A unified semi-supervised community detection method integrating content information

Abstract

The present invention belongs to the technical field of complex network analysis, and specifically relates to a semi-supervised community detection method for unified fusion content information. The steps of the present invention are: formalizing the topology and content information in a network with node content; using a generation framework based on non-negative matrix decomposition to realize a topology sub-model based on standard NMF and SNMF, calculating the structural similarity to construct must-link prior information to adjust the node community membership, drawing on the idea of ​​pLSA topic model, and constructing a content sub-model based on non-negative matrix decomposition; introducing a balance factor to unify and fuse the topology sub-model and content sub-model with prior information, and then constructing a unified fusion node content semi-supervised community detection model, finally, using the gradient descent method to learn model parameters, obtain the community membership matrix of the node, clustering to mine the community structure in the network, and using the standardized mutual information entropy NMI and the adjusted Rand coefficient ARI to evaluate the model performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network analysis, and in particular relates to a semi-supervised community detection method that unifies and integrates content information. Background Art

[0002] There are a lot of network data such as social networks in the real world, which can be transformed into complex networks. Analyzing complex networks has important research significance and wide application value. Mining communities composed of closely linked nodes in the network is one of the hot research in the field of complex network analysis. Studies have found that complex networks contain both network topology and node content. Node content helps to mitigate the impact of noise and missing links in the topology and improve the accuracy of community detection. At the same time, there are different complex structures in the network topology, which affect the topology's ability to represent community structure. In order to solve the above two problems, how to effectively improve the integration of topology, prior information and content information for community detection, as well as the related research theories of semi-supervised community detection, a new method of semi-supervised community detection that unifies the integration of network topology, prior information and node content information is urgently needed. Summary of the invention

[0003] The present invention provides a semi-supervised community detection method that unifies and integrates content information, mainly based on the following two starting points: first, the must-link prior information contained in the topological information can enhance the network topology, thereby improving the model robustness and performance; second, the model integrates node content information to mitigate the negative impact caused by noise or missing links in the topological information, and plays a certain supplementary role in the topological information, thereby enhancing the performance of the model. The present invention uses the topological information of the nodes to calculate the structural similarity of the nodes to realize the construction of must-link prior information; uses a generation framework based on non-negative matrix decomposition to construct a topological sub-model and a content sub-model; unifies and integrates the topological information, content information, and topological prior information to improve the model robustness and community detection accuracy.

[0004] The technical solution adopted by the present invention is:

[0005] A semi-supervised community detection method that unifies and integrates content information includes the following steps:

[0006] S1. The network with node content information can be described as G = (V, E, F), where V = {v1, v2, ..., v n} represents the set of nodes in the network, E = {e1, e2, ..., e m} represents the set of links in the network, F = {f1, f2, ..., f l} represents the collection of node contents in the network;

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

[0008] S3, using topological information to build a topological sub-model based on standard NMF and SNMF, using the topological information of nodes in the network to construct the prior information of must-link, adjusting the node community membership to build a topological sub-model that integrates prior information, and using the node content information to build a content sub-model based on NMF;

[0009] S4. Use the generative framework to merge the topological sub-model and content sub-model that integrate prior information in step S3 into a unified semi-supervised community detection model, apply the model to real network data, and use the standardized mutual information entropy NMI and adjusted Rand coefficient ARI to quantitatively evaluate the performance of different models under the same framework.

[0010] As a preferred technical solution of the present invention: the specific process of step S2 is as follows:

[0011] S2.1. The specific operation of formalizing topological information is as follows: Use the adjacency matrix A = {a ij}∈R n×n To represent the network topology information, if the node v i and v j If there is a link between ij =1, otherwise a ij =0;

[0012] S2.2. The specific operation of formalizing content information is as follows: Use the content matrix B = {b ij}∈R n×l To represent the node content information, if the node v i If b contains the jth content ij =1, otherwise b ij =0.

[0013] As a preferred technical solution of the present invention: the specific process of step S3 is as follows:

[0014] S3.1. Constructing a topological sub-model integrating prior information:

[0015] (I) First, use the matrix X∈R n×k Describe the distribution of node community membership, then in the entire network k communities v i and v j The expected number of links between is expressed as:

[0016]

[0017] Among them, x ij Represents node v iThe tendency to belong to the jth community. The link between nodes in the network depends on the probability that the two nodes belong to the same community, x it x jt Represents node v in community t i and v j The number of links generated between them; this is used to construct the expected adjacency matrix Right now To fit the adjacency matrix A;

[0018] Therefore, the loss function of the topology sub-model is:

[0019]

[0020] The idea of ​​data dimensionality reduction based on non-negative matrix decomposition can map the original data into a low-dimensional space to capture the community structure information contained in the topological information, thereby constructing a topological sub-model based on the standard NMF, and its loss function is:

[0021]

[0022] Where W∈R n×k is called the basis matrix, and X is called the representation matrix;

[0023] (II) Then, we use the similarity of node topology to construct must-link prior information and use the neighborhood of the node to describe the node topology. Then, the node v i and v j The topology-based structural similarity is defined as:

[0024]

[0025] Where, neighborhood D(i) = {v j ∈V|(v i ,v j )∈E}∪{v i} is used to represent node v i The topological structure of

[0026] Formula (4) can be used to calculate the structural similarity between any two nodes in the network and construct the similarity matrix S = {s ij}∈R n×n , constructing prior information based on the following idea: if there is a link between two nodes in the network and the structural similarity is very high, then there is a must-link relationship between the two nodes, and they are classified into the same community, so the constraint matrix Ω = {ω ij}∈R n×n It can be defined as:

[0027]

[0028] Where ε is a neighborhood hyperparameter that adjusts the number of must-links; calculate the connected components P in the constraint matrix Ω = {p1, p2, …, p q}, then the nodes in each connected component satisfy the must-link relationship, that is, the nodes of the same connected component should be classified into the same community; then the node community membership matrix X is expressed as:

[0029] X=CY (6)

[0030] Where C∈R n×q is the indicator matrix, which records the connected components to which each node belongs to represent the prior information; Y∈R q ×k is a non-negative auxiliary matrix introduced;

[0031] From formula (6), we can see that if the node v i and v j There is a must-link between them, then c i. =c j. , so x i. =c i. Y=c j. Y = x j. , that is, nodes v with the same membership distribution i and v j must be classified in the same community;

[0032] (III) Finally, from formula (6), we can see that the community membership matrix X can be reconstructed by the indicator matrix C and the auxiliary matrix Y, so as to realize the integration of prior information. The loss function of the topological sub-model that integrates prior information can be further modified as follows:

[0033]

[0034]

[0035] Among them, X represents the community membership matrix, C represents the indicator matrix, and Y represents the auxiliary matrix;

[0036] S3.2. Content sub-model construction: We build a content sub-model by drawing on the idea of ​​the pLSA topic model. We regard each node in the network as a document. The community corresponds to the topic in the document set, and the attributes of the node content correspond to the words in the document. Then the node v i The relationship between and the j-th feature is expressed as:

[0037]

[0038] Among them, h jt represents the tendency of community t to contain the jth word, xit h jt Represents node v i The tendency to belong to the t-th community and the community contains the j-th word;

[0039] Use formula (9) to generate the expected content matrix Right now To fit the content matrix B, the loss function of the content sub-model is:

[0040]

[0041] in, represents the expected content matrix, and B represents the content matrix.

[0042] As a preferred technical solution of the present invention: the specific process of step S4 is as follows:

[0043] S4.1. For the fusion prior information topology sub-model and content sub-model described in S3, balance factors α and β are used to integrate the two sub-models to construct different models under a unified framework. The final objective functions of the different models are:

[0044]

[0045]

[0046] Among them, α and β are used to control the proportion of content information in the model;

[0047] S4.2, based on the minimization of the objective function and the Oja learning rule, the model parameters W, Y, and H are updated until the value of the objective function converges;

[0048] S4.3. Clustering based on matrix X for community detection.

[0049] 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 idea based on non-negative matrix decomposition to model topology information and content information, and introduces a balance factor to unify and integrate network topology and node content; on the other hand, the must-link prior information is introduced to adjust the node membership matrix by calculating the structural similarity in the topology information; not only the network topology, prior information and content information are unified and integrated, but also the performance and robustness of the network community detection model with topology and node content are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the method of the present invention. DETAILED DESCRIPTION

[0051] 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.

[0052] See also Figure 1 , a semi-supervised community detection method that unifies and integrates content information, comprising the following steps:

[0053] S1. The network with node content information can be described as G = (V, E, F), where V = {v1, v2, ..., v n} represents the set of nodes in the network, E = {e1, e2, ..., e m} represents the set of links in the network, F = {f1, f2, ..., f l} represents the collection of node contents in the network;

[0054] S2, formalize the topology information and content information of the network G;

[0055] S3, using topological information to build a topological sub-model based on standard NMF and SNMF, using the topological information of nodes in the network to construct the prior information of must-link, adjusting the node community membership to build a topological sub-model that integrates prior information, and using the node content information to build a content sub-model based on NMF;

[0056] S4. Use the generative framework to merge the topological sub-model and content sub-model that integrate prior information in step S3 into a unified semi-supervised community detection model, apply the model to real network data, and use the standardized mutual information entropy NMI and adjusted Rand coefficient ARI to quantitatively evaluate the performance of different models under the same framework.

[0057] The specific process of step S2 is as follows:

[0058] S2.1. The specific operation of formalizing topological information is as follows: Use the adjacency matrix A = {a ij}∈R n×n To represent the network topology information, if the node v i and v j If there is a link between ij =1, otherwise a ij =0;

[0059] S2.2. The specific operation of formalizing content information is as follows: Use the content matrix B = {b ij}∈R n×l To represent the node content information, if the node v i If b contains the jth content ij =1, otherwise b ij =0.

[0060] As a preferred technical solution of the present invention: the specific process of step S3 is as follows:

[0061] S3.1. Constructing a topological sub-model integrating prior information:

[0062] (I) First, use the matrix X∈R n×k Describe the distribution of node community membership, then in the entire network k communities v i and v j The expected number of links between is expressed as:

[0063]

[0064] Among them, x ij Represents node v i The tendency to belong to the jth community. The link between nodes in the network depends on the probability that the two nodes belong to the same community, x it x jt Represents node v in community t i and v j The number of links generated between them; this is used to construct the expected adjacency matrix Right now To fit the adjacency matrix A;

[0065] Therefore, the loss function of the topology sub-model is:

[0066]

[0067] The idea of ​​data dimensionality reduction based on non-negative matrix decomposition can map the original data into a low-dimensional space to capture the community structure information contained in the topological information, thereby constructing a topological sub-model based on the standard NMF, and its loss function is:

[0068]

[0069] Where W∈R n×k is called the basis matrix, and X is called the representation matrix;

[0070] (II) Then, we use the similarity of node topology to construct must-link prior information and use the neighborhood of the node to describe the node topology. Then, the node v i and v j The topology-based structural similarity is defined as:

[0071]

[0072] Where, neighborhood D(i) = {v j ∈V|(v i ,v j)∈E}∪{v i} is used to represent node v i The topological structure of

[0073] Formula (4) can be used to calculate the structural similarity between any two nodes in the network and construct the similarity matrix S = {s ij}∈R n×n , constructing prior information based on the following idea: if there is a link between two nodes in the network and the structural similarity is very high, then there is a must-link relationship between the two nodes, and they are classified into the same community, so the constraint matrix Ω = {ω ij}∈R n×n It can be defined as:

[0074]

[0075] Where ε is a neighborhood hyperparameter that adjusts the number of must-links; calculate the connected components P in the constraint matrix Ω = {p1, p2, …, p q}, then the nodes in each connected component satisfy the must-link relationship, that is, the nodes of the same connected component should be classified into the same community; then the node community membership matrix X is expressed as:

[0076] X=CY (6)

[0077] Where C∈R n×q is the indicator matrix, which records the connected components to which each node belongs to represent the prior information; Y∈R q ×k is a non-negative auxiliary matrix introduced;

[0078] From formula (6), we can see that if the node v i and v j There is a must-link between them, then c i. =c j. , so x i .=c i .Y=c j .Y=x j ., that is, nodes with the same membership distribution v i and v j must be classified in the same community;

[0079] (III) Finally, from formula (6), we can see that the community membership matrix X can be reconstructed by the indicator matrix C and the auxiliary matrix Y, so as to realize the integration of prior information. The loss function of the topological sub-model that integrates prior information can be further modified as follows:

[0080]

[0081]

[0082] Among them, X represents the community membership matrix, C represents the indicator matrix, and Y represents the auxiliary matrix;

[0083] S3.2. Content sub-model construction: We build a content sub-model by referring to the idea of ​​pLSA topic model. We regard each node in the network as a document. The community corresponds to the topic in the document set, and the attributes of the node content correspond to the words in the document. Then the node v i The relationship between and the j-th feature is expressed as:

[0084]

[0085] Among them, h jt represents the tendency of community t to contain the jth word, x it h jt Represents node v i The tendency to belong to the t-th community and the community contains the j-th word;

[0086] Use formula (9) to generate the expected content matrix Right now To fit the content matrix B, the loss function of the content sub-model is:

[0087]

[0088] in, represents the expected content matrix, and B represents the content matrix.

[0089] The specific process of step S4 is as follows:

[0090] S4.1. For the fusion prior information topology sub-model and content sub-model described in S3, balance factors α and β are used to integrate the two sub-models to construct different models under a unified framework. The final objective functions of the different models are:

[0091]

[0092]

[0093] Among them, α and β are used to control the proportion of content information in the model;

[0094] S4.2, based on the minimization of the objective function and the Oja learning rule, the model parameters W, Y, and H are updated until the value of the objective function converges;

[0095] S4.3. Clustering based on matrix X for community detection.

[0096] For specific implementation, see Figure 1 , Table 1 and Table 2, a semi-supervised community detection method for unified fusion content information provided by the present invention,

[0097] (1) Obtain data set information and use the public data set to obtain network information. The network G = (V, E, F), where V = {v1, v2, ..., v n} represents the set of nodes in the network, E = {e1, e2, ..., e m} represents the set of links in the network, F = {f1, f2, ..., f l} represents the set of node content vectors in the network, k is the number of communities, and the experimental data of the semi-supervised community detection framework that unifies and integrates content information of the present invention is shown in Table 1.

[0098] Table 1 Experimental data information

[0099]

[0100]

[0101] The dataset uses the WebKB network, which consists of four sub-networks. These sub-networks are web pages collected from four universities: Cornell, Texas, Washington, and Wisconsin, and the hyperlinks between them. Nodes in the network represent web pages, and links represent hyperlinks between two web pages. Each web page has 1588, 1498, 1578, and 1623-dimensional binary word attributes, respectively. Each sub-network contains 5 communities.

[0102] (2) The steps for obtaining topology and node content information in (1) are as follows:

[0103] 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 F

[0104] (3) Use topology and node content to construct the topology sub-model, must-link prior information and content sub-model respectively. Use the adjacency matrix A, the prior information indicator matrix C and the node content feature matrix B. If there is a link between two nodes in the network and the structural similarity is very high, then there is a must-link relationship between the two nodes. They can be classified into the same community. The indicator matrix is ​​used to adjust the node community membership. At the same time, the node membership matrix is ​​used as the representation matrix of the content sub-model. The objective function under the same framework is obtained as follows:

[0105]

[0106]

[0107] (4) Based on the minimization of the objective function, the model parameters Y and H are updated based on the Oja learning rule until the value of the objective function converges, and the community membership matrix X of the nodes is obtained. Clustering is performed based on the matrix X to perform community detection.

[0108] (5) Use normalized mutual information (NMI) and adjusted Rand index (ARI) as evaluation indicators of the model. The value range of NMI is [0,1]. The larger the value, the more accurate the community detected by the model. * And the community division obtained by detection The component g in the matrix G ij Indicates that both belong to partition G * The i-th group and the one belonging to the partition The number of nodes in the jth group, partition G * (or ) contains k * (or ) communities, the specific expression of NMI is as follows:

[0109]

[0110] ARI is an improvement on the Rand index (RI). It solves the problem that the expected value of RI between two random partitions is not a constant (for example, 0) when using RI to evaluate clustering results. This evaluation method only focuses on the clustering effect of the model and evaluates various types of models indiscriminately. Its value range is [-1,1]. The larger the value, the more accurate the model is in detecting the community structure. The specific expression of ARI is as follows:

[0111]

[0112] Among them, t ij is an element in the contingency table T, indicating the number of nodes that appear in both the real community i and the detected community j.

[0113] (6) This experiment tests the model under the same framework of the present invention on four public data sets. The experimental results of the semi-supervised community detection framework of the present invention that unifies and integrates content information are shown in Table 2:

[0114] Table 2 compares the performance of various methods with the change of ε, using NMI and ARI as evaluation indicators.

[0115]

[0116]

[0117] As can be seen from Table 2, the model under the framework proposed by the present invention is run on 4 public data sets with node content, and the model validity is verified by calculating the standard mutual information entropy (NMI) and the adjusted Rand coefficient (ARI). On different data sets, as the number of must-links increases, the community divisions calculated based on NMI and ARI and the real community divisions of the two models under the framework are gradually closer, verifying that the fusion of prior information achieves the performance improvement of the model. Among them, the community detection execution of the model under the framework proposed by the present invention has obvious advantages, and the community detection accuracy based on NMI calculation is higher than the compared semi-supervised community detection model. It should be noted that when ε takes the value of 0.85 and 0.9, the model ECD has model learning anomalies, so there is no community detection result, marked as "-". Based on the evaluation method ARI that is independent of the clustering method, the community detection accuracy of the models SCDNC_SYM and SCDNC_LSE under the framework proposed by the present invention also shows competitive performance in Cornell, Washington, and Wisconsin.

[0118] The steps of the present invention are as follows: formalizing the topology and content information in a network with node content; using a generation framework based on non-negative matrix decomposition to realize a topology sub-model based on standard NMF and SNMF, calculating the structural similarity to construct must-link prior information to adjust the node community membership, drawing on the idea of ​​the pLSA topic model, and constructing a content sub-model based on non-negative matrix decomposition; introducing a balance factor to unify and fuse the topology sub-model and the content sub-model with prior information, and then constructing a unified fusion node content semi-supervised community detection model, finally, using the gradient descent method to learn model parameters, obtaining the community membership matrix of the node, clustering to mine the community structure in the network, and using the standardized mutual information entropy NMI and the adjusted Rand coefficient ARI to evaluate the model performance.

[0119] The specific implementation scheme described above further describes in detail the purpose, technical scheme and beneficial effects of the present invention. It should be understood that the above is only a specific implementation scheme of the present invention and is not intended to limit the scope of the present invention. Any equivalent changes and modifications made by any technician in the field without departing from the concept and principle of the present invention should fall within the scope of protection of the present invention.

Claims

1. A semi-supervised community detection method that unifies and integrates content information, characterized in that: The following steps are involved: S1. The network with node content information can be described as G = (V, E, F), where V = {v1, v2, ..., v n } represents the set of nodes in the network, E = {e1, e2, ..., e m } represents the set of links in the network, F = {f1, f2, ..., f l } represents the collection of node contents in the network; S2, formalize the topology information and content information of the network G; S3, using topological information to build a topological sub-model based on standard NMF and SNMF, using the topological information of nodes in the network to construct the prior information of must-link, adjusting the node community membership to build a topological sub-model that integrates prior information, and using the node content information to build a content sub-model based on NMF; S4. Use the generative framework to combine the topological sub-model and content sub-model that integrate prior information in step S3 into a unified semi-supervised community detection model, apply the model to real network data, and use the normalized mutual information entropy NMI and adjusted Rand coefficient ARI to quantitatively evaluate the performance of different models under the same framework. The specific process of step S3 is as follows: S3.

1. Constructing a topological sub-model integrating prior information: (I) First, use the matrix X∈R n×k Describe the distribution of node community membership, then in the entire network k communities v i and v j The expected number of links between is expressed as: Among them, x ij Represents node v i The tendency to belong to the jth community. The link between nodes in the network depends on the probability that the two nodes belong to the same community, x it x jt Represents node v in community t i and v j The number of links generated between them; this is used to construct the expected adjacency matrix Right now To fit the adjacency matrix A; Therefore, the loss function of the topology sub-model is: The idea of ​​data dimensionality reduction based on non-negative matrix decomposition can map the original data into a low-dimensional space to capture the community structure information contained in the topological information, thereby constructing a topological sub-model based on the standard NMF, and its loss function is: Where W∈R n×k is called the basis matrix, and X is called the representation matrix; (II) Then, we use the similarity of node topology to construct must-link prior information and use the neighborhood of the node to describe the node topology. Then, the node v i and v j The topology-based structural similarity is defined as: Where, neighborhood D(i) = {v j ∈V|(v i ,v j )∈E}∪{v i } is used to represent the topological structure of node vi; Formula (4) can be used to calculate the structural similarity between any two nodes in the network and construct the similarity matrix S = {s ij }∈R n×n , constructing prior information based on the following idea: if there is a link between two nodes in the network and the structural similarity is very high, then there is a must-link relationship between the two nodes, and they are classified into the same community, so the constraint matrix Ω = {w ij }∈R n×n It can be defined as: Where ε is a neighborhood hyperparameter that adjusts the number of must-links; calculate the connected components P in the constraint matrix Ω = {p1, p2, …, p q }, then the nodes in each connected component satisfy the must-link relationship, that is, the nodes of the same connected component should be classified into the same community; then the node community membership matrix X is expressed as: X=CY (6) Where C∈R n×q is the indicator matrix, which records the connected components to which each node belongs to represent the prior information; Y∈R q×k is a non-negative auxiliary matrix introduced; From formula (6), we can see that if the node v i and v j There is a must-link between them, then c i. =c j. , so x i. =c i. Y=c j .Y=x j ., that is, nodes with the same membership distribution v i and v j must be classified in the same community; (III) Finally, from formula (6), we can see that the community membership matrix X can be reconstructed by the indicator matrix C and the auxiliary matrix Y, so as to realize the integration of prior information. The loss function of the topological sub-model that integrates prior information can be further modified as follows: Among them, X represents the community membership matrix, C represents the indicator matrix, and Y represents the auxiliary matrix; S3.

2. Content sub-model construction: We build a content sub-model by drawing on the idea of ​​the pLSA topic model. We regard each node in the network as a document. The community corresponds to the topic in the document set, and the attributes of the node content correspond to the words in the document. Then the node v i The relationship between and the j-th feature is expressed as: Among them, h jt represents the tendency of community t to contain the jth word, x it h jt Represents node v i The tendency to belong to the t-th community and the community contains the j-th word; Use formula (9) to generate the expected content matrix Right now To fit the content matrix B, the loss function of the content sub-model is: in, represents the expected content matrix, and B represents the content matrix.

2. The semi-supervised community detection method of unified fusion content information according to claim 1 is characterized in that: The specific process of step S2 is as follows: S2.

1. The specific operation of formalizing topological information is as follows: Use the adjacency matrix A = {a ij }∈R n×n To represent the network topology information, if the node v i and v j If there is a link between ij =1, otherwise a ij =0; S2.

2. The specific operation of formalizing content information is as follows: Use the content matrix B = {b ij }∈R n×l To represent the node content information, if the node v i If b contains the jth content ij =1, otherwise b ij =0.

3. The semi-supervised community detection method of unified fusion content information according to claim 2 is characterized in that: The specific process of step S4 is as follows: S4.

1. For the fusion prior information topology sub-model and content sub-model described in S3, balance factors α and β are used to integrate the two sub-models to construct different models under a unified framework. The final objective functions of the different models are: Among them, α and β are used to control the proportion of content information in the model; S4.2, based on the minimization of the objective function and the Oja learning rule, the model parameters W, Y, and H are updated until the value of the objective function converges; S4.

3. Clustering based on matrix X for community detection.

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