An ultra-graph enhanced semi-supervised graph reconstruction method and an overlapping community detection method

Abstract

The application belongs to the field of graph reconstruction and overlapping community detection, and discloses a hypergraph enhanced semi-supervised graph reconstruction method and an overlapping community detection method, which comprises the following steps: obtaining an attribute graph and a prior matrix, and obtaining an attribute graph adjacency matrix according to the attribute graph; inputting the attribute matrix of the attribute graph and the attribute graph adjacency matrix into a dual attention convolutional encoder to obtain a node representation matrix output by the dual attention convolutional encoder; mapping the attribute matrix of the attribute graph into a hypergraph, performing graph reconstruction on the hypergraph and the node representation matrix, outputting a new attribute graph adjacency matrix, and calculating a graph reconstruction loss function; calculating a semi-supervised loss function based on the prior matrix and the node representation matrix; calculating a modularity maximization loss function based on the attribute graph adjacency matrix and the node representation matrix; and comprehensively training and updating the dual attention convolutional encoder until the training is completed. The application improves the accuracy of graph reconstruction learning and enhances the perception ability of community structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of graph reconstruction and overlapping community detection, and particularly relates to a hypergraph enhanced semi-supervised graph reconstruction method and an overlapping community detection method. BACKGROUND

[0002] Attribute network (attribute graph) is a key concept in the field of complex system modeling and analysis. Attribute network changes the traditional graph data structure by integrating rich attribute information into the network. Among them, overlapping community detection is one of the hot topics in the field of attribute network analysis, which not only provides important technical support for in-depth analysis of complex network structure and information propagation mechanism, but also effectively enables personalized recommendation system and realizes precise service.

[0003] The overlapping community detection method based on attribute graph has experienced a transition from traditional machine learning to deep learning. The traditional machine learning method mainly relies on hand-crafted features and shallow models to detect overlapping communities, which can be mainly divided into the following four categories:

[0004] (1) Method based on faction filtering: the core idea of this method is to extract a faction of size k from the network, and then calculate the overlapping matrix based on the faction to discover overlapping communities. However, due to the uncertainty of faction size, this method is prone to unstable community detection results.

[0005] (2) Method based on label propagation: the core idea of this method is to explore the multi-dimensional label attributes of nodes, determine the label attributes of nodes through label membership, and then divide the nodes accordingly. However, this method relies too much on label attributes and is prone to local optimization.

[0006] (3) Method based on link density: the core idea of this method is to take the edge as the main research object, analyze the features of the edge, and then distinguish the nodes according to the analysis results of the edge. However, this method faces great challenges when dealing with graphs with strong edge sparsity.

[0007] (4) Method based on local expansion: the core idea of this method is to take a seed node as an initial community, then calculate the contribution of nodes according to the fitness function, and detect the community to which the node belongs. However, this method has limitations when dealing with high-dimensional attributes.

[0008] However, although traditional machine learning methods can detect overlapping communities, they perform poorly in complex scenarios and face great challenges in terms of accuracy and computational complexity.

[0009] In addition, the deep learning-based overlapping community detection method mainly focuses on the representation learning of the relationship and features between nodes, and the representative method is the method based on GCN and its variants. In recent years, with the development of GCN, scholars have begun to apply GCN to the field of network analysis, and it is found that the method based on GCN is helpful to obtain network topology and attribute information. For example, the prior art combines GCN with a Markov random field to detect communities, but this method does not fully learn the attribute information. The prior art combines a label sampling model with GCN to encode high-dimensional attributes, and realizes fine-grained learning of attribute information. However, the above methods do not consider the influence of high attribute dimension and network data noise on the performance of the model, which leads to the model being unable to accurately learn the representation information of the nodes, and thus reduces the accuracy of overlapping community detection.

[0010] At the same time, some scholars have begun to improve the effectiveness of overlapping community detection from the perspective of graph reconstruction. For example, the Bernoulli distribution is combined with node representation to alleviate the problem of inaccurate calculation of the connection probability between nodes in the graph reconstruction process, but the information distortion problem is not considered, thereby reducing the accuracy of graph reconstruction. Or a self-supervised adaptive graph convolutional network model is proposed, which optimizes graph reconstruction learning by introducing non-negative matrix factorization, but also does not consider the information distortion problem. There is prior art that uses a topological graph and a feature graph to enhance the learning ability of the decoder for graph reconstruction, but ignores the important influence of high-order information of the graph in the graph reconstruction process, so that the adaptability of the model in complex networks is poor. SUMMARY

[0011] The purpose of the present application is to provide a hypergraph enhanced semi-supervised graph reconstruction method and an overlapping community detection method to improve the accuracy of graph reconstruction learning and enhance the perception ability of community structure.

[0012] To achieve the above purpose, the technical solution adopted by the present application is:

[0013] The first aspect: providing a hypergraph enhanced semi-supervised graph reconstruction method for overlapping community detection, comprising:

[0014] Obtaining an attribute graph and a prior matrix, and obtaining an attribute graph adjacency matrix from the attribute graph;

[0015] Inputting the attribute matrix of the attribute graph and the attribute graph adjacency matrix into a dual attention convolutional encoder to obtain a node representation matrix output by the dual attention convolutional encoder;

[0016] Mapping the attribute matrix of the attribute graph into a hypergraph, performing graph reconstruction according to the hypergraph and the node representation matrix, outputting a new attribute graph adjacency matrix, and calculating a graph reconstruction loss function;

[0017] Based on the prior matrix and the node representation matrix, a semi-supervised loss function is calculated;

[0018] The modularity maximization loss function is calculated based on the attribute graph adjacency matrix and node representation matrix.

[0019] The dual attention convolutional encoder is trained and updated using a combination of graph reconstruction loss function, semi-supervised loss function, and modularity maximization loss function until training ends.

[0020] Several alternative methods are provided below, but they are not intended as additional limitations on the overall solution above. They are merely further additions or optimizations. Provided there are no technical or logical contradictions, each alternative method can be combined individually with respect to the overall solution above, or multiple alternative methods can be combined with each other.

[0021] Preferably, the dual attention convolutional encoder adopts a two-layer graph convolutional architecture. The first-layer graph convolutional architecture includes graph convolutional operations, multi-head attention mechanism, ReLU activation function and regularization method connected in sequence. The second-layer graph convolutional architecture includes graph convolutional operations, multi-head attention mechanism and SoftMax activation function connected in sequence.

[0022] Preferably, the dual attention convolutional encoder introduces a noise adjustment strategy based on a uniform matrix distribution, and the output of the first layer graph convolutional architecture is used as the input of the second layer graph convolutional architecture after passing through the noise adjustment strategy.

[0023] The noise reduction strategy is expressed as follows:

[0024]

[0025] In the formula, This represents the output of the noise conditioning strategy. This represents the input to the noise modulation strategy, i.e., the output of the first-layer graph convolutional architecture. Indicates from arrive Uniformly distributed noise It refers to the number of attributes in the attribute graph. It is a hyperparameter for controlling noise intensity.

[0026] Preferably, the step of reconstructing the graph based on the hypergraph and the node representation matrix to output a new attribute graph adjacency matrix includes:

[0027] Generate a hypergraph incidence matrix from the hypergraph, multiply the transpose of the hypergraph incidence matrix by the hypergraph incidence matrix to obtain the cell unit, and then standardize the cell unit.

[0028] The graph is reconstructed based on the standardized cell unit and node representation matrices, as shown in the following formula:

[0029]

[0030]

[0031] In the formula, Represents the new attribute graph adjacency matrix The first in Line 1 Column elements, Represents nodes in the new attribute graph and nodes The connection probability, Represents nodes in the new attribute graph and nodes The probability of no connection. It is an activation function. It is a standardized cell unit. Represents the node representation matrix. Represents the standardized cell unit With node representation matrix The nodes obtained after multiplication The representation vector, Represents the nodes in the node representation matrix The transpose of the representation vector.

[0032] Preferably, the computational graph reconstruction loss function includes:

[0033] Generate the hypergraph adjacency matrix from the hypergraph;

[0034] Based on the hypergraph adjacency matrix and the new attribute graph adjacency matrix, the cross-entropy loss is used to calculate the graph reconstruction loss function.

[0035] Preferably, the calculation of the modularity maximization loss function based on the attribute graph adjacency matrix and node representation matrix includes:

[0036]

[0037]

[0038] In the formula, Represents the modularity matrix The Middle Line 1 Column elements, Representation of the adjacency matrix of the attribute graph The Middle Line 1 Column elements, Represents a node The degree, Represents a node The degree, This indicates the number of edges in the attribute graph. This represents the loss function that maximizes modularity. Represents the trace of a matrix. Representation of the node representation matrix The transpose of .

[0039] As a preferred option, the total loss function in training and updating is: The graph reconstruction loss function is multiplied by the semi-supervised loss function, then subtracted. Maximize the loss function by a factor of 100. and These are the weight hyperparameters.

[0040] The second aspect: Provides an overlapping community detection method, including:

[0041] The dual attention convolutional encoder after training is obtained by using the hypergraph-enhanced semi-supervised graph reconstruction method described above.

[0042] Obtain the attribute map to be detected, and obtain the corresponding node representation matrix through a dual attention convolutional encoder;

[0043] Based on the node representation matrix, a soft clustering method is used to detect overlapping communities.

[0044] Preferably, the method of detecting overlapping communities based on the node representation matrix and using soft clustering includes:

[0045] The community segmentation threshold was determined using a soft clustering method.

[0046] Obtain nodes from the node representation matrix Corresponding representation vector ;

[0047] If the representation vector The first in If any element is greater than or equal to the community partitioning threshold, then the node will be... Divided to the number One community; otherwise, no node. Divide the area into communities;

[0048] Traverse all nodes in the attribute graph to be detected to obtain the set of overlapping communities, thus completing the overlapping community detection.

[0049] This invention provides a hypergraph-enhanced semi-supervised graph reconstruction method and an overlapping community detection method. First, a dual-attention convolutional encoder based on a multi-head attention mechanism is proposed to mine fine-grained high-dimensional attributes. Simultaneously, a noise modulation strategy based on a uniform matrix distribution is embedded in the encoder to alleviate network data noise. Second, a graph reconstruction method based on hypergraph enhancement is proposed to capture high-order information of the graph and alleviate information distortion, thereby improving the accuracy of graph reconstruction learning. Then, a semi-supervised module is constructed to integrate prior information of the graph, and modularity maximization is used to enhance the dual-attention convolutional encoder's ability to perceive community structures. Attached Figure Description

[0050] Figure 1 This is a flowchart of the hypergraph enhancement semi-supervised graph reconstruction method of the present invention;

[0051] Figure 2 This is a schematic diagram of the architecture (single layer) of the dual multi-head attention mechanism of the present invention;

[0052] Figure 3 This is a schematic diagram of the generation of synthetic network attributes in the experiment of this invention;

[0053] Figure 4 This invention provides a performance comparison experiment on different real networks. The experimental results are shown in the figure.

[0054] Figure 5 Different experiments in this invention The experimental results of the SG1 performance comparison are shown in the figure below;

[0055] Figure 6 Different experiments in this invention The experimental results of the Fb_1684 performance comparison are shown in the figure below;

[0056] Figure 7 Different experiments in this invention The experimental results of the SG1 performance comparison are shown in the figure below;

[0057] Figure 8 Different experiments in this invention The experimental results of the Fb_1684 performance comparison are shown in the figure. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting of the application.

[0060] Embodiment 1: As shown in the figure, the embodiment proposes a hypergraph enhanced semi-supervised graph reconstruction method (hereinafter referred to as HSGRL) for overlapping community detection, which specifically includes the following steps: Figure 1

[0061] Step 1, obtain the attribute graph and prior matrix, and obtain the attribute graph adjacency matrix according to the attribute graph.

[0062] The embodiment defines the attribute graph as , wherein represents a node set, represents an edge set, represents an attribute matrix of a node, represents an attribute space, the number of nodes is , the number of edges is , and the number of attributes is . And get the attribute graph adjacency matrix of the attribute graph .

[0063] The embodiment defines the prior information as the known “node-community” label. The label represents the community number, such as 1, 2, and 3. The “node-community” label matrix (prior matrix) is composed of the prior information of the network, wherein is the number of nodes, is the number of communities. represents that node belongs to community , and vice versa represents that node does not belong to community .

[0064] Step 2, input the attribute matrix and the attribute graph adjacency matrix of the attribute graph to the dual attention convolutional encoder to obtain the node representation matrix output by the dual attention convolutional encoder.

[0065] The dual attention convolutional encoder (hereinafter referred to as DACE encoder) adopts a double-layer graph convolution architecture improved through three stages. The double-layer graph convolution architecture is an improved graph neural network. The embodiment enhances the learning ability and robustness of the model by integrating a dual multi-head attention mechanism and a uniform matrix distribution noise adjustment strategy.

[0066] In the first stage, the first layer of the graph convolution architecture contains a graph convolution operation​ an activation function plus a regularization method as shown in equation (1). The second layer of the graph convolutional architecture comprises a graph convolution operation and an activation function as shown in equation (2).

[0067] (1)

[0068] (2)

[0069] (3)

[0070] wherein denotes the output of the layer of the first layer graph convolutional architecture, denotes the output of the layer of the second layer graph convolutional architecture, denotes the output of the layer of the first layer graph convolutional architecture (initial value denotes the attribute matrix of the nodes ), denotes the adjacency matrix with self-loop, denotes the identity matrix, denotes the diagonal matrix of , and and denote the parameter matrices of the layer and the layer, respectively, which are initialized using the Xavier initialization method. The layer, the layer, the layer, etc. herein denote the layers of the first layer graph convolutional architecture and the second layer graph convolutional architecture in turn named in the repeated iterative training of the dual attention convolutional encoder.

[0071] As can be seen from equations (1) and (2), the activation functions of the double-layer graph convolutional architecture are and respectively. In addition, as can be seen from equation (1), the DACE encoder can adaptively fuse the connection information and attribute information of the attributed graph without the need for parameters to balance the two types of information.

[0072] As can be seen from equations (1) and (2), if the dimension of the node attribute matrix reaches several hundred or even more, the node representation matrix ​​The initial dimension of the attribute matrix will increase, which will greatly affect the representation learning of the node and make it difficult for the model to distinguish between valid and invalid attributes. To solve the problem of high attribute dimension, the dual multi-head attention mechanism is added to the double-layer graph convolution architecture in the embodiment. Therefore, in the second stage, the double-layer graph convolution architecture of the DACE encoder is further improved, as shown in equations (4) and (5).

[0073] (4)

[0074] (5)

[0075] In the formula, indicates the multi-head attention mechanism, and the architecture thereof is shown in Figure 2 . Figure 2 , and respectively represent three different linear transformation matrices. is , and is the number of sets.To prevent the dual multi-head attention mechanism from relying too much on specific relationships, the embodiment adds an attention dropout layer after . The attention dropout layer makes more robust when processing new data, thereby reducing the risk of overfitting. In addition, the purpose of adding layer normalization is to accelerate the training of the dual multi-head attention mechanism.

[0076] In addition, the embodiment proposes a noise adjustment strategy based on uniform matrix distribution (referred to as NTSUMD strategy) to alleviate the network data noise problem in overlapping community detection, and designs a noise strategy according to the attribute matrix of different nodes. In the NTSUMD strategy, different uniform noises are added to the node representation according to different node attributes. Therefore, in the third stage, the embodiment improves the double-layer graph convolution architecture of the DACE encoder by using the NTSUMD strategy, thereby improving the robustness of the model to network data noise, as shown in equation (6).

[0077] (6)

[0078] wherein, indicates the output of the layer of the DACE encoder after using the NTSUMD strategy, indicates the uniformly distributed noise from to , is the number of attributes in the attribute graph, is a hyperparameter to control the noise intensity. The output of the first layer graph convolutional architecture is input to the second layer graph convolutional architecture after the noise adjustment strategy. The NTSUMD strategy is essentially a data augmentation strategy. By injecting uniform noise in the node representation, the NTSUMD strategy not only enhances data diversity, but also effectively improves the generalization ability of the model. The output of the second layer graph convolutional architecture of the final DACE encoder is denoted as the output of the DACE encoder, i.e., the node representation matrix .

[0079] Step 3, map the attribute matrix of the attribute graph to a hypergraph, perform graph reconstruction according to the hypergraph and the node representation matrix, output a new attribute graph adjacency matrix, and calculate the graph reconstruction loss function.

[0080] Based on the hypergraph enhancement, the present embodiment proposes a hypergraph decoder. The hypergraph decoder aims to decode the output of the DACE encoder into a new adjacency matrix . Then, the DACE encoder continues to encode the new adjacency matrix to generate . With the increase of the number of training times, and are prone to information loss and change, i.e., information distortion, in the continuous encoding and decoding process. The information distortion reduces the accuracy of graph reconstruction. Therefore, the hypergraph decoder designs a cell unit to alleviate the information distortion problem, as shown in equation (7). The core idea of the cell unit is to map the node attribute matrix to a hypergraph. The columns of the node attribute matrix are mapped to hyperedges, and nodes with the same attribute belong to the same hyperedge. The present embodiment defines the hypergraph as , where and represent the node set and the hyperedge set, respectively. Each hyperedge of the hypergraph contains at least two nodes. Each has an associated matrix and an adjacency matrix

[0081] . (7)

[0082] In the formula, is the number of nodes, is the number of hyperedges, , and represent the dimension information of the matrix. represents the transpose matrix of . represents the hypergraph The generated correlation matrix is ​​shown in formula (8). At this stage, formula (9) needs to be used to... Row standardization is necessary; otherwise, effective graph training cannot be achieved.

[0083] (8)

[0084] (9)

[0085] In the formula, express The Line 1 Elements in the column It is a node , It is a super-edge , express No. Standardization of lines express The standardization results express The OK, express The Line 1 Elements in the column.

[0086] In the graph reconstruction process, the cell unit is... The reconstruction provides sufficient attribute information to prevent information distortion from reducing the accuracy of graph reconstruction, as shown in formulas (10) and (11).

[0087] (10)

[0088] (11)

[0089] In the formula, express The Line 1 Column elements, Represents nodes in the new attribute graph and The connection probability, on the contrary This represents the probability of no connection. Represents a node Represents the transpose of a vector. It is an activation function. Indicates inclusion nodes The characterization, i.e., the standardized cell unit With node representation matrix the representation vector of the node after multiplication. The cell mainly consists of the incidence matrix of the hypergraph . Nodes with the same attribute can be aggregated in the same hyperedge. When a node encounters information distortion, the cell can use the attribute information of other nodes with the same attribute to supplement the attribute information of the affected node. Therefore, the core mechanism of the cell is the transmission of attribute information between nodes. This mechanism ensures that the attribute information of the nodes is fully utilized in each encoding and decoding of the graph to alleviate the problem of information distortion and improve the accuracy of graph reconstruction.

[0090] After the hypergraph-enhanced hypergraph decoder converts the node attribute matrix into a hypergraph, the adjacency matrix of the hypergraph can be calculated by formula (12). Since is derived from the connection information of the hyperedge (attribute) rather than the node, the aggregated information is not limited to low-order information (first-order information) such as adjacent nodes. From the perspective of the hyperedge (attribute), can capture higher-order information such as long-range node relationships and structures.

[0091] (12)

[0092] In the formula, represents the element in the th row and the th column of the matrix , and represents the number of hyperedges shared between nodes and .

[0093] In addition, the attribute information of a node can reflect its preference characteristics. The more attributes nodes share, the more similar their preferences are. When captures high-order information, the hypergraph cleverly realizes the aggregation of nodes with similar preferences by gathering nodes within the same hyperedge. In other words, different preferences of nodes are also reflected in through different hyperedges. also represents the preference similarity value between nodes and . Using node preferences as the weight of edges in the attributed graph enhances the ability of the hypergraph decoder to learn edge differences. Therefore, the hypergraph decoder optimizes graph reconstruction based on , and uses cross-entropy loss to calculate the graph reconstruction loss function, as shown in formula (13). Before calculation Row normalization must also be performed according to formula (9).

[0094] (13)

[0095] In the formula, is the loss function of graph reconstruction. The hypergraph decoder not only alleviates the information distortion problem in the graph reconstruction process, but also effectively excavates the high-order information of the graph, thereby improving the accuracy of graph reconstruction.

[0096] Step 4, based on the prior matrix and the node representation matrix, calculate the semi-supervised loss function.

[0097] The semi-supervised module aims to provide factual constraints to node representation learning by integrating prior information, thereby improving the accuracy of community detection. The semi-supervised loss function used in this embodiment is , as shown in formula (14).

[0098] (14)

[0099] In the formula, denotes the set of labeled node indexes, is the number of communities, denotes the element in the th row and the th column of the prior matrix , denotes the element in the th row and the th column of the node representation matrix .

[0100] Step 5, calculate the modularity maximization loss function based on the attribute graph adjacency matrix and the node representation matrix.

[0101] Modularity is an index for measuring the strength of network structure and has been well applied in deep learning, as shown in formula (15). Formula (16) is used as the modularity maximization loss function in this embodiment.

[0102] (15)

[0103] (16)

[0104] In the formula, is the number of edges, denotes the trace of a matrix, denotes the transpose of , denotes the modularity matrix , and are the node and the degree of, denotes the element in the row and the column, denotes the element in the row and the column. The modularity maximization is conducive to the training of the model in a community-oriented structure, so that the model can more effectively identify the structural differences between overlapping communities. The joint use of modularity maximization and semi-supervised modules helps to facilitate the effective implementation of modularity maximization and ensure that the model accurately learns the overlapping community structure.

[0105] Step 6, integrate the graph reconstruction loss function, the semi-supervised loss function and the modularity maximization loss function to train and update (such as updating the parameters using the Adam optimizer) the dual attention convolutional encoder until the training is completed.

[0106] The total loss function in the training and updating of this embodiment is times the graph reconstruction loss function plus the semi-supervised loss function minus times the modularity maximization loss function , and are the weight hyperparameters of different losses, as shown in equation (17).

[0107] (17)

[0108] The present application not only fuses connection information and attribute information through a dual multi-head attention mechanism, but also enhances the modeling ability of the model for complex network information by exploring the influence of high-dimensional attributes and edge differences on node representation, thereby realizing the improvement of community detection performance. At the same time, a noise adjustment strategy is proposed to reduce the interference of network data noise on overlapping community detection performance. And based on hypergraph enhancement to capture high-order information of the graph, thereby relieving the information distortion in the graph reconstruction process.

[0109] Embodiment 2: This embodiment provides an overlapping community detection method based on the hypergraph-enhanced semi-supervised graph reconstruction method provided in embodiment 1. First, the dual attention convolutional encoder after the training in embodiment 1 is obtained; then the attribute graph to be detected is obtained, and the corresponding node representation matrix is obtained through the dual attention convolutional encoder; finally, based on the node representation matrix, a soft clustering method is used to complete the overlapping community detection.

[0110] With the training of the model, the elements of the node representation matrix gradually tend to be stable, but it is still not clear which community each node belongs to. Therefore, the embodiment utilizes soft clustering to find the threshold for dividing the community , as shown in formula (18).

[0111] (18)

[0112] Then, in the overlapping community division, the node is obtained from the node representation matrix ; if the th element in the representation vector is greater than or equal to the community division threshold, the node is divided into the th community; otherwise, the node is not divided into the community; all nodes in the attribute graph to be detected are traversed to obtain an overlapping community set , and the overlapping community detection is completed.

[0113] In order to intuitively show the advantages of the method proposed in the application, the following provides specific experiments for illustration

[0114] (I) Experimental setup.

[0115] (1) Experimental environment: the experiment is hybrid coded using Python 3.7 and Matlab 2018b. The HSGRL model is trained on a server with 512GB memory, X86_64 processor architecture, and Ubuntu 20.04.06 LTS operating system. The GPU is NVIDIA A800. The number of heads is set to 4. The dropout ratio is set to 0.1. The noise intensity hyperparameter is set to 0.1. The learning rate of the synthetic network is set to 0.005. The learning rate of the real network is set to 0.01. The maximum number of iterations of SG1, SG2, Fb_1684, Fb_1912, Mag_eng and Mag_cs is 300, 300, 300, 300, 600 and 400, respectively.

[0116] (2) Synthetic network: the experiment uses the famous LFR benchmark model to generate two synthetic networks with overlapping community detection function: SG1 and SG2. The specific parameters of the synthetic network are shown in Table 1. However, SG1 and SG2 do not have attribute information. Therefore, the experiment generates the attribute information of the synthetic network according to the following rules. 1) Set the dimension of the attribute set to , where is the number of communities (SG1 and SG2 are 25 and 27, respectively), is the number of attributes (all set to 8 uniformly), and the attribute dimension of each node is also . Initialize an attribute matrix of a node with rows and columns, all of whose elements are initially set to 0. 2) If the node belongs to the qth community (q is the minimum value of 1), set the attribute values from the th to the th position to 1 with a probability . 3) Set the remaining attribute values to 1 with a probability . An attribute generation example is provided, in which the parameters , Figure 3 and are set to 3, 3 and 6, respectively. Table 1. Synthetic network information

[0117] Table 2. Real network information

[0118]

[0119] (3) Real network: In this experiment, four real attribute networks, Fb_1684, Fb_1912, Mag_eng and Mag_cs, are selected. Fb_1684 and Fb_1912 belong to a small self-network set of Facebook, in which the community represents a user circle (such as a class circle, a family circle), the node attribute represents the user's personal characteristics, and the edge represents the social relationship between users. Mag_eng and Mag_cs belong to a collaborative author network set, in which the community represents a research field, the node attribute represents the keywords in the author's published papers, and the edge represents the collaboration relationship between authors. The above four real networks are benchmark datasets for overlapping community detection, each of which contains a node attribute matrix, a link matrix and a label matrix. In the data preprocessing stage, the self-loop of the node in the benchmark dataset is deleted, while the remaining part remains unchanged. The relevant information of the four real networks is shown in Table 2.

[0120] Table 2. Real network information

[0121]

[0122] (4) Baseline: In this experiment, the current mainstream unsupervised and semi-supervised community detection methods are selected as the comparative baseline, including: (A) Unsupervised methods:

[0123] ​The SCI method is derived from the paper WANG X, JIN D, CAO X C, YANG L, & ZHANG W X. Semantic community identification in large attribute networks. In Proceedings of the 30th AAAI conference on artificial intelligence, 2016, February 12-17, Phoenix, USA, pp. 265-271.

[0124] The NOCD method is derived from the paper SHCHUR O, & GUNNEMANN S. Overlapping community detection with graph neural networks. In Proceedings of the 25th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2019, August 5, Alaska, USA, pp. 1-7.

[0125] The EOCMM method is derived from the paper CHENG S L, YANG S, CHENG X F, & WANG W Y. An effective overlapping community merging method oriented to multidimensional attribute social networks. Expert Systems, 2023, 40(10), e13433.

[0126] The UCODE-X method is derived from the paper MORADAN A, DRAGANOV A, MOTTIN D, & ASSENT I. Ucode: Unified community detection with graph convolutional networks. Machine Learning, 2023, 112(12), 5057-5080.

[0127] CPGC-X method, derived from the paper LIU H T, WEI J H, & XU T Y. Community detection based on community perspective and graph convolutional network. Expert Systems with Applications, 2023, 231, 120748.

[0128] (B) Semi-supervised methods:

[0129] WSCDSM method, derived from the paper WANG W J, LIU X, JIAO P F, CHEN X, & JIN D. A unified weakly supervised framework for community detection and semantic matching. In Proceedings of the 22th Pacific-Asia Conference on Knowledge Discovery and Data Mining, 2018, June 3-6, Melbourne, Australia, pp. 218-230.

[0130] PSSNMTF method, derived from the paper JIN D, HE J, CHAI B F, & HE D X. Semi-supervised community detection on attributed networks using non-negative matrix tri-factorization with node popularity. Frontiers of Computer Science, 2021, 15, 1-11.

[0131] SSGCAE method, derived from the literature HECB, ZHENG YL, CHENG JW, TANG Y, CHEN GH, & LIU H. Semi-supervised overlapping community detection in attributed graph with graph convolutional autoencoder. Information Sciences, 2022, 608, 1464-1479.

[0132] CLARE method, derived from the literature WUXX, XIONG Y, ZHANG Y, JIAO YZ, SHAN CH, & SUN YH, et al. CLARE: A semi-supervised community detection algorithm. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2022, August 14-18, Washington, USA, pp. 2059-2069.

[0133] DSSC method, derived from the literature BERAHMAND K, LI YF, & XU Y. A deep semi-supervised community detection based on point-wise mutual information. IEEE Transactions on Computational Social Systems, 2024, 11(3), 3444-3456.

[0134] SLSS method, derived from the literature NIL, GE JN, ZHANG YW, LUO WJ, & SHENG VS. Semi-supervised local community detection. IEEE Transactions on Knowledge and Data Engineering, 2024, 36(2), 823-839.

[0135] (5) Hyperparameter settings: and respectively, are the loss weights of graph reconstruction and modularity maximization in the present application, and the present experiment sets and to 10 -7 and 10 -6 , respectively.

[0136] (B) Ablation experiment.

[0137] To analyze the role of each module in HSGRL in the task of overlapping community detection, the present experiment performed an ablation experiment on six data sets. Then, the present experiment removed the DACE encoder, the hypergraph decoder, the modularity maximization, and the semi-supervised module from HSGRL, respectively, to obtain the corresponding SGR w / o DACE, SGR w / o Hyper, SGR w / o Mod, and SGR w / o Semi methods. Since the encoder is one of the core modules of HSGRL, complete removal will cause the model to fail to run normally. Therefore, in SGR w / o DACE, the present experiment replaced the DACE encoder with a traditional two-layer GCN model. Similarly, in SGR w / o Hyper, the present experiment replaced the hypergraph decoder with a standard decoder. The specific experimental results are shown in Table 3.

[0138] Table 3 Comparison results of ablation experiment

[0139]

[0140] Note: The optimal value is shown in bold. In SGR w / o DACE, SGR w / o Hyper, SGR w / o Mod, and HSGRL, the parameters , and are set to 2%, 0%, and 0%, respectively. In SGR w / o Semi mode, the parameters , and are set to 0%, 0%, and 0%, respectively.

[0141] As can be seen from Table 3, the overall performance of HSGRL in detecting overlapping communities is better than that of other ablation methods. The removal of any module will reduce the performance of HSGRL, so each module is an indispensable part of HSGRL. On the Fb_1912 data set, the present experiment found that SGR w / o Hyper outperformed HSGRL in the F1 index. Compared with other networks, Fb_1912 contains too many overlapping nodes, accounting for 34.57% of the total number of nodes, and has a higher network density. Therefore, in the graph reconstruction process, the overlapping nodes suffer greater loss of topological information. Since the hypergraph decoder optimizes graph reconstruction from the perspective of attribute information, HSGRL does not achieve the best performance on Fb_1912.

[0142] The average performance reduction of SGR w / o DACE, SGR w / o Hyper, SGR w / o Mod and SGR w / o Semi compared with HSGRL are 0.0712, 0.0239, 0.0580 and 0.5294, respectively. Therefore, the performance contribution of each module to HSGRL from large to small is SGR w / o Semi, SGR w / o DACE, SGR w / o Mod and SGR w / o Hyper. In addition, SGR w / o Semi has the worst performance. The reason is that SGR w / o Semi is a semi-supervised method that relies on prior information. However, when When set to 2% (at this time, SGR w / o Semi is equivalent to the complete HSGRL), the performance of SGR w / o Semi is greatly improved. Among them, the index ONMI represents the overlapping normalized mutual information index, and the value range of ONMI is [0, 1]. The larger the value of ONMI, the better the performance of the model. The index F1 represents the average F1-score. The larger the F1 value, the better the performance of the model.

[0143] (Three) Prior information analysis.

[0144] This experiment analyzes the influence of different baselines on the proportion of prior information in synthetic networks and real networks on the performance. This experiment evaluates the performance of different methods for overlapping community detection in the range of 0% to 10% of (step size 2%). The proportion of attribute noise and the proportion of topology noise are both set to 0%.

[0145] (1) Prior information analysis of synthetic networks: From Table 4 and Table 5, when is 0%, the performance of semi-supervised methods such as HSGRL for detecting overlapping communities is weaker than that of unsupervised methods UCODE-X and CPGC-X. The main reason is that the performance of unsupervised methods does not depend on prior information. When is 2%, the performance of HSGRL is greatly improved. With the increase of , the performance of HSGRL is always better than that of other comparative baselines, which shows that HSGRL can more effectively detect overlapping communities on synthetic networks.

[0146] Table 4 Comparison of ONMI index of SG1 and SG2 under different prior information proportions

[0147]

[0148] Table 5. Comparison of F1 index of SG1 and SG2 under different prior information proportion

[0149]

[0150] Note: The optimal value in Table 4 and Table 5 is shown in bold.

[0151] (2) Prior information analysis on real networks: As shown in Figure 4 , (a) of the figure is the experimental result of Fb_1684 network, (b) of the figure is the experimental result of Fb_1912 network, (c) of the figure is the experimental result of Mag_eng network, and (d) of the figure is the experimental result of Mag_cs network. When is 0%, the performance of HSGRL on real networks is similar to its performance on synthetic networks. The performance of HSGRL is weaker than that of unsupervised methods UCODE-X and CPGC-X. However, with the increase of , the performance of HSGRL on real networks is generally better than that of other comparative baselines. HSGRL shows excellent performance on both synthetic networks and real networks, and the main reasons are as follows: 1) HSGRL can effectively fuse prior information, link information and attribute information. 2) HSGRL not only makes full use of high-dimensional attribute information, but also alleviates information distortion in graph reconstruction, thereby improving the accuracy of overlapping community detection.

[0152] (Four) Experiment of data noise.

[0153] A high-performance community detection method should not only have excellent detection effect, but also show good robustness to network data noise. Therefore, in order to verify the robustness of HSGRL to network data noise, this paper selects SG1 and Fb_1684 as verification networks, and sets it to 2%. This paper synthesizes network data noise from two aspects of attribute information and topological structure. The first method of synthesizing network data noise has the following steps: 1) randomly select (percent) nodes from the network. 2) Randomly exchange the attribute vectors of the selected nodes in the node attribute matrix to generate a new attribute matrix. 3) Take the new node attribute matrix as the input of HSGRL. The experimental results are shown in Figure 5 and 6 . The second method of synthesizing network data noise has the following steps: 1) randomly select (percent) nodes from the network. 2) Randomly exchange the selected nodes to construct a new network. 3) Take the new network as the input of HSGRL. The experimental results are shown in Figure 7 and 8 .

[0154] ByFigure 5 、 6 , 7, 8, it can be seen that HSGRL can effectively detect overlapping communities even in noisy networks. To further verify the robustness of HSGRL to network data noise, this section sets and to 60% and 12% respectively, and performs comparative experiments on four real networks. The specific experimental results are shown in Tables 6 and 7 respectively. and

[0155] Table 6 Performance comparison of various methods when is set to 60%

[0156]

[0157] Note: The optimal value is in bold.

[0158] Table 7 Performance comparison of various methods when is set to 12%

[0159]

[0160] Note: The optimal value is in bold.

[0161] From Tables 6 and 7, it can be seen that the performance of HSGRL in detecting overlapping communities is better than that of the baseline, indicating that HSGRL is more robust to network data noise. The robustness of HSGRL mainly benefits from the following two aspects: 1) The proposed noise fine-tuning strategy with uniform matrix distribution injects noise bias into node representation, preventing the model from overfitting to specific attributes or node relationships during training, thereby improving the robustness of HSGRL. 2) HSGRL introduces modularity maximization, making the entire learning process community structure-oriented, reducing the impact of network data noise on overlapping community detection.

[0162] The HSGRL method proposed in the application is used to detect overlapping communities. HSGRL reduces the negative impact of high attribute dimension on community detection through a dual multi-head attention mechanism, and also uses hypergraphs to capture high-order information of graphs, and to alleviate information distortion in graph reconstruction. In view of the problem of network data noise existing in real scenarios, HSGRL introduces a noise fine-tuning strategy with uniform matrix distribution to improve the robustness of the model to network data noise during training. In addition, this paper proposes a semi-supervised module to enhance the learning ability of HSGRL to node representation by introducing prior information. Finally, modularity maximization effectively mines the structural information of communities in a community-oriented manner. Extensive experiments verify that HSGRL can improve the accuracy of overlapping community detection.

[0163] ​​​Any combination of the technical features in the above-described embodiments can be made, and for the sake of brevity, not all possible combinations are described, however, as long as there is no conflict, any combination of the technical features should be considered within the scope of the present disclosure.

[0164] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but should not be understood as a limitation on the scope of the present application. It should be pointed out that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A supergraph enhanced semi-supervised graph reconstruction method for overlapping community detection, characterized in that, The supergraph enhanced semi-supervised graph reconstruction method comprises: An attribute graph and a priori matrix are obtained, and an attribute graph adjacency matrix is obtained according to the attribute graph; An attribute matrix of the attribute graph and the attribute graph adjacency matrix are input into a dual attention convolutional encoder to obtain a node representation matrix output by the dual attention convolutional encoder; The attribute matrix of the attribute graph is mapped into a supergraph, graph reconstruction is performed according to the supergraph and the node representation matrix, a new attribute graph adjacency matrix is output, and a graph reconstruction loss function is calculated; A semi-supervised loss function is calculated based on the priori matrix and the node representation matrix; A modularity maximization loss function is calculated based on the attribute graph adjacency matrix and the node representation matrix; The dual attention convolutional encoder is trained and updated by comprehensively combining the graph reconstruction loss function, the semi-supervised loss function and the modularity maximization loss function until the training is completed.

2. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 1, wherein, The dual attention convolutional encoder adopts a double-layer graph convolution architecture, the first layer of the graph convolution architecture comprises a graph convolution operation, a multi-head attention mechanism, a ReLU activation function and a regularization method connected in sequence, and the second layer of the graph convolution architecture comprises a graph convolution operation, a multi-head attention mechanism and a SoftMax activation function connected in sequence.

3. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 2, wherein, The dual attention convolutional encoder introduces a noise adjustment strategy based on a uniform matrix distribution, and the output of the first layer of the graph convolution architecture is taken as the input of the second layer of the graph convolution architecture after being subjected to the noise adjustment strategy. The noise adjustment strategy is represented as follows: ； wherein, output representing the noise regulation strategy, input representing the noise regulation strategy, i.e. the output of the first layer graph convolutional architecture, represents the noise intensity, represents the noise intensity, uniformly distributed noise, is the number of attributes in the attributed graph, is a hyperparameter controlling the noise intensity.

4. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 1, wherein, The graph reconstruction is performed according to the supergraph and the node representation matrix, and a new attribute graph adjacency matrix is output, which comprises: A supergraph association matrix is generated according to the supergraph, a cell unit is taken as the transpose matrix of the supergraph association matrix multiplied by the supergraph association matrix, and the cell unit is standardized; Graph reconstruction is performed according to the standardized cell unit and the node representation matrix, and the formula is represented as follows: ； ； In the formula, represents the new attribute graph adjacency matrix in the row and the column element, represents the connection probability of the node and the node in the new attribute graph, represents the non-connection probability of the node and the node in the new attribute graph, is an activation function, is a normalized cell unit, represents a node representation matrix, represents a representation vector of a node obtained after the normalized cell unit is multiplied by the node representation matrix, represents the transpose of the representation vector of the node in the node representation matrix.​ 5. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 1, wherein, The graph reconstruction loss function is calculated, which comprises: A supergraph adjacency matrix is generated according to the supergraph; Based on the supergraph adjacency matrix and the new attribute graph adjacency matrix, a cross-entropy loss is used to calculate the graph reconstruction loss function.

6. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 1, wherein, The modularity maximization loss function is calculated based on the attribute graph adjacency matrix and the node representation matrix, which comprises: ； ； In the formula, Represents the modularity matrix The Middle Line 1 Column elements, Representation of the adjacency matrix of the attribute graph The Middle Line 1 Column elements, Represents a node The degree, Represents a node The degree, This indicates the number of edges in the attribute graph. This represents the loss function that maximizes modularity. Represents the trace of a matrix. Representation of the node representation matrix The transpose of .

7. The hypergraph-enhanced semi-supervised graph reconstruction method of claim 1, wherein, The total loss function in the training update is the semi-supervised loss function, minus times the modularity maximization loss function, and are weight hyperparameters, respectively.

8. An overlapping community detection method characterized by, The overlapping community detection method comprises: The supergraph enhanced semi-supervised graph reconstruction method in any one of claims 1 to 7 is used to obtain the dual attention convolutional encoder after the training is completed; An attribute graph to be detected is obtained, and a corresponding node representation matrix is obtained through the dual attention convolutional encoder; Based on the node representation matrix, a soft clustering method is used to complete the overlapping community detection.

9. The overlapping community detection method of claim 8, wherein, Based on the node representation matrix, the soft clustering method is used to complete the overlapping community detection, which comprises: A community division threshold is determined by using the soft clustering method; obtaining nodes from a node representation matrix corresponding representation vectors ; If the representation vector The first in If any element is greater than or equal to the community partitioning threshold, then the node will be... Divided to the number One community; otherwise, no node. Divide the area into communities; All nodes in the attribute graph to be detected are traversed to obtain an overlapping community set, and the overlapping community detection is completed. All nodes in the attribute graph to be detected are traversed to obtain an overlapping community set, and the overlapping community detection is completed.

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