Attribute community detection method based on latent representation and graph-regularized non-negative matrix factorization

Abstract

The present invention proposes an attribute community detection method based on potential representation and graph regularized non-negative matrix decomposition, which mainly solves the problem that the existing methods do not fully utilize the rich attribute information in the network. The scheme includes: 1) inputting network data; 2) processing the data and calculating the affinity matrix of the attribute information; 3) defining and initializing two transfer matrices; 4) defining and initializing three non-negative matrix decomposition factor matrices related to the topological graph and the attribute graph; 5) setting iterations to obtain the update formulas of the three non-negative matrix decomposition factor matrices and the two transfer matrices; 6) iterating repeatedly to obtain the updated final node member distribution matrix and the final attribute class distribution matrix; 7) judging the community to which the node belongs according to the final matrix obtained by iterative update, obtaining the community detection result and outputting it. The present invention can make full use of the rich attribute information in the network and effectively improve the accuracy of community distribution detection.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and further relates to a community detection method, specifically an attribute community detection method based on latent representation and graph regularized non-negative matrix decomposition, which can be used for community transmission prevention and control of infectious diseases and recommendation systems, etc. Background Art

[0002] With the continuous progress of science and technology, the study of complex networks has attracted the attention of scholars in various disciplines. Whether it is neurobiology or statistical physics, they are all studying the practical significance of complex networks. Common in life, such as communication networks, transportation networks, power networks and social networks, similar complex network structures have filled every aspect of our lives. Not only that, each node in the network covers many complex information expressions, so the attribute community detection of complex networks has become a hot topic at present. The community structure of a complex network refers to the fact that the nodes in the community in the network are closely connected, while the nodes between communities are sparsely connected. Community detection of attribute networks is of great significance for revealing the structure, function and semantics of the network. Commonly used community detection algorithms include non-negative matrix decomposition method, label propagation method, spectral clustering method, hierarchical clustering method, evolutionary computing method and deep learning method.

[0003] Compared with other models used to solve community detection, the method based on non-negative matrix factorization (NMF) shows some unique advantages: higher interpretability of community detection results and more flexible use of prior information. For example, given a complex network, it can be represented as a non-negative feature matrix (adjacency matrix). The feature matrix is ​​decomposed by NMF to obtain the membership matrix of the node. Since the matrix has a non-negative constraint, each element in the matrix can be naturally regarded as the strength of the corresponding node in the corresponding community. Community detection is essentially a clustering problem, and its clustering objects are nodes in complex networks. Both k-means and spectral clustering models have shown good results in dealing with node clustering problems. Therefore, NMF can be naturally used to detect communities. In fact, most existing community detection methods based on NMF achieve better performance by improving the clustering ability of NMF.

[0004] However, for attribute networks, their network nodes generally contain rich information. For example, in social networks, users generally contain many attributes, such as age, gender, occupation, etc. The traditional NMF algorithm only uses the topological structure of the network and cannot solve the complex attribute information of the attribute network very well. Therefore, how to effectively integrate the topological structure and attribute information has become a problem of concern to many researchers, and some solutions have been proposed. In 2018, Jin Di et al. published an article entitled "Robust and Strongly Explanatory Community Discovery Method for Complex Networks with Attributes" in the Journal of Computers, Vol. 41, No. 7, pp. 1476-1489. They proposed a robust and highly interpretable community discovery model RSECD. The model innovatively uses a priori transition probability matrix to characterize the intrinsic relationship between network communities and content clusters, and uses a non-negative matrix decomposition model to integrate the two types of information, network topology and node content, into a unified framework. However, this method still has shortcomings. For rich attribute information, the potential structure is not well mined, so the community detection effect is not good.

[0005] In 2021, Meng Qin et al. published an article titled "Dual-channel hybrid community detection in attributed networks" in Information Sciences, Volume 551, Pages 146-167. They also proposed an attribute network community detection algorithm, namely dual-channel hybrid community detection (DHCD). This algorithm is based on a new perspective of separating cluster structures, integrating network structure and semantic information, and using two channels to handle community detection problems for different networks. However, this method does not explore attribute information in depth, but only uses non-negative matrix decomposition to obtain the distribution structure, without considering the potential association of nodes in the attribute information. Summary of the invention

[0006] The purpose of the present invention is to solve the problems existing in the above-mentioned existing methods, and propose an attribute community detection method based on potential representation and graph regularized non-negative matrix decomposition, which is used to solve the problem that the node attribute information of the attribute network in the existing methods is not rich, the topological information of the nodes is inconsistent with the attribute information, and the rich attribute information in the network cannot be fully utilized, resulting in poor detection effect. In the existing methods, attribute information is usually only used as auxiliary information in community detection, and the weight between topological information and attribute information in different networks cannot be measured.

[0007] The idea of ​​achieving the purpose of the present invention is: first, the topological information and attribute information in the attribute network are decomposed respectively using the model of non-negative matrix decomposition to obtain the member distribution matrix of the node and the node attribute distribution matrix. Secondly, an affinity matrix is ​​constructed for the attribute matrix, and the potential representation of the attribute information is obtained by the method of potential representation learning. In addition, a transfer matrix is ​​constructed according to the Markov transition probability to link the node member distribution matrix and the attribute distribution matrix. Finally, a model dominated by the topological structure and a model dominated by the attribute information are constructed, and a graph regularization term is introduced to guide the model to obtain more accurate community detection.

[0008] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0009] (1) Input the relevant data of the attribute network, which includes the topological structure and node attribute information; let n represent the number of nodes in the network and m represent the number of attributes in the network. The relevant data set of the attribute network generally includes the topological structure of the network nodes and the attribute information of the nodes. The basic information of the attribute network mainly includes the number of nodes in the network, the number of edges in the network, the number of attributes of the nodes, and the number of communities;

[0010] (2) Processing relevant data in the attribute network:

[0011] The topological matrix A∈R is obtained based on the edge information of the network nodes in the topological structure. n×n , according to the node attribute information, we get the attribute matrix Z∈R n×m , and use the attribute matrix Z to construct the affinity matrix B∈R n×n , the element in the i-th row and j-th column of the affinity matrix is ​​b ij :

[0012]

[0013] Where i, j = 1, 2, ..., n; z i and z j denote the i-th row and j-th row in the attribute matrix, i.e., the i-th node and j-th node in the attribute matrix, σ denotes the bandwidth parameter of the Gaussian function, and exp(·) denotes the exponential operation;

[0014] (3) Define three non-negative matrix decomposition factor matrices and initialize them:

[0015] Define the non-negative matrix decomposition factor matrix related to the topological graph: the node member distribution matrix U, and randomly initialize it to an n×k dimensional matrix; define the non-negative matrix decomposition factor matrix related to the attribute graph: the attribute class distribution matrix X and the attribute class description matrix Y, and randomly initialize them to n×k dimensional and m×k dimensional matrices respectively;

[0016] (4) Establish the mapping relationship between the node member distribution matrix U and the attribute class distribution matrix X:

[0017] This step needs to establish a mapping relationship between the topological structure and the attribute information. Referring to the transition probability in the Markov chain, two transfer matrices are defined, namely the first transfer matrix P and the second transfer matrix Q; the attribute class distribution matrix X is converted into the first transfer matrix P and the node member distribution matrix U, that is, X = UP, or the node member distribution matrix U is converted into the second transfer matrix Q and the attribute class distribution matrix X, that is, U = XQ; and both transfer matrices are randomly initialized to k × k dimensional matrices, where k represents the number of communities in the network;

[0018] (5) Set the maximum number of iterations Max_iter = 100, the current number of iterations is it, and initialize it = 1;

[0019] (6) Obtain the update formulas for three non-negative matrix decomposition factor matrices and two transfer matrices:

[0020] (6a) Define the objective function formula of latent representation and graph regularized non-negative matrix factorization, that is, the objective function O(U,Y,P) dominated by the topology structure LRL_GNMFT and the objective function O(X,Y,Q) dominated by attribute information LRL_GNMFA :

[0021]

[0022]

[0023] Among them, α represents O(U,Y,P) LRL_GNMFT The parameter of attribute information in the objective function, β represents O(X,Y,Q) LRL_GNMFA The parameters of the topological structure in the objective function, λ represents the influence parameter of the potential representation, θ represents the graph regularization parameter, It is expressed as the square of the F-norm of the matrix ·. The Euclidean distance between the two matrices is obtained by calculating the square of the F-norm of the difference between the two matrices. Tr(·) represents the trace of the matrix ·, and T represents the transpose operation. L1=D1-A represents the Laplace matrix of the topological matrix, and D1 represents the diagonal matrix of the topological matrix. L2=D2-B represents the Laplace matrix of the affinity matrix, and D2 represents the diagonal matrix of the affinity matrix. and All elements in are 1;

[0024] (6b) Using the objective function formula defined in step (6a), the node member distribution matrix update formula, the attribute class distribution matrix update formula, the attribute class description matrix update formula and the transfer matrix update formula are obtained, which are as follows:

[0025] The node member distribution matrix update formula in the objective function dominated by the topology structure is:

[0026]

[0027] in, and Respectively represent the element values ​​of the i-th row and j-th column of the node member distribution matrix U at the it+1th and itth iterations;

[0028] The attribute class description matrix update formula in the objective function dominated by topology is:

[0029]

[0030] Where, d = 1, 2, ..., m, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations;

[0031] The first transfer matrix update formula in the topology-dominated objective function is:

[0032]

[0033] Where l,r=1,2,…,k, and Respectively represent the element values ​​of the lth row and rth column of the first transfer matrix P at the it+1th and itth iterations;

[0034] The attribute class distribution matrix update formula in the objective function dominated by attribute information is:

[0035]

[0036] in, and Respectively represent the element values ​​of the i-th row and j-th column of the attribute class distribution matrix X at the it+1th and itth iterations;

[0037] The attribute class description matrix update formula in the objective function dominated by attribute information is:

[0038]

[0039] in, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations;

[0040] The second transfer matrix update formula in the objective function dominated by attribute information is:

[0041]

[0042] in, and Respectively represent the element values ​​of the lth row and rth column of the second transfer matrix Q at the it+1th and itth iterations;

[0043] (7) In the it-th iteration, the three non-negative matrix decomposition factor matrices and the two transfer matrices are updated respectively using the update formula obtained in step (6) to obtain the updated node member distribution matrix, attribute class description matrix, first transfer matrix, attribute class distribution matrix, attribute class description matrix, and second transfer matrix;

[0044] (8) Determine whether the current number of iterations it reaches the preset maximum number of iterations Max_iter. If so, obtain the final node member distribution matrix U' and the final attribute class distribution matrix X' after iterative update, and execute step (9); otherwise, add 1 to it and return to execute step (7);

[0045] (9) Community detection and output of detection results:

[0046] According to the final node member distribution matrix U' or the final attribute class distribution matrix X' after iterative update, the community to which the node belongs is determined, and the community detection result is obtained and output.

[0047] Compared with the existing method, the present invention has the following advantages:

[0048] First, since the present invention constructs an affinity matrix for attribute information to represent the node association in the attribute information, and then uses the non-negative matrix decomposition method to establish a model for the affinity matrix to obtain the potential representation of the attribute matrix; thereby fully mining the potential information in the node attributes and effectively improving the accuracy of attribute community detection.

[0049] Second, the present invention establishes a mapping relationship by designing a transfer matrix, which can decompose the community results obtained from the node topology information into the node attribute community results and the transfer matrix; similarly, the node attribute community can also be converted into the topology community results and the transfer matrix; thus, the topology information and the attribute information are well integrated, further improving the accuracy of community detection;

[0050] Third, since the present invention establishes models for topological information and attribute information separately, and then uses the transfer matrix to link the two, two models are established, one dominated by topological structure and the other dominated by attribute information. Finally, regularization is introduced into the obtained community detection results, thereby guiding the model to learn more accurate community allocation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1It is a flow chart of the implementation of the present invention;

[0052] Figure 2 is the community detection node distribution diagram of the present invention and the existing method and the distribution diagram of the real community, where Figure 2 (a) is the real community node distribution diagram of the selected network Texas. Figure 2 (b) is the community distribution diagram of nodes obtained using the DHCD method. Figure 2 (c) is a community distribution diagram of nodes obtained by using the present invention. DETAILED DESCRIPTION

[0053] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0054] Reference Figure 1 The attribute community detection method based on potential representation and graph regularized non-negative matrix decomposition provided by the present invention specifically includes the following steps:

[0055] Step 1: Input the relevant data of the attribute network, which includes the topological structure and node attribute information; let n represent the number of nodes in the network and m represent the number of attributes in the network;

[0056] Step 2: Process the relevant data in the attribute network:

[0057] The topological matrix (i.e., adjacency matrix) A∈R is obtained based on the edge information of the network nodes in the topological structure. n×n , according to the node attribute information, we get the attribute matrix Z∈R n×m , and use the attribute matrix Z to construct the affinity matrix B∈R n×n The affinity matrix in the present invention is constructed using the relevant information of the attribute matrix, and its main purpose is to fully explore the potential associations of nodes in the attribute information and improve the accuracy of community detection.

[0058] The element in row i and column j of the affinity matrix is ​​b ij :

[0059]

[0060] Where i, j = 1, 2, ..., n; z i and z j denote the i-th row and j-th row in the attribute matrix, i.e., the i-th node and j-th node in the attribute matrix, σ denotes the bandwidth parameter of the Gaussian function, and exp(·) denotes the exponential operation;

[0061] Step 3: Define three non-negative matrix decomposition factor matrices and initialize them:

[0062] Define the non-negative matrix decomposition factor matrix related to the topological graph: the node member distribution matrix U, and randomly initialize it to an n×k dimensional matrix; define the non-negative matrix decomposition factor matrix related to the attribute graph: the attribute class distribution matrix X and the attribute class description matrix Y, and randomly initialize them to n×k dimensional and m×k dimensional matrices respectively;

[0063] Step 4: Establish the mapping relationship between the node member distribution matrix U and the attribute class distribution matrix X:

[0064] Define two transfer matrices, namely the first transfer matrix P and the second transfer matrix Q; transform the attribute class distribution matrix X into the first transfer matrix P and the node member distribution matrix U, namely X=UP, or transform the node member distribution matrix U into the second transfer matrix Q and the attribute class distribution matrix X, namely U=XQ; and randomly initialize both transfer matrices to k×k dimensional matrices, where k represents the number of communities in the network;

[0065] Here, according to the concept of transition probability in the Markov chain, each element in the first transfer matrix P and the second transfer matrix Q is non-negative, and the sum of the elements in each row is 1, that is, there are the following constraints:

[0066] Step 5: Set the maximum number of iterations Max_iter = 100, the current number of iterations is it, and initialize it = 1;

[0067] Step 6: Get the update formulas for three non-negative matrix decomposition factor matrices and two transfer matrices:

[0068] (6a) Define the objective function formula of latent representation and graph regularized non-negative matrix factorization:

[0069] Because the attribute information in the attribute network is different from the information in the topological structure, the attribute information in some attribute networks is much higher than that in the topological structure, while the opposite is true for some other networks; therefore, the present invention proposes an objective function dominated by the topological structure and an objective function dominated by the attribute information. LRL_GNMFT and the objective function O(X,Y,Q) dominated by attribute information LRL_GNMFA The expression is as follows:

[0070]

[0071]

[0072] Among them, α represents O(U,Y,P) LRL_GNMFT The parameter of attribute information in the objective function, β represents O(X,Y,Q) LRL_GNMFAThe parameters of the topological structure in the objective function, λ represents the influence parameter of the potential representation, θ represents the graph regularization parameter, It is expressed as the square of the F-norm of the matrix ·. The Euclidean distance between the two matrices is obtained by calculating the square of the F-norm of the difference between the two matrices. Tr(·) represents the trace of the matrix ·, and T represents the transpose operation. L1=D1-A represents the Laplace matrix of the topological matrix, and D1 represents the diagonal matrix of the topological matrix. L2=D2-B represents the Laplace matrix of the affinity matrix, and D2 represents the diagonal matrix of the affinity matrix. and All elements in are 1;

[0073] Here we define the objective function formula of potential representation and graph regularized non-negative matrix decomposition. First, we use the non-negative matrix decomposition formula to obtain the functional relationship between the node member distribution matrix and the topology matrix. Functional relationship between attribute class distribution matrix, attribute class description matrix and attribute matrix According to the method of potential representation learning, the functional relationship between the attribute class distribution matrix and the affinity matrix is ​​obtained Then, the graph regularization term Tr(U T L1U) and Tr(XTL2X), thus obtaining the objective function O(U,Y,P) dominated by the topological structure LRL_GNMFT and the objective function O(X,Y,Q) dominated by attribute information LRL_GNMFA .

[0074] In the present invention, different objective functions are adopted for different networks. For example, for networks with rich attribute information, O(X, Y, Q) is generally used. LRL_GNMFA It can achieve better community detection results, and for some networks whose attribute information is not as good as the topological structure, O(U,Y,P) is used. LRL_GNMFT Better community detection results can be achieved. At the same time, applying graph regularization constraints to the distribution matrix can guide the model to learn more accurate community distribution conditions.

[0075] (6b) Using the objective function formula defined in step 6a, we obtain the node member distribution matrix update formula, attribute class distribution matrix update formula, attribute class description matrix update formula, and transfer matrix update formula:

[0076] (6b1) Expressed as Tr(MMT), we get O(U,Y,P) LRL_GNMFT and O(X,Y,Q) LRL_GNMFA New expression:

[0077]

[0078]

[0079] (6b2) Using the function O(U,Y,P) LRL_GNMFT Calculate partial derivatives of the node member distribution matrix, attribute class description matrix and first transfer matrix, and obtain the node member distribution matrix update formula, attribute class description matrix update formula and first transfer matrix update formula according to the Karush-Kuhn-Tucker condition;

[0080] Using the function O(X,Y,Q) LRL_GNMFA The partial derivatives of the attribute distribution matrix, the attribute description matrix and the second transfer matrix are calculated, and the Karush-Kuhn-Tucker condition is used to obtain the attribute distribution matrix update formula, the attribute description matrix update formula and the second transfer matrix update formula; the details are as follows:

[0081] The node member distribution matrix update formula in the objective function dominated by the topology structure is:

[0082]

[0083] in, and Respectively represent the element values ​​of the i-th row and j-th column of the node member distribution matrix U at the it+1th and itth iterations;

[0084] The attribute class description matrix update formula in the objective function dominated by topology is:

[0085]

[0086] Where, d = 1, 2, ..., m, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations;

[0087] The first transfer matrix update formula in the topology-dominated objective function is:

[0088]

[0089] Where l,r=1,2,…,k, and Respectively represent the element values ​​of the lth row and rth column of the first transfer matrix P at the it+1th and itth iterations;

[0090] The attribute class distribution matrix update formula in the objective function dominated by attribute information is:

[0091]

[0092] in, and Respectively represent the element values ​​of the i-th row and j-th column of the attribute class distribution matrix X at the it+1th and itth iterations;

[0093] The attribute class description matrix update formula in the objective function dominated by attribute information is:

[0094]

[0095] in, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations;

[0096] The second transfer matrix update formula in the objective function dominated by attribute information is:

[0097]

[0098] in, and Respectively represent the element values ​​of the lth row and rth column of the second transfer matrix Q at the it+1th and itth iterations;

[0099] Step 7: In the it-th iteration, the update formula obtained in step 6 is used to update the three non-negative matrix decomposition factor matrices and the two transfer matrices respectively to obtain the updated node member distribution matrix, attribute class description matrix, first transfer matrix, attribute class distribution matrix, attribute class description matrix, and second transfer matrix. Specifically, the node member distribution matrix is ​​updated using the node member distribution matrix update formula to obtain an updated node member distribution matrix; the attribute class description matrix update formula in the topology-dominated model is used to update the attribute class description matrix to obtain an updated attribute class description matrix; the transfer matrix update formula in the topology-dominated model is used to update the transfer matrix to obtain an updated transfer matrix; the attribute class distribution matrix update formula is used to update the attribute class distribution matrix to obtain an updated attribute class distribution matrix; the attribute class description matrix update formula in the attribute information-dominated model is used to update the attribute class description matrix to obtain an updated attribute class description matrix; the transfer matrix update formula in the attribute information-dominated model is used to update the transfer matrix to obtain an updated transfer matrix.

[0100] Step 8: Determine whether the current number of iterations it reaches the preset maximum number of iterations Max_iter. If so, obtain the final node member distribution matrix U' and the final attribute class distribution matrix X' after iterative update, and execute step 9; otherwise, add 1 to it and return to execute step 7;

[0101] Step 9: Community detection and output of detection results:

[0102] According to the final node member distribution matrix U' or the final attribute class distribution matrix X' after iterative update, the community to which the node belongs is determined, and the community detection result is obtained and output.

[0103] For the objective function dominated by the topological structure, the final node member distribution matrix can be obtained through iterative updating; for the objective function dominated by the attribute information, the final attribute class distribution matrix can be obtained through iterative updating; the community to which the node belongs is determined according to the final node member distribution matrix U' or the final attribute class distribution matrix X' after iterative updating, specifically, the community to which node i belongs is determined according to the maximum value of the i-th row in the final node member distribution matrix U' or the maximum value of the i-th row in the final attribute class distribution matrix X'; for different networks, the community results obtained by these two matrices are generally different, so it is necessary to select a specific community detection result based on the actual network. For different networks, if the communities of node i obtained by the two matrices U' and X' are different, then for networks with attribute information higher than that in the topological structure, the community detection result obtained by the matrix X' is selected; otherwise, the community detection result obtained by the matrix U' is selected.

[0104] The present invention adopts a non-negative matrix decomposition algorithm to establish two models for attribute networks, namely a model with topological structure as the main factor and attribute information as the auxiliary factor, and a model with attribute information as the main factor and topological structure as the auxiliary factor. For networks with different degrees of attribute information richness in attribute networks, using different models is beneficial to the accuracy of community detection. At the same time, adding graph regularization constraints to the distribution matrix of the community can enhance the effect of community detection.

[0105] The technical effects of the present invention are further described in detail below in conjunction with simulation experiments.

[0106] 1. Simulation conditions and contents:

[0107] The simulation experiment of the present invention is carried out using Matlab R2018b software on a computer configured with Intel(R) Core(TM) i5-9300HCPU@2.40GHz, 16GB memory, and WINDOWS 10 system.

[0108] 2. Analysis of simulation results:

[0109] The simulation experiment of the present invention uses the Texas network diagram as the input network. The Texas network diagram is the content of the web page of the computer science department of a university in the United States, including hyperlink relationships and page text content. The download URL of the Texas network is http: / / www.cs.cmu.edu / afs / cs / project / theo-20 / www / data / . The network has a total of 187 nodes, 310 connections between nodes, 1703 attributes of each node, and 5 communities to which the node belongs. Figure 2 As shown, Figure 2 The numbers 1 to 187 in the diagram represent the node numbers in the Texas network diagram. Figure 2 It can be clearly seen that the nodes are divided into five clusters, which represent the five communities of the Texas network.

[0110] Figure 2 (a) is the real node community distribution diagram of the network. Figure 2 (b) is the community distribution diagram of nodes obtained using the DHCD method. Figure 2 (c) is a community distribution diagram of nodes obtained through simulation experiments using the present invention.

[0111] Depend on Figure 2 It can be seen that the community distribution map obtained by the present invention has better effect and is closer to the actual community distribution. Therefore, the present invention has a good community detection effect, lays a foundation for accurate community detection, and is a reasonable and effective attribute community detection method based on potential representation and graph regularized non-negative matrix decomposition.

[0112] The above simulation analysis proves the correctness and effectiveness of the method proposed in the present invention.

[0113] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, they may make various modifications and changes in form and details without departing from the principles and structures of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. An attribute community detection method based on latent representation and graph regularized non-negative matrix factorization, characterized in that: The steps include: (1) Inputting relevant data of the attribute network, the data including topological structure and node attribute information; let n represent the number of nodes in the network, and m represent the number of attributes in the network; the network of the attribute network is a social network, and the attributes are user attributes; (2) Processing relevant data in the attribute network: The topological matrix A∈R is obtained based on the edge information of the network nodes in the topological structure. n×n , according to the node attribute information, we get the attribute matrix Z∈R n×m , and use the attribute matrix Z to construct the affinity matrix B∈R n×n , the element in the i-th row and j-th column of the affinity matrix is ​​b ij : Where i, j = 1, 2, ..., n; z i and z j denote the i-th row and j-th row in the attribute matrix, i.e., the i-th node and j-th node in the attribute matrix, σ denotes the bandwidth parameter of the Gaussian function, and exp(·) denotes the exponential operation; (3) Define three non-negative matrix decomposition factor matrices and initialize them: Define the non-negative matrix decomposition factor matrix related to the topological graph: the node member distribution matrix U, and randomly initialize it to an n×k dimensional matrix; define the non-negative matrix decomposition factor matrix related to the attribute graph: the attribute class distribution matrix X and the attribute class description matrix Y, and randomly initialize them to n×k dimensional and m×k dimensional matrices respectively; (4) Establish the mapping relationship between the node member distribution matrix U and the attribute class distribution matrix X: Define two transfer matrices, namely the first transfer matrix P and the second transfer matrix Q; transform the attribute class distribution matrix X into the first transfer matrix P and the node member distribution matrix U, namely X=UP, or transform the node member distribution matrix U into the second transfer matrix Q and the attribute class distribution matrix X, namely U=XQ; and randomly initialize both transfer matrices to k×k dimensional matrices, where k represents the number of communities in the network; (5) Set the maximum number of iterations Max_iter = 100, the current number of iterations is it, and initialize it = 1; (6) Obtain the update formulas for three non-negative matrix decomposition factor matrices and two transfer matrices: (6a) Define the objective function formula of latent representation and graph regularized non-negative matrix factorization, that is, the objective function O(U,Y,P) dominated by the topology structure LRL_GNMFT and the objective function O(X,Y,Q) dominated by attribute information LRL_GNMFA : Among them, α represents O(U,Y,P) LRL_GNMFT The parameter of attribute information in the objective function, β represents O(X,Y,Q) LRL_GNMFA The parameters of the topological structure in the objective function, λ represents the influence parameter of the potential representation, θ represents the graph regularization parameter, It is expressed as the square of the F-norm of the matrix ·. The Euclidean distance between the two matrices is obtained by calculating the square of the F-norm of the difference between the two matrices. Tr(·) represents the trace of the matrix ·, and T represents the transpose operation. L1=D1-A represents the Laplace matrix of the topological matrix, and D1 represents the diagonal matrix of the topological matrix. L2=D2-B represents the Laplace matrix of the affinity matrix, and D2 represents the diagonal matrix of the affinity matrix. and All elements in are 1; (6b) Using the objective function formula defined in step (6a), the node member distribution matrix update formula, the attribute class distribution matrix update formula, the attribute class description matrix update formula and the transfer matrix update formula are obtained, which are as follows: The node member distribution matrix update formula in the objective function dominated by the topology structure is: in, and Respectively represent the element values ​​of the i-th row and j-th column of the node member distribution matrix U at the it+1th and itth iterations; The attribute class description matrix update formula in the objective function dominated by topology is: Where, d = 1, 2, ..., m, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations; The first transfer matrix update formula in the topology-dominated objective function is: Where l,r=1,2,…,k, and Respectively represent the element values ​​of the lth row and rth column of the first transfer matrix P at the it+1th and itth iterations; The attribute class distribution matrix update formula in the objective function dominated by attribute information is: in, and Respectively represent the element values ​​of the i-th row and j-th column of the attribute class distribution matrix X at the it+1th and itth iterations; The attribute class description matrix update formula in the objective function dominated by attribute information is: in, and Respectively represent the element values ​​of the i-th row and d-th column of the attribute class description matrix Y at the it+1th and itth iterations; The second transfer matrix update formula in the objective function dominated by attribute information is: in, and Respectively represent the element values ​​of the lth row and rth column of the second transfer matrix Q at the it+1th and itth iterations; (7) In the it-th iteration, the three non-negative matrix decomposition factor matrices and the two transfer matrices are updated respectively using the update formula obtained in step (6) to obtain the updated node member distribution matrix, attribute class description matrix, first transfer matrix, attribute class distribution matrix, attribute class description matrix, and second transfer matrix; (8) Determine whether the current number of iterations it reaches the preset maximum number of iterations Max_iter. If so, obtain the final node member distribution matrix U' and the final attribute class distribution matrix X' after iterative update, and execute step (9); otherwise, add 1 to it and return to execute step (7); (9) Community detection and output of detection results: According to the final node member distribution matrix U' or the final attribute class distribution matrix X' after iterative update, the community to which the node belongs is determined, and the community detection result is obtained and output.

2. The method according to claim 1, characterized in that: In the two transfer matrices described in step (4), according to the concept of transition probability in the Markov chain, each element in the first transfer matrix P and the second transfer matrix Q is non-negative, and the sum of the elements in each row is 1, that is, there are the following constraints:

3. The method according to claim 1, characterized in that: The objective function formulas of latent representation and graph regularized non-negative matrix factorization are defined in step (6a) as follows: (6a1) Using the non-negative matrix decomposition formula, we can obtain the functional relationship between the node member distribution matrix and the topology matrix: Functional relationship between attribute class distribution matrix, attribute class description matrix and attribute matrix According to the method of potential representation learning, the functional relationship between the attribute class distribution matrix and the affinity matrix is ​​obtained (6a2) Add the graph regularization term Tr(U T L1U) and Tr(X T L2X), and obtain the objective function O(U,Y,P) dominated by the topological structure LRL_GNMFT and the objective function O(X,Y,Q) dominated by attribute information LRL_GNMFA .

4. The method according to claim 1, characterized in that: In step (6b), the objective function formula defined in step (6a) is used to obtain the node member distribution matrix update formula, the attribute class distribution matrix update formula, the attribute class description matrix update formula and the transfer matrix update formula. The implementation steps are as follows: (6b1) Use Tr(MM T ) to get O(U,Y,P) LRL_GNMFT and O(X,Y,Q) LRL_GNMFA New expression: (6b2) Using the function O(U,Y,P) LRL_GNMFT Calculate partial derivatives of the node member distribution matrix, attribute class description matrix and first transfer matrix, and obtain the node member distribution matrix update formula, attribute class description matrix update formula and first transfer matrix update formula according to the Karush-Kuhn-Tucker condition; Using the function O(X,Y,Q) LRL_GNMFA The partial derivatives of the attribute distribution matrix, the attribute description matrix and the second transfer matrix are calculated, and the Karush-Kuhn-Tucker condition is used to obtain the attribute distribution matrix update formula, the attribute description matrix update formula and the second transfer matrix update formula.

5. The method according to claim 1, characterized in that: In step (9), the community to which the node belongs is determined according to the final node member distribution matrix U' or the final attribute class distribution matrix X' after iterative update. Specifically, the community to which node i belongs is determined according to the maximum value of the i-th row in the final node member distribution matrix U' or the maximum value of the i-th row in the final attribute class distribution matrix X'. For different networks, if the communities of node i obtained by the two matrices U' and X' are different, then for the network whose attribute information is higher than the information in the topological structure, the community detection result obtained by the matrix X' is selected; otherwise, the community detection result obtained by the matrix U' is selected.

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