping process of the decoder is as shown in formula (4), in, is the decoding weight matrix of the decoder, is the decoding bias vector of the decoder, σ is the activation function Sigmoid function, minimizing the modularity matrix B and the reconstruction matrix The mean square error of is used to train the fuzzy autoencoder. The objective function (5) of the fuzzy autoencoder is as follows: Where θ={W enc , l enc , W dec , l dec } are the parameters that the fuzzy autoencoder needs to learn.
4. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The step S3 comprises the following steps: Step S31: Construct graph regularization term Ω and design node structure similarity matrix where z ij Indicates p i With p j The ratio of the number of nodes with common neighbors to the total number of their neighbor nodes reflects the local structure between nodes. The neighborhood structure of a node Δ(p i )={p j ∈P|e(p i ,p j )∈E}∪{p i } Using the node and its neighbor nodes, the element z of Z ij It is expressed as: According to formula (6), the Laplace matrix is L = YZ, where is a diagonal matrix, where Step S32: introduce the Laplace matrix L to control the overfitting of the model. The smoothness of the fuzzy membership representation is expressed as: The graph regularization term (7) is introduced into formula (5) using the balancing factor λ, and the value of λ is set to 0.
1. The objective function of the graph regularized fuzzy autoencoder is expressed as:
5. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: In step 4, the objective function (8) is minimized, and the graph regularized fuzzy autoencoder is trained to obtain the fuzzy membership matrix, and the column with the maximum membership of each node is selected to classify the current node into the cluster.
6. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The specific process of step 5 is as follows: according to the fuzzy membership matrix H' and the strong correlation threshold ε, the candidate overlapping nodes are obtained using formula (9):
7. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The specific process of step 6 is as follows: Step S61: define the group approximation region based on the rough set theory and set a series of overlapping thresholds δ jk The distribution of different clusters is divided into different approximate areas. Multiple nodes with strong correlation to a certain cluster are regarded as a fuzzy set. The adaptive threshold parameter of a certain cluster is used to form a clear division of the cluster. The overlap threshold δ of different clusters is calculated using formula (10): jk , h' ji and h' ki They are p i A certain fuzzy membership degree h' ji and only less than h' ji The fuzzy membership degree h' ki ; Step S62: Calculate h' ji and h' ki If the difference is less than δ jk , then it means that node p i Belong to cluster c j and c k , otherwise the node p i Only belongs to cluster c j .
8. The overlapping cluster detection method of the graph regularized fuzzy autoencoder according to claim 1, characterized in that: The specific process of step 7 is as follows: non-overlapping nodes are combined with overlapping nodes to form a final overlapping cluster structure.