Robust semi-supervised community detection method and system based on correlation entropy symmetric non-negative matrix factorization

Abstract

The invention relates to the technical field of community detection, and discloses a robust semi-supervised community detection method and system based on correlation entropy symmetric non-negative matrix factorization, and the method comprises the following specific steps: collecting community nodes, and constructing a community detection network model; constructing an initial adjacency matrix based on a community detection network model; on the basis of a pairwise constraint propagation algorithm, supervised information learning is carried out on the adjacency matrix to obtain a new adjacency matrix; a Gaussian kernel is adopted as a kernel function, and correlation entropy is constructed; constructing an optimization problem of non-negative matrix factorization of a new adjacent matrix based on correlation entropy and graph regularization; and solving an optimization problem by adopting a semi-quadratic optimization method to obtain an optimization matrix, and obtaining a final community detection result. The method solves the problem that a constraint propagation mechanism from constraint nodes to unconstraint nodes is lacked in the prior art, and has the characteristic of high anti-noise performance.

Description

Technical Field

[0001] The present invention relates to the technical field of community detection, and more specifically, to a robust semi-supervised community detection method and system based on correlation entropy symmetric non-negative matrix decomposition. Background Art

[0002] As a powerful analytical tool, the network can reveal the complex network relationships in social, biological, economic and other systems. One of the most notable properties of the network is its inherent community structure, which plays a key role in explaining its operating mechanism. The networks we display are usually diverse and complex. Different networks usually contain many different communities, and these communities have their own unique structures. Therefore, the core task of community detection is to identify the potential community structure in complex networks and reveal the relationship between potential communities and communities in the network structure, and between nodes in the community. In addition, community detection also has a profound impact on all aspects of our lives. For example, in social networks, community detection can be classified and processed according to the specific needs of users, and the content required by users can be accurately pushed; in the field of transportation, community detection can help us optimize the layout of urban transportation routes, build intelligent transportation systems, and improve the operating efficiency of urban transportation; in the medical field, community detection algorithms can help us identify signs of diseases, detect diseases earlier, and improve the cure rate of related diseases. Therefore, the research on community detection algorithms is of great significance both to complex networks and to our display life and production.

[0003] In the past decade, the method of non-negative matrix factorization has made considerable achievements in community detection due to its high computational efficiency and strong interpretability. When applied to networks, the main goal of the community detector of non-negative matrix factorization is to decompose the adjacency matrix of the network into two non-negative latent factor matrices, namely the basis matrix of nodes and communities and the response weight matrix of community membership matrix. Through matrix decomposition, iteration and optimization, the latent community structure matrix inherent in the target network is finally obtained. In many practical applications, completely unsupervised methods may not be able to capture all community structures. Semi-supervised non-negative matrix factorization algorithms can combine a small amount of labeled data to guide the decomposition process, so that the discovered communities are more consistent with the actual structure and semantics, thereby improving the quality of detection results. In recent years, studies have shown that there are two main strategies for using prior information to guide community detection methods in complex networks. The first strategy involves using prior information to construct a more informative adjacency matrix, and the second strategy integrates prior information into the graph regularization term. Both methods have demonstrated the ability to improve community detection performance. Therefore, it also promotes researchers to continue to explore semi-supervised non-negative matrix factorization in community detection.

[0004] The prior art has a community detection method based on semi-supervised non-negative matrix decomposition with similarity and dissimilarity constraints. The method mainly includes: 1) converting the edge connection data of the community complex network into an adjacency matrix A; 2) randomly extracting link information according to a ratio to obtain a priori subsets, and then constructing a Must-link matrix M and a Cannot-link matrix C respectively; 3) setting the maximum number of iterations maxiter and the non-negative feature dimension k, and randomly initializing the base matrix W and the coefficient matrix G; 4) obtaining the category label of the community according to the updated coefficient matrix G. The present invention proposes a semi-supervised community detection algorithm based on non-negative matrix decomposition, and introduces a priori information of must-link and cannot-link, respectively constructs similarity constraints and dissimilarity constraints between data samples, improves the representation ability of community network nodes, and is experimentally verified and analyzed through real community network data sets.

[0005] However, the existing technology lacks a constraint propagation mechanism from constrained nodes to unconstrained nodes. Therefore, how to invent a robust semi-supervised community detection method that considers pairwise constraint propagation is a technical problem that needs to be solved urgently in this technical field. Summary of the invention

[0006] In order to solve the problem that the prior art lacks a constraint propagation mechanism from constrained nodes to unconstrained nodes, the present invention provides a robust semi-supervised community detection method and system based on correlated entropy symmetric non-negative matrix decomposition, which has the characteristic of strong anti-noise performance.

[0007] In order to achieve the above-mentioned purpose of the present invention, the technical scheme adopted is as follows:

[0008] A robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization includes the following specific steps:

[0009] Collect community nodes and build a community detection network model;

[0010] Construct an initial adjacency matrix based on the community detection network model;

[0011] Based on the pairwise constraint propagation algorithm, supervised information learning is performed on the adjacency matrix to obtain a new adjacency matrix;

[0012] Gaussian kernel is used as kernel function to construct correlation entropy; the optimization problem of non-negative matrix decomposition of a new adjacency matrix is ​​constructed based on correlation entropy and graph regularization;

[0013] The semi-quadratic optimization method is used to solve the optimization problem, obtain the optimization matrix, and get the final community detection result.

[0014] Preferably, the community detection network model is specifically represented by a graph G=(X,E), where X={xij |i,j=1,2,...,n} represents a set of n nodes, E={e ij |i,j=1,2,...,n} represents a set of edges.

[0015] Furthermore, an initial adjacency matrix is ​​constructed based on the community detection network model, specifically: G is replaced by the adjacency matrix A = [a ij ]∈R n×n Indicates that a ij Represents two nodes x i and x j The interaction relationship between them; in the adjacency matrix A:

[0016]

[0017] Furthermore, the pairwise constraint propagation algorithm is specifically:

[0018] Constructing the link M = {(x i ,x j )|l i = l j ,l≤i,j≤n}∈R n×n Constraints and unlinkable C={(x i ,x j )|l i ≠l j ,l≤i,j≤n}∈R n×n Constraints, where l i For node x i Community tags.

[0019] Furthermore, supervised information learning is performed on the adjacency matrix to obtain a new adjacency matrix. The specific steps are:

[0020] Combine A, pairwise constraint matrix Z, and parameter β∈(0,1) to perform iterative optimization, t is the number of iterations, and finally output the new adjacency matrix The detailed steps are:

[0021] Calculate the initial pairwise constraint matrix Z = [z ij ]∈R n×n :

[0022]

[0023] Calculate the Laplace matrix The diagonal matrix

[0024] Repeat F v (t+1)=βLF v (t)+(1-β)Z until convergence, Fv Denotes constraint propagation F * vertical transmission;

[0025] Repeat Until convergence, F h Denotes constraint propagation F * Horizontal propagation of Yes {F v (t)} limit;

[0026] make in Yes {F h (t)} limit;

[0027] Calculate the new adjacency matrix using F and A

[0028]

[0029] Output the new adjacency matrix

[0030] Furthermore, the Gaussian kernel is used as the kernel function to construct the correlation entropy. The specific steps are:

[0031] Define a concept to estimate the probability distribution of data using the Parzen window method; the definition of quadratic entropy between random variables X and Y is expressed as:

[0032] Cor(X,Y)=E[κ σ (x,y)]=∫κ σ (x,y)dF XY (x,y),

[0033] Where E[·] is the expectation operator, κ σ (·,·) is the shift-invariant Mercer kernel function, F XY (x, y) is the joint distribution function of (x, y); the Gaussian kernel is used as the selected kernel function, and its mathematical definition is:

[0034]

[0035] Where σ>0 is the bandwidth parameter of the Gaussian kernel, which determines the characteristics of the Gaussian kernel;

[0036] Using a limited data sample set To estimate F XY The correlation coefficient of (x, y) gives the phase entropy:

[0037]

[0038] Furthermore, the optimization problem of non-negative matrix factorization of a new adjacency matrix is ​​constructed based on correlation entropy and graph regularization. The specific steps are:

[0039] Based on the correlation entropy, the similarity measure is used to replace the Frobenius norm in the symmetric illegal matrix decomposition algorithm to construct a new decomposition model of the adjacency matrix:

[0040]

[0041] Where n is the number of nodes, and V refers to the community optimization matrix;

[0042] Based on the clustering hypothesis, a new graph regularization model of the adjacency matrix is ​​constructed:

[0043]

[0044] Where Tr(·) represents the trace of the matrix, vi * represents the i-th row vector of V, is the graph Laplacian matrix, express The diagonal matrix of ;

[0045] Combining the decomposition model and the graph regularization model, we construct an optimization problem for symmetric semi-supervised illegal matrix decomposition:

[0046]

[0047] Furthermore, the semi-quadratic optimization method is used to solve the optimization problem, specifically:

[0048] Assume there exists a convex conjugate function of g(z) have:

[0049]

[0050] where ρ is a scalar variable, and for fixed z, the maximum value is reached at ρ = -g(z);

[0051] The optimization problem is further transformed into:

[0052]

[0053] Where ρ=[ρ 1 ,ρ 2 ,...,ρ n ] T is the auxiliary vector;

[0054] Fix V to maximize the optimization problem after deformation relative to ρ and calculate the auxiliary parameter ρ i :

[0055]

[0056] Calculate the parameter σ:

[0057]

[0058] The optimization problem for determining ρ and σ is obtained:

[0059]

[0060] in, Represents the objective function, and H is a diagonal matrix:

[0061]

[0062] Let φ=[φ ij ]∈R n×k To constrain the Langrangian multiplier matrix when V ≥ 0, the Lagrangian function of the optimization problem for determining ρ and σ is defined as:

[0063]

[0064] Assume the first-order derivative of J with respect to V, we have:

[0065]

[0066] According to KKT condition φ ij v ij =0, we get:

[0067]

[0068] consider Get the update rule based on gradient descent:

[0069]

[0070] Based on the update rule and the optimization problem, a multiplicative update method is used to solve the optimization problem.

[0071] Furthermore, the optimization problem is solved, the optimization matrix is ​​obtained, and the final community detection result is obtained, specifically: an update rule based on gradient descent is applied, and the update rule is repeatedly applied until the convergence condition of the optimization problem is met, and the final optimization matrix is ​​obtained; in the final optimization matrix, each column and row is used to indicate the community assignment of the corresponding node.

[0072] A robust semi-supervised community detection system based on correlation entropy symmetric non-negative matrix factorization, including a community detection network model building module, an adjacency matrix building module, a pairwise constraint propagation module, an optimization problem building module, and an optimization solution module;

[0073] The community detection network model building module is used to collect community nodes and build a community detection network model;

[0074] The adjacency matrix construction module is used to construct an initial adjacency matrix based on the community detection network model;

[0075] The pairwise constraint propagation module is used to perform supervised information learning on the adjacency matrix based on the pairwise constraint propagation algorithm to obtain a new adjacency matrix;

[0076] The optimization problem construction module is used to construct the correlation entropy using the Gaussian kernel as the kernel function; the optimization problem of constructing the non-negative matrix decomposition of a new adjacency matrix based on the correlation entropy and graph regularization;

[0077] The optimization solution module is used to solve the optimization problem using a semi-quadratic optimization method, obtain an optimization matrix, and obtain the final community detection result.

[0078] The beneficial effects of the present invention are as follows:

[0079] The present invention proposes a new symmetric non-negative matrix decomposition algorithm based on correlation entropy for community detection tasks in complex networks, which can enhance the performance of community detection tasks in complex networks; the present invention adopts a pairwise constraint propagation algorithm to effectively utilize limited pairwise constraint supervision information to reconstruct a more informative adjacency matrix, and plays a dual role in the symmetric non-negative matrix decomposition model and graph regularization process. The present invention adopts correlation entropy as a similarity measure, which improves robustness, effectively reduces the adverse effects of non-Gaussian noise and outliers in the data, and improves overall reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a flow chart of a robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix decomposition of the present invention.

[0081] Figure 2 It is a flow chart of a robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix decomposition in the embodiment of the present invention. DETAILED DESCRIPTION

[0082] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0083] Example 1

[0084] like Figure 1 As shown, a robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix decomposition includes the following specific steps:

[0085] Collect community nodes and build a community detection network model;

[0086] Construct an initial adjacency matrix based on the community detection network model;

[0087] Based on the pairwise constraint propagation algorithm, supervised information learning is performed on the adjacency matrix to obtain a new adjacency matrix;

[0088] Gaussian kernel is used as kernel function to construct correlation entropy; the optimization problem of non-negative matrix decomposition of a new adjacency matrix is ​​constructed based on correlation entropy and graph regularization;

[0089] The semi-quadratic optimization method is used to solve the optimization problem, obtain the optimization matrix, and get the final community detection result.

[0090] In this embodiment, considering the label matrix constraint may cause the model to be not flexible enough in handling unlabeled data, there are problems in computational efficiency and scalability, and self-supervised learning may produce misleading results when the label quality is not high or the data noise is large. Improper design of self-supervised tasks may also lead to problems such as the model's inability to effectively utilize unlabeled data. A pairwise constraint propagation algorithm is used to make full use of the labeled data and unlabeled data in the prior information, and at the same time construct the link relationship between the same community and the non-link relationship between different communities, and then propagate it to the entire adjacency matrix through constraints, so that the learned decomposition matrix has more information, thereby making more full use of limited supervision information.

[0091] In this embodiment, correlation entropy quantifies the similarity of two random variables (expressed as X and Y) in a specific region of their joint space, with particular emphasis on the probability distribution within the defined region. Due to its robustness in dealing with non-Gaussian noise and outliers, correlation entropy has gained significant attention and utilization in various applications. The present invention solves the problem of weak noise resistance and robustness of traditional semi-supervised non-negative matrix factorization technology by introducing the correlation coefficient.

[0092] In this embodiment, the graph regularization technology applies the new adjacency matrix generated by constraint propagation to the graph regularization processing, and uses the landmark information in the constraint propagation process to overcome the problems of category overlap and boundary fuzziness. At the same time, the link and non-link relationship between nodes solves the deviation caused by data imbalance, thereby ensuring the consistency of generated supervision data and sample data.

[0093] Example 2

[0094] More specifically, Figure 2 As shown, a robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix decomposition includes the following specific steps:

[0095] Collect community nodes and build a community detection network model;

[0096] In this embodiment, there are 4 communities, and the community nodes include unlinked nodes and linked nodes;

[0097] Construct an initial adjacency matrix based on the community detection network model to record the direct connection relationship between nodes;

[0098] Based on the pairwise constraint propagation algorithm, supervised information learning is performed on the adjacency matrix, and the known pairwise constraints are applied to the node pairs that are not directly constrained to obtain a new adjacency matrix; in the new adjacency matrix, the red dense blocks reflect the close connection within the community, and the blue sparse areas indicate the sparse connection across communities, which reflects the less interaction between communities;

[0099] The Gaussian kernel is used as the kernel function to measure the similarity between samples and construct the correlation entropy to further capture the complex relationship between nodes. The optimization problem of non-negative matrix decomposition of the new adjacency matrix is ​​constructed based on the correlation entropy and graph regularization. Among them, graph regularization is to add constraints on the graph structure in the optimization problem.

[0100] The semi-quadratic optimization method is used to solve the optimization problem, and the basis matrix and coefficient matrix are updated to approach the optimal solution to obtain the optimization matrix; the rows of the optimization matrix (W) represent each node, and the columns represent possible communities. Each value (W[i][j]) represents the degree to which node (i) belongs to community (j) and obtains the final community detection result. For each node, identify the column with the maximum value of the row corresponding to the node in (W). The index of the column is used as the community label of the node, that is, the node is assigned to the community with the maximum correlation with it, and finally all nodes are assigned to the four most suitable communities.

[0101] In a specific embodiment, the community detection network model is specifically represented by a graph G=(X,E), where X={x ij |i,j=1,2,...,n} represents a set of n nodes, E={e ij |i,j=1,2,...,n} represents a set of edges.

[0102] Furthermore, an initial adjacency matrix is ​​constructed based on the community detection network model, specifically: G is replaced by the adjacency matrix A = [a ij ]∈R n×n Indicates that a ij Represents two nodes x i and x j The interaction relationship between them; in the adjacency matrix A:

[0103]

[0104] In a specific embodiment, the pairwise constraint propagation algorithm is specifically:

[0105] For practical community detection tasks, a small amount of supervision information in the form of pairwise constraints is obtained in complex networks, including M = {(x i ,x j )|l i = l j ,l≤i,j≤n}∈R n×n Constraints and unlinkable C={(x i ,x j )|l i ≠l j ,l≤i,j≤n}∈R n×n Constraints, where l i For node x i Community tags.

[0106] In a specific embodiment, the present invention adopts a pairwise constraint propagation algorithm to make full use of supervised information to learn a better adjacency matrix. The supervised information learning is performed on the adjacency matrix to obtain a new adjacency matrix. The specific steps are:

[0107] Combine A, pairwise constraint matrix Z, and parameter β∈(0,1) to perform iterative optimization, t is the number of iterations, and finally output the new adjacency matrix The detailed steps are:

[0108] Calculate the initial pairwise constraint matrix Z = [z ij ]∈R n×n :

[0109]

[0110] Calculate the Laplace matrix The diagonal matrix

[0111] Repeat F v (t+1)=βLF v (t)+(1-β)Z until convergence, F v Denotes constraint propagation F * vertical transmission;

[0112] Repeat Until convergence, F h Denotes constraint propagation F * Horizontal propagation of Yes {F v (t)} limit;

[0113] make in Yes {F h (t)} limit;

[0114] Calculate the new adjacency matrix using F and A

[0115]

[0116] Output the new adjacency matrix

[0117] In a specific embodiment, a Gaussian kernel is used as a kernel function to construct the correlation entropy, and the specific steps are:

[0118] Correlation entropy is intrinsically linked to Renyi’s quadratic entropy, which defines a concept for estimating the probability distribution of data using the Parzen window method; the definition of quadratic entropy between random variables X and Y is expressed as:

[0119] Cor(X,Y)=E[κ σ (x,y)]=∫κ σ (x,y)dF XY (x,y),

[0120] Where E[·] is the expectation operator, κ σ (·,·) is the shift-invariant Mercer kernel function, F XY (x, y) is the joint distribution function of (x, y); the Gaussian kernel is used as the selected kernel function, and its mathematical definition is:

[0121]

[0122] Where σ>0 is the bandwidth parameter of the Gaussian kernel, which determines the characteristics of the Gaussian kernel;

[0123] Using a limited data sample set To estimate F XY The correlation coefficient of (x, y) gives the phase entropy:

[0124]

[0125] In a specific embodiment, the optimization problem of constructing a new adjacency matrix based on non-negative matrix decomposition based on correlation entropy and graph regularization is as follows:

[0126] Given that the adjacency matrix A is typically symmetric in most cases, in order to enhance the robustness of the existing semi-supervised decomposition method, based on the correlation entropy, the similarity measure is used to replace the Frobenius norm in the symmetric illegal matrix decomposition algorithm to construct a new decomposition model of the adjacency matrix:

[0127]

[0128] Where n is the number of nodes, and V refers to the community optimization matrix;

[0129] In this embodiment, the method proposed by the present invention not only uses the learned adjacency matrix as the decomposition matrix of the decomposition model, but also integrates it into the graph regularization to obtain a more discriminative group indicator matrix.

[0130] Based on the clustering hypothesis, a new graph regularization model of the adjacency matrix is ​​constructed:

[0131]

[0132] Where Tr(·) represents the trace of the matrix, vi * represents the i-th row vector of V, is the graph Laplacian matrix, express The diagonal matrix of ;

[0133] Combining the decomposition model and the graph regularization model, we construct an optimization problem for symmetric semi-supervised illegal matrix decomposition:

[0134]

[0135] In this embodiment, in order to solve the optimization problem inherent in this method, a semi-quadratic optimization method is usually used, which is grounded in the conjugate function theory. This method involves converting the objective function based on the correlation coefficient into a quadratic function in multiplicative form. Then, a multiplicative update method is used to solve the optimization problem.

[0136] In a specific embodiment, a semi-quadratic optimization method is used to solve the optimization problem, specifically:

[0137] Assume there exists a convex conjugate function of g(z) have:

[0138]

[0139] where ρ is a scalar variable, and for fixed z, the maximum value is reached at ρ = -g(z);

[0140] The optimization problem is further transformed into:

[0141]

[0142] Where ρ=[ρ 1 ,ρ 2 ,...,ρ n ] T is the auxiliary vector;

[0143] Fix V to maximize the optimization problem after deformation relative to ρ and calculate the auxiliary parameter ρ i :

[0144]

[0145] Calculate the parameter σ:

[0146]

[0147] The optimization problem for determining ρ and σ is obtained:

[0148]

[0149] in, Represents the objective function, and H is a diagonal matrix:

[0150]

[0151] Let φ=[φ ij ]∈R n×k To constrain the Langrangian multiplier matrix when V ≥ 0, the Lagrangian function of the optimization problem for determining ρ and σ is defined as:

[0152]

[0153] Assume the first-order derivative of J with respect to V, we have:

[0154]

[0155] According to KKT condition φ ij v ij =0, we get:

[0156]

[0157] consider Get the update rule based on gradient descent:

[0158]

[0159] Based on the update rule and the optimization problem, a multiplicative update method is used to solve the optimization problem.

[0160] In a specific embodiment, solving the optimization problem, obtaining the optimization matrix, and obtaining the final community detection result are specifically: applying an update rule based on gradient descent, repeatedly applying the update rule until the convergence condition of the optimization problem is met, and obtaining the final optimization matrix; in the final optimization matrix, each column and row is used to indicate the community assignment of the corresponding node.

[0161] In this embodiment, an update rule based on gradient descent is applied. When the update rule is repeatedly applied, the regularization parameter α and the parameter β responsible for adjusting the pairwise constraint propagation are configured to 0.01 and 0.5 respectively to achieve the best optimization performance.

[0162] In this embodiment, the present invention breaks through the limitations of traditional semi-supervised non-negative matrix decomposition methods in community detection. This method not only constructs a single constraint matrix of node-to-node link relationships based on prior information, but also forms a pairwise constraint matrix by constructing link relationships between the same nodes and non-link relationships between different nodes, thereby making more effective use of limited supervisory information and improving the efficiency of supervisory information utilization.

[0163] In this embodiment, the present invention focuses on solving the problem that the traditional semi-supervised model is not strong in noise resistance and robustness, and uses the method of correlation entropy to replace the square Frobenius norm or L 2,1 The deficiencies in processing non-Gaussian noise and abnormal data caused by the norm further improve the model's ability to process abnormal data and its anti-interference ability, making the performance of the present invention in complex network community detection more accurate and robust.

[0164] In this embodiment, the existing semi-supervised non-negative matrix factorization algorithm is often highly dependent on the quality and quantity of prior information when learning the regularization term. Too much or too little will affect the regularization effect, and is not conducive to the model's exploration of the deeper structure of the community within the group. The present invention overcomes the dependence of traditional semi-supervised non-negative matrix factorization on prior information by using paired constraint propagation to learn the adjacency matrix as the regularization term input matrix, and can better learn the community structure characteristics within the group.

[0165] Example 3

[0166] A robust semi-supervised community detection system based on correlation entropy symmetric non-negative matrix factorization, including a community detection network model building module, an adjacency matrix building module, a pairwise constraint propagation module, an optimization problem building module, and an optimization solution module;

[0167] The community detection network model building module is used to collect community nodes and build a community detection network model;

[0168] The adjacency matrix construction module is used to construct an initial adjacency matrix based on the community detection network model;

[0169] The pairwise constraint propagation module is used to perform supervised information learning on the adjacency matrix based on the pairwise constraint propagation algorithm to obtain a new adjacency matrix;

[0170] The optimization problem construction module is used to construct the correlation entropy using the Gaussian kernel as the kernel function; the optimization problem of constructing the non-negative matrix decomposition of a new adjacency matrix based on the correlation entropy and graph regularization;

[0171] The optimization solution module is used to solve the optimization problem using a semi-quadratic optimization method, obtain an optimization matrix, and obtain the final community detection result.

[0172] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization, characterized by: The specific steps include: Collect community nodes and build a community detection network model; Construct an initial adjacency matrix based on the community detection network model; Based on the pairwise constraint propagation algorithm, supervised information learning is performed on the adjacency matrix to obtain a new adjacency matrix; Gaussian kernel is used as kernel function to construct correlation entropy; The optimization problem of non-negative matrix factorization based on correlation entropy and graph regularization to construct a new adjacency matrix; The semi-quadratic optimization method is used to solve the optimization problem, obtain the optimization matrix, and get the final community detection result.

2. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 1, characterized in that: The community detection network model is specifically represented by a graph G = (X, E), where X = {x ij |i,j=1,2,...,n} represents a set of n nodes, E={e ij |i,j=1,2,...,n} represents a set of edges.

3. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 2, characterized in that: The initial adjacency matrix is ​​constructed based on the community detection network model, specifically: G is replaced by the adjacency matrix A = [a ij ]∈R n×n Indicates that a ij Represents two nodes x i and x j The interaction relationship between them; in the adjacency matrix A:

4. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 3, characterized in that: The pairwise constraint propagation algorithm is specifically: Constructing the link M = {(x i ,x j )|l i = l j ,l≤i,j≤n}∈R n×n Constraints and unlinkable C={(x i ,x j )|l i ≠l j ,l≤i,j≤n}∈R n×n Constraints, where l i For node x i Community tags.

5. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 4, characterized in that: Perform supervised information learning on the adjacency matrix to obtain a new adjacency matrix. The specific steps are: Combine A, pairwise constraint matrix Z, and parameter β∈(0,1) to perform iterative optimization, t is the number of iterations, and finally output the new adjacency matrix The detailed steps are: Calculate the initial pairwise constraint matrix Z = [z ij ]∈R n×n : Calculate the Laplace matrix The diagonal matrix Repeat F v (t+1)=βLF v (t)+(1-β)Z until convergence, F v Denotes constraint propagation F * vertical transmission; Repeat Until convergence, F h Denotes constraint propagation F * Horizontal propagation of Yes {F v (t)} limit; make in Yes {F h (t)} limit; Calculate the new adjacency matrix using F and A ∈R n×n : Output the new adjacency matrix 6. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 5, characterized in that: The Gaussian kernel is used as the kernel function to construct the correlation entropy. The specific steps are: Define a concept to estimate the probability distribution of data using the Parzen window method; the definition of quadratic entropy between random variables X and Y is expressed as: Cor(X,Y)=E[κ σ (x,y)]=∫κ σ (x,y)dF XY (x,y), Where E[·] is the expectation operator, κ σ (·,·) is the shift-invariant Mercer kernel function, F XY (x, y) is the joint distribution function of (x, y); the Gaussian kernel is used as the selected kernel function, and its mathematical definition is: Where σ>0 is the bandwidth parameter of the Gaussian kernel, which determines the characteristics of the Gaussian kernel; Using a limited data sample set To estimate F XY The correlation coefficient of (x, y) gives the phase entropy:

7. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 6, characterized in that: The optimization problem of non-negative matrix factorization based on correlation entropy and graph regularization to construct a new adjacency matrix is ​​as follows: Based on the correlation entropy, the similarity measure is used to replace the Frobenius norm in the symmetric illegal matrix decomposition algorithm to construct a new decomposition model of the adjacency matrix: Where n is the number of nodes, and V refers to the community optimization matrix; Based on the clustering hypothesis, a new graph regularization model of the adjacency matrix is ​​constructed: Where Tr(·) represents the trace of the matrix, v i* represents the i-th row vector of V, is the graph Laplacian matrix, express The diagonal matrix of ; Combining the decomposition model and the graph regularization model, we construct an optimization problem for symmetric semi-supervised illegal matrix decomposition:

8. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 7, characterized in that: The semi-quadratic optimization method is used to solve the optimization problem, specifically: Assume there exists a convex conjugate function of g(z) have: where ρ is a scalar variable, and for fixed z, the maximum value is reached at ρ = -g(z); The optimization problem is further transformed into: Where ρ=[ρ1,ρ2,...,ρ n ] T is the auxiliary vector; Fix V to maximize the optimization problem after deformation relative to ρ and calculate the auxiliary parameter ρ i : Calculate the parameter σ: The optimization problem for determining ρ and σ is obtained: in, Represents the objective function, and H is a diagonal matrix: Let φ=[φ ij ]∈R n×k To constrain the Langrangian multiplier matrix when V ≥ 0, the Lagrangian function of the optimization problem for determining ρ and σ is defined as: Assume the first-order derivative of J with respect to V, we have: According to KKT condition φ ij v ij =0, we get: consider Get the update rule based on gradient descent: Based on the update rule and the optimization problem, a multiplicative update method is used to solve the optimization problem.

9. The robust semi-supervised community detection method based on correlation entropy symmetric non-negative matrix factorization according to claim 6, characterized in that: Solve the optimization problem, obtain the optimization matrix, and obtain the final community detection result, specifically: apply the update rule based on gradient descent, repeatedly apply the update rule until the convergence condition of the optimization problem is met, and obtain the final optimization matrix; in the final optimization matrix, each column and row is used to indicate the community assignment of the corresponding node.

10. A robust semi-supervised community detection system based on correlation entropy symmetric non-negative matrix factorization, characterized by: It includes community detection network model building module, adjacency matrix building module, pairwise constraint propagation module, optimization problem building module, and optimization solution module; The community detection network model building module is used to collect community nodes and build a community detection network model; The adjacency matrix construction module is used to construct an initial adjacency matrix based on the community detection network model; The pairwise constraint propagation module is used to perform supervised information learning on the adjacency matrix based on the pairwise constraint propagation algorithm to obtain a new adjacency matrix; The optimization problem building module is used to use a Gaussian kernel as a kernel function to build a correlation entropy; The optimization problem of non-negative matrix factorization based on correlation entropy and graph regularization to construct a new adjacency matrix; The optimization solution module is used to solve the optimization problem using a semi-quadratic optimization method, obtain an optimization matrix, and obtain the final community detection result.

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