A community detection method based on graph regularization integrating heterogeneous topology and node content

Abstract

The invention discloses a community detection method based on graph regularization to fuse heterogeneous topology and node content, belonging to the technical field of complex network analysis. The method identifies community structure in network data with content information, uses non-negative matrix decomposition and graph regularization of random block framework to model topology and content respectively, and based on the subspace clustering idea of ​​"nodes with similar content are likely to belong to the same community", fuses topology and content to construct a community detection model based on graph regularization non-negative matrix decomposition; finally, an evaluation algorithm is used to normalize mutual information entropy to evaluate the effectiveness of the model. The invention has the beneficial effects of: using graph regularization to fuse topology and content, and at the same time, proposing node popularity and K nearest neighbor consistency to process topology and content characteristics respectively, thereby improving community detection capability.

Description

Technical Field

[0001] The present invention relates to the technical field of complex network analysis, and in particular to a community detection method based on graph regularization and fusion of heterogeneous topologies and node contents. Background Art

[0002] A large amount of networked data, such as social networks and scientific paper networks, exists in all aspects of our lives, and they can be transformed into complex networks. Detecting communities composed of closely linked nodes in the network is one of the hot research topics in the field of complex network analysis. Generally speaking, community detection can mine user clusters with the same hobbies in social networks, and can also predict new research hotspots in scientific paper networks. According to research, complex networks contain both topological and content information, among which content information contains community information to assist the network and improve the accuracy of community detection. However, existing community detection methods fuse topology and content based on the homogeneity of information, without considering the heterogeneous characteristics of these two types of information, and there is still room for improvement in fusion efficiency. Based on the above analysis, how to improve the efficiency of community detection that fuses topological and content information, as well as the research theory related to community detection involving heterogeneous information characteristics, requires a new community detection method that simultaneously improves the efficiency of information fusion in the network and characterizes heterogeneous characteristics. Summary of the invention

[0003] The present invention provides a community detection method based on graph regularization to fuse heterogeneous topologies and node contents. The method mainly aims at the efficiency problem of topology and node content fusion in community detection and the technical problem of community detection with heterogeneous information characteristics. The present invention is based on a generation framework and subspace clustering ideas to achieve fusion of topology and node content; designs node popularity parameters and uses the k-nearest neighbor consistency principle to respectively process the heterogeneous characteristics of topology and node content to improve the accuracy of community detection of fused topology and node content; and expands the relevant theories of fused topology and node content community detection.

[0004] The idea of ​​the present invention is as follows: the first step is to formalize the topological information of the links between nodes, the node content information of the feature vector and other data; the second step is to construct a generative model based on non-negative matrix decomposition and a subspace-based graph regularization to model the topology and node content respectively; the third step is to design node popularity parameters and use the k-nearest neighbor consistency principle to deal with the node degree imbalance and the non-Euclidean characteristics of the node content information space respectively, so as to construct a community detection model based on graph regularization that integrates heterogeneous network topology and node content; finally, based on the Oja learning rule model optimization, the model parameters are derived, the node membership matrix is ​​obtained, clustering is performed, and the evaluation algorithm is used to evaluate the performance of the model.

[0005] The technical solution adopted by the present invention is: a method for detecting communities based on graph regularization integrating heterogeneous topology and node content, the method comprising the following steps:

[0006] S1. The network with content is represented as G = (V, E, Q), where V = {v1, v2, ..., v n} represents the set of nodes, E = {e1, e2, ..., e m} represents the set of topologies, Q = {q1, q2, ..., q n} represents the set of all node content vectors;

[0007] S2, formalize the topology and node content of the network G;

[0008] S3, using the topology representation matrix and the node content representation matrix to model the topology and node content of the network G respectively, respectively implementing the two sub-models in the model corresponding to this method, and then proposing the node popularity and k-nearest neighbor consistency principle to deal with heterogeneity;

[0009] S4. Use the generative framework and graph regularization to combine the two sub-models described in step S3 into one model, run the model on a real network dataset, and use normalized mutual information entropy to quantify the model effectiveness and evaluation.

[0010] The present invention provides a further optimized solution for a community detection method based on graph regularization integrating heterogeneous topology and node content, wherein step S2 specifically includes:

[0011] S2.1. The specific operation of formalizing the topology is as follows: Convert the network G into an adjacency matrix Node v in the network i and v j There is a link between ij =1 means that there is no link between the two nodes. ij =0 indicates.

[0012] S2.2. The specific operation of formalizing node content is as follows: the characteristic matrix of the content vector set Q of all nodes in the network G Among them, the r-dimensional vector q i Represents a node v i Then, the feature matrix Q is transformed into the node content similarity matrix Node v i and v j The cosine similarity of the feature vector is composed of components s ij express.

[0013] The present invention provides a further optimization scheme for the method of detecting community based on graph regularization fusion of heterogeneous topology and node content, wherein step S3 specifically comprises:

[0014] S3.1. Construct sub-model 1: Use the adjacency matrix A representing the topology, adopt the generative framework, and design the model parameters x icDescribes the node v that belongs to community c i The tendency to generate a link, x ic x jc That is, the node v in the community i and v j There is a tendency for a link between them. Next, summing up all the communities in the network G, we can get node v i and v j The expectation of creating a link between The expectation matrix is ​​constructed using the expectations of the links between these different nodes To fit the adjacency matrix A of the network G, the community membership matrix Indicates the tendency of nodes to belong to different communities. The objective function of sub-model 1 is as follows:

[0015]

[0016] S3.2. Construct sub-model 2: Use the similarity matrix S representing node content information. According to the assumption, if two nodes v i and v j Similarity in content ij is very high, then we promote their community membership vector x i and x j Similarly, vice versa, here, use u i represents the cth column of matrix X, D = diag (d1, d2, ..., d n ) represents a diagonal matrix, d i is the sum of the elements in the ith row of the similarity matrix S. The graph Laplacian matrix L = D–S, tr(*) represents the trace operation of the matrix. The objective function of sub-model 2 is as follows:

[0017]

[0018] S3.3, Heterogeneous topology and node content include different nodes with different popularity and node content similarity calculation based on non-Euclidean space. Here, the design parameter w i Characterize node v i The popularity of i The common factors of the elements in are The k-nearest neighbor consistency principle is used to characterize the non-Euclidean space of node content, which is formalized as retaining the node v in the matrix S i The non-zero elements of the nearest neighbors of s ij .

[0019] The present invention provides a further optimized solution for a community detection method based on graph regularization integrating heterogeneous topology and node content, wherein step S4 specifically comprises:

[0020] Using the adjacency matrix A, the node content similarity matrix S, and the graph Laplacian matrix L, we force the community membership of two nodes with high node content similarity to be similar. We use the generative framework to model the topology and the graph regularization to model the node content. We also consider the heterogeneity of topology and node content, and model the community membership with node popularity in a hard-constrained way. The specific objective function that integrates heterogeneous topology and content information is:

[0021]

[0022]

[0023] The matrix W consists of components w i A diagonal matrix with diagonal elements, and They represent C-dimensional vectors with all elements being 1 and N-dimensional vectors with all elements being 1, respectively. Next, the soft constraints are transformed into hard constraints, and the final objective function that integrates heterogeneous topology and content information is:

[0024]

[0025] Based on the minimization of the objective function, the model parameters X and W are updated based on the Oja learning rule until the value of the objective function converges, the community membership matrix X of the nodes is obtained, and clustering is performed based on the matrix X for community detection.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows: on the one hand, the present invention utilizes the generative framework to model topological information and the graph regularization to model node content information, and integrates network topology and node content according to the subspace clustering idea; on the other hand, the node popularity parameter is introduced and the k-nearest neighbor consistency principle is used to respectively process the heterogeneous characteristics of topological and node content information; not only heterogeneous topology and content are integrated, but also the quality of community detection in social networks with heterogeneous topology and node content is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0028] Figure 1 It is a schematic diagram of the overall process of the method for detecting community of heterogeneous topology and node content based on graph regularization fusion in the present invention. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0030] Example 1

[0031] See also Figure 1 , Table 1 and Table 2, the present invention provides a technical solution, a method for detecting communities based on graph regularization, fusion of heterogeneous topology and node content,

[0032] (1) Obtain community information of the dataset. Use the public dataset to obtain community information, community information G = (V, E, U): V = {v1, v2, ..., v n} is a node set, E = {e1, e2, ..., e m} is a link set, Q = {q1, q2, ..., q n} is the content vector set of all nodes, C is the number of communities, and the experimental data of the method for detecting community of heterogeneous topology and node content based on graph regularization fusion is shown in Table 1.

[0033] Among them, Cora is a scientific paper citation network, consisting of 2708 scientific papers in 7 sub-fields, with 5429 paper citation relationships. Facebook is an ego network, containing 1045 users, 26745 user relationships, user background information with content information consisting of 576 words, and has 7 "circle" communities. The WebKB network consists of 4 networks, in which web pages collected from the universities of Texas and Wisconsin have 1703 dimensions of word attributes and contain 5 communities.

[0034] Table 1 Experimental data information

[0035]

[0036] (2) The steps to obtain topology and node content information according to (1) are as follows:

[0037] According to the data in Table 1, the network G is formalized into an adjacency matrix The feature matrix of the node content vector set Q Among them, the r-dimensional vector q i Represents a node v i Then, the feature matrix Q is transformed into the node content similarity matrix Node v i and v j The cosine similarity of the feature vector is composed of components s ij express.

[0038] (3) Use topology and node content to construct sub-model 1 and sub-model 2 respectively. Use the adjacency matrix A, node content similarity matrix S, and graph Laplacian matrix L. According to the two nodes with high node content similarity, we force their community membership to be similar. Use the generative framework to model the topology and the graph regularization to model the node content. Considering the heterogeneity of topology and node content, we model the community membership with node popularity in a hard-constrained way. The objective function is:

[0039]

[0040] (4) Based on the minimization of the objective function, the model parameters X and W are updated based on the Oja learning rule until the value of the objective function converges, the community membership matrix X of the nodes is obtained, and clustering is performed based on the matrix X to perform community detection.

[0041] (5) Use normalized mutual information (NMI) as the evaluation index of the model. Its value range is [0, 1]. The larger the value, the more accurate the community detected by the model. * And the community division obtained by detection Component c in matrix C ij Indicates that it belongs to partition C * The i-th group and the one belonging to the partition The number of nodes in the jth group, partition C * (or ) contains c C* (or ) communities, the specific expression of NMI is as follows:

[0042]

[0043] (6) This experiment tests the proposed model on four public data sets. The experimental results of the method for detecting community based on graph regularization fusion of heterogeneous topology and node content are shown in Table 2:

[0044] Table 2 Test results based on public datasets

[0045]

[0046] As can be seen from Table 2, the proposed method is run on 4 public data sets with node content, and the model validity is verified based on the standard mutual information entropy (NMI), and the average value is calculated. On Cora, Facebook and Texas, the community divisions calculated by the method based on NMI are 40.50, 32.76 and 34.32 similar to the real community divisions, respectively, which are all higher than the average level of 32.59. Although the NMI value of the proposed method on the Wisconsin data set is 22.59, the method is still competitive in detecting community structures in real data sets based on graph regularization and fusion of heterogeneous topology and content information.

[0047] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A community detection method based on graph regularization that integrates heterogeneous topology and node content, applied to predict new research hotspots in scientific paper networks, characterized by: The community detection method comprises the following steps: S1. The network with node content is represented as G = (V, E, Q), where V = {v1, v2, ..., v n } represents the set of nodes, E = {e1, e2, ..., e m } represents the set of topologies, Q = {q1, q2, ..., q n } represents the content vector set of all nodes; The network is Cora, a scientific paper citation network consisting of 2708 scientific papers in 7 subfields, with 5429 paper citation relationships; S2, formalize the topology and node content of the network G; S3, using the topology representation matrix and the node content representation matrix to model the topology and node content of the network G respectively, respectively implementing the two sub-models in the model corresponding to this method, and then proposing the node popularity and k-nearest neighbor consistency principle to deal with heterogeneity; The specific process of step S3 is as follows: S3.

1. Construct sub-model 1: Use the adjacency matrix A representing the topology, adopt the generative framework, and design the model parameters x ic Describes the node v that belongs to community c i The tendency to generate a link, x ic x jc is the node v in the community i and v j There is a tendency for a link between them. By summing up all the communities in the network G, we can get node v i and v j The expectation of creating a link between The expectation matrix is ​​constructed using the expectations of the links between these different nodes To fit the adjacency matrix A of the network G, the community membership matrix Indicates the tendency of nodes to belong to different communities. The objective function of sub-model 1 is as follows: S3.

2. Construct sub-model 2: Use the similarity matrix S representing node content information. According to the assumption, if two nodes v i and v j Similarity in content ij High, which makes their community membership vector x i and x j Similarly, vice versa, here, use u i represents the cth column of matrix X, D = diag (d1, d2, ..., d n ) represents a diagonal matrix, d i is the sum of the elements in the ith row of the similarity matrix S. The graph Laplacian matrix L = D–S, tr(*) represents the trace operation of the matrix. The objective function of sub-model 2 is as follows: S3.3, Heterogeneous topology and node content include different nodes with different popularity and node content similarity calculation based on non-Euclidean space. Here, the design parameter w i Characterize node v i The popularity of i The common factors of the elements in are The k-nearest neighbor consistency principle is used to characterize the non-Euclidean space of node content, which is formalized as retaining the node v in the matrix S i The non-zero elements of the nearest neighbors of s ij ; S4. Use the generative framework and graph regularization to combine the two sub-models described in step S3 into one model, run the model on a real network dataset, and use normalized mutual information entropy to quantify the model effectiveness and evaluation.

2. The community detection method based on graph regularization and fusion of heterogeneous topology and node content according to claim 1 is characterized in that: The specific process of step S2 is as follows: S2.

1. The specific operation of formalizing the topology is as follows: Convert the network G into an adjacency matrix Node v in the network i and v j There is a link between ij =1 means that there is no link between the two nodes. ij =0 means; S2.

2. The specific operation of formalizing node content is as follows: the characteristic matrix of the content vector set Q of all nodes in the network G Among them, the r-dimensional vector q i Represents a node v i Then, the feature matrix Q is transformed into the node content similarity matrix Node v i and v j The cosine similarity of the feature vector is composed of components s ij express.

3. The community detection method based on graph regularization and fusion of heterogeneous topology and node content according to claim 1 is characterized in that: The specific process of step S4 is as follows: Using the adjacency matrix A, the node content similarity matrix S, and the graph Laplacian matrix L, we make the community membership of two nodes with high node content similarity similar. We use the generative framework to model the topology and the graph regularization to model the node content. We also consider the heterogeneity of topology and node content, and model the community membership with node popularity in a hard-constrained way. The specific objective function that integrates heterogeneous topology and content information is: The matrix W consists of components w i As a diagonal matrix with diagonal elements, and They represent C-dimensional vectors with all elements being 1 and N-dimensional vectors with all elements being 1, respectively. The soft constraints are transformed into hard constraints, and the final objective function that integrates heterogeneous topology and content information is: Based on the minimization of the objective function, the model parameters X and W are updated based on the Oja learning rule until the value of the objective function converges, the community membership matrix X of the nodes is obtained, and clustering is performed based on the matrix X for community detection.

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