Core-peripheral random block model clustering aggregation method for literature reference network

Abstract

The invention relates to the technical field of literature citation network analysis and graph model research, and particularly discloses a literature citation network core-peripheral random block model clustering aggregation method which comprises the following steps: S1, defining a literature citation network; s2, constructing a core-peripheral random block model of the literature reference network; s3, constructing a spoke model and a hierarchical model; s4, inferring the core-peripheral random block model of the literature reference network by adopting Bayesian reasoning; s5, on the basis of a model minimum description length (MDL) principle, optimizing and evaluating the literature reference network core-peripheral random block model; s6, carrying out structure aggregation on the literature reference network core-peripheral random block model; and S7, obtaining an influence literature, namely a core node. According to the scheme, through combination of Bayesian inference and the random block model, priori knowledge in the literature reference network can be encoded, the model fitting capability is enhanced, and the representation precision of the core-peripheral structure can be optimized through local weighted aggregation.

Description

Technical Field

[0001] The present invention relates to the field of network science, in particular to the technical field of literature citation network analysis and graph model research, and proposes a literature citation network core-periphery random block model clustering aggregation method, specifically a Bayesian optimization-driven literature citation network core-periphery random block model clustering aggregation method, which is used for literature influence analysis and scientific research dynamics prediction. Background Art

[0002] In the process of continuous deepening of academic research and knowledge accumulation, literature citation network, as an important carrier of knowledge dissemination and academic exchange, has gradually attracted widespread attention. Literature citation network is composed of academic papers and their mutual citation relationships, reflecting the inheritance of academic ideas, the cross-integration of disciplines and the evolution of research hotspots. Literature citation network is similar to social network, whose nodes represent specific academic documents and edges represent citation relationships between documents. Identifying influential documents is of great significance for understanding and mastering literature citation network.

[0003] Existing research still has limitations in understanding the structural characteristics and knowledge flow patterns of literature citation networks, especially in how to accurately identify and analyze the core-periphery structure in the network. Although traditional network analysis methods such as centrality analysis and clustering algorithms can provide certain insights, they are often difficult to effectively capture the global characteristics and local differences of the network when dealing with large-scale, complex and changeable literature citation networks. In addition, the core-periphery structures obtained by different methods may be inconsistent, making the comprehensive analysis and understanding of the network structure challenging. Therefore, how to propose a method that can accurately characterize the core-periphery structure of the literature citation network and conduct effective structural aggregation and analysis on this basis has become an important issue in current academic research.

[0004] The application of existing core-periphery structure analysis methods in academic citation networks has the following problems: 1) There are large differences in the core-periphery structures obtained by different methods, and there is a lack of unified evaluation standards; 2) It is difficult for traditional methods to introduce prior knowledge into the model, which affects the accuracy of the results; 3) The clustering aggregation scheme of existing methods does not fully consider the weight of local features. If it is directly applied to network analysis, it may lead to insufficient network representation capabilities. Therefore, in order to solve the above problems, it is necessary to propose a clustering aggregation method for the core-periphery random block model of literature citation networks. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a document citation network core-periphery random block model clustering aggregation method, specifically a Bayesian optimization driven document citation network core-periphery random block model clustering aggregation method, which can be used for document influence analysis and scientific research dynamics prediction, and solves the inconsistency and accuracy problems existing in existing methods when analyzing the core-periphery structure of document citation networks.

[0006] This method divides the nodes (papers) in the literature citation network into core nodes and peripheral nodes by constructing a core-periphery random block model to reveal the dissemination path and influence distribution of academic knowledge. The Bayesian prior is introduced to combine network data and prior knowledge to improve the accuracy of core-periphery structure identification. At the same time, the minimum description length (MDL) of the model is used as the optimization target to avoid model overfitting and improve the robustness and generalization ability of the model. In addition, using the idea of ​​clustering aggregation, a core-periphery structure aggregation scheme is designed. By calculating the uncertainty and reliability of the node set and determining the local aggregation weight, multiple core-periphery structures are aggregated into a comprehensive consensus core-periphery structure, which more accurately reflects the overall characteristics of the academic citation network and the influence of core papers. This method significantly improves the accuracy and robustness of the core-periphery structure analysis of the literature citation network, and provides more precise theoretical support for academic influence analysis.

[0007] To achieve the above object, the present invention adopts the following technical solution: a document citation network core-periphery random block model clustering method, comprising the following steps:

[0008] S1. Define the literature citation network; give the definition of the literature citation network G(V, E), G(V, E) includes a set V consisting of N nodes and a set E consisting of M unweighted directed edges, where each unweighted directed edge represents a specific citation record of the document;

[0009] S2, constructing a core-periphery random block model of literature citation network;

[0010] S3, construct hub-and-spoke model and hierarchical model;

[0011] S4, using Bayesian inference to infer the core-periphery random block model of the literature citation network;

[0012] S5: Based on the principle of minimum description length of the model, the core-periphery random block model of the literature citation network is optimized and evaluated;

[0013] S6: Structural aggregation of the core-periphery random block model of the literature citation network;

[0014] S7: Obtain influential documents, i.e. core nodes.

[0015] Furthermore, constructing the literature citation network core-periphery random block model in step S2 includes the following steps:

[0016] S21: The model assumptions of the core-periphery random block model of the literature citation network are given, that is, the core nodes and peripheral nodes are assigned to different blocks, and based on the defined G(V, E) a given The corresponding adjacency matrix of the literature citation network of nodes is , Nodes are randomly assigned to M blocks;

[0017] S22: The length of the The block allocation vector D represents the block allocation of nodes in the literature citation network, which is specifically expressed as , where the node is assigned to block s and is represented accordingly as ; The connection probability of any two nodes in G(V, E) is expressed by the matrix express, represents the probability of connecting a node in block s to a node in block t; in the core-periphery random block model of the reference network, the connection probability between two nodes depends on the block assignment matrix D and the block connection matrix ;

[0018] S23: Based on the Bayesian method, with the block allocation vector D and the block connection matrix The prior probability is connected to get formula 1: ;in, Symbols indicate proportions, Indicates that when the adjacency matrix is ​​observed Under the condition that the block allocation vector and block connection matrix The joint probability distribution of represents the prior distribution of the block allocation vector, represents the prior distribution of the block connectivity matrix, Indicates a given and Generate an adjacency matrix probability.

[0019] Furthermore, the hub-and-spoke model in S3 is obtained by combining the two-block model with the core-periphery random block model of the literature citation network; the two-block model divides the network nodes into core blocks and peripheral blocks, and connects them through the block connection matrix A structural model that defines the probability of connections between nodes; in the hub-and-spoke model, network nodes are divided into two sets of nodes: core nodes and peripheral nodes. Core nodes are connected to each other, core nodes are connected to some peripheral nodes, and peripheral nodes are not connected to each other.

[0020] The core block of the hub-and-spoke model is encoded as , the peripheral block is encoded as ; The specific definition is and ( ),in, represents the connection probability of the internal nodes of the core block. In the hub-and-spoke model, , that is, the core nodes are fully connected, represents the connection probability between the core block and the peripheral block, represents the connection probability of the internal nodes of the peripheral block;

[0021] The prior constraints of the block connection matrix R of the hub-and-spoke model are expressed by Formula 2 and Formula 3: Formula 2 is: ; Formula 3 is ;in, is an indicator function used to define the block connection matrix in the hub-and-spoke model The legal constraints Represents the block connectivity matrix The prior probability distribution of .

[0022] Furthermore, the hierarchical model in S3 is obtained by combining the k-core model with the core-periphery random block model of the literature citation network; in the hierarchical model, the network nodes are layered based on the k-core decomposition method, where the k-core represents the set of all nodes in the network that are connected to at least k other nodes;

[0023] The prior constraints of the block connection matrix R of the hierarchical model are expressed by Formula 4 and Formula 5; Formula 4 is , Formula 5 is ;in, is an indicator function that ensures that the block connectivity matrix of the hierarchical model In line with its structural assumptions, Represents the block connectivity matrix The prior probability distribution of .

[0024] Furthermore, in S4, Bayesian reasoning is used to infer the core-periphery random block model of the literature citation network, which specifically includes the following sub-steps:

[0025] S41: Based on the Gibbs sampling idea, alternate sampling block allocation vector D and block connection matrix , that is, first fix the block allocation vector D and update the block connection matrix , and then fix the updated block connection matrix And further update the block allocation vector D;

[0026] S42: Gibbs sampling process node The most frequently allocated block s is used as the statistical block allocation, i.e. ; For two blocks s and t, two quantities are specified: the two quantities are specifically the number of edges that actually exist in the block and the maximum number of edges that can exist ;

[0027] S43: According to and , the expectation of the edges from block s to other blocks in the core-periphery random block model of the literature citation network is expressed as , the expectation without edge connection is ;

[0028] Posterior distribution of the core-periphery random block model of literature citation networks It is expressed by formula 6: ;in, Indicates that in a given block The connection probability Under the conditions, it was observed The probability of an edge, Representation Block The connection probability Representation Block The number of potential unconnected edges, is an indicator function used to enforce a priori constraints on the hierarchical model;

[0029] S44: Using Markov Chain Monte Carlo simulation method based on Get the posterior distribution ; Randomly allocate blocks to nodes in the literature citation network. After a certain number of iterations, randomly select a node And update its block tag ;

[0030] S45: Random sampling is used for Select its new block tag ,Right now , where L is the number of model layers; Reverse and get the new block allocation ;

[0031] S46: According to the Metropolis-Hastings criterion, calculate the acceptance The probability is calculated by formula 7, which is: ;in, Represents the connectivity matrix in a given block and the adjacency matrix Under the condition of The posterior probability of and Respectively represent the old allocation Transfer to New Allocation The proposed distribution probability and the probability of reverse transition.

[0032] Further, step S5 is specifically as follows: using variation information measurement to quantify the differences between different core-periphery structures, and using the minimum description length model to evaluate the fit and network feature representation ability of each core-periphery structure; the evaluation indicators of the core-periphery structure provided are as follows:

[0033] Select a node from the citation network , Belongs to the node collection The probability of is expressed by formula eight, which is: ,in and They are and the number of nodes contained in the literature citation network; define a length of A discrete random variable, The variables correspond to the core-periphery division The number of sets contained in ; discrete random variables The entropy of is expressed by formula nine, which is: ;

[0034] Given two different core-periphery node partitions and ,exist The node collection in correspond The node collection in ;Will In the division Belongs to the node set And in the division Belongs to the node set The joint probability distribution of is expressed by formula 10, which is ;in, Indicated in and It is divided into Also divided into The number of nodes;

[0035] Using mutual information to describe About the division Information; Select in the network , exist The uncertainty in ; and The MI value is expressed by Formula 11, which is: ;in, represents the amount of shared information between the two partitions. By subtracting the shared information from the total uncertainty, we get the difference between the two. Indicates that the node belongs to The cth set and Middle The joint probability of a set of Indicates that the node belongs to a partition The probability of the cth set in Indicates that the node belongs to a partition Middle The probability of a set;

[0036] Will and Considered as a division and division The uncertainty of the node set, Representation Division and division The known information shared in the network is used to calculate the sum of uncertainties and eliminate the influence of shared information to obtain the VI distance between different core-periphery node partitions. The value of the VI distance is expressed by Formula 12, which is: .

[0037] Furthermore, when using the minimum description length model to evaluate the fit and network feature representation ability of each core-periphery structure, the evaluation of the core-periphery random block model is divided into the number of bits of the core-periphery random block model itself and the number of bits required by the core-periphery random block model to describe the network data, that is, ; The model length describing the network data is approximately expressed by Formula 13, which is: ;in, represents the minimum description length of the core-periphery random block model; represents the coding length of the model M, i.e. the number of bits required to describe the core-periphery random block model structure itself; Indicates that under a given model M, the encoding data block is allocated , block connection matrix , adjacency matrix The number of bits required; Indicates that a given block is allocated , connection matrix Under model M, the adjacency matrix The likelihood function of ;

[0038] Using Monte Carlo simulations in Get indivual The sample of the approximate model describes the integral of the length; the sum of the intervals between the samples obtained by sampling is 1, and the distribution probability of the intervals is consistent and randomly combined. Describe the sample ,Right now ;

[0039] Taking the logarithm of the core-periphery random block model description length, the core-periphery random block model description length is obtained as a formula, which is specifically expressed by Formula 14. Formula 14 is: ;in, ; Indicates that a given block is allocated and block connection matrix The log-likelihood function of the adjacency matrix A is Under a given model M, we observe the adjacency matrix A and the block assignment The joint probability of Indicates that under model M, block allocation The prior probability of .

[0040] Furthermore, in step S6, the core-periphery random block model of the literature citation network is subjected to structural aggregation, including estimating the uncertainty of the core-periphery structure in each core-periphery partition using the concept of information entropy, specifically:

[0041] Given a set of nodes Core and Periphery Division ,in and Respectively represent all node sets and core-periphery partition sets, , ; for The uncertainty is taken into account How do the nodes in Calculate from formula 15 Each node in The node collection in The distribution of , formula 15 is: ;in, Indicates that it belongs to the node set at the same time and division A subset of The number of nodes; Indicates belonging to a set The number of nodes;

[0042] Further distribution for The uncertainty of is specifically expressed by Formula 16, which is: ;in, Is a collection of nodes and division A subset of The distribution ratio of

[0043] Introducing the core-periphery structure into the calculation of uncertainty ,get For the core-periphery partition set Uncertainty , expressed by Formula 17, Formula 17 is: ;in, Represents a node collection In the division local uncertainty in Indicates the kth core peripheral partition The minimum description length.

[0044] Furthermore, in step S6, the core-periphery random block model of the literature citation network is subjected to structural aggregation, including using an integrated driven clustering index to represent the reliability corresponding to each node set; given the core-periphery partition set and , There are a total of Core periphery partition, node set of It is expressed by formula 18, which is: ; Among them, the parameters To balance the instability The impact of growth, Represents a node collection The combined uncertainty in the core-periphery partition set P;

[0045] Based on the local weighted core-periphery structure aggregation method of bipartite graph, the nodes in the literature citation network, the core node set and the peripheral node set are all taken as the nodes of the bipartite graph. Indicators and core-periphery division Combined;

[0046] Define a bipartite graph ,in , represents all nodes, S represents the union of the core node set and the peripheral node set, and W represents The weight matrix of the edges between two different sets of nodes in , ;

[0047] Nodes belonging to different sets and The edge weight between The definition of is shown in Formula 19: ;

[0048] Calculate the degree matrix U of the nodes in the bipartite graph. The elements in the matrix ; According to the degree matrix U and weight Calculate the normalized weight matrix , and find out The length k feature matrix ;Will Each row of is normalized to unit length, Each row of is the k-dimensional embedding of a node in the bipartite graph. K-means is used to cluster the nodes. Nodes in the same part of the clustering result are considered to belong to the same set, and the partition result of the bipartite graph is obtained. The partition result of the bipartite graph corresponds to the consensus core-periphery structure after aggregation.

[0049] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0050] 1. This solution can solve the inconsistency and accuracy problems in the core-periphery structure analysis of the literature citation network. By introducing Bayesian priors and the model minimum description length (MDL) optimization aggregation scheme, this method significantly improves the accuracy and robustness of the model. It can use Bayesian priors combined with network data to more accurately identify core and peripheral papers and reveal the dissemination path and influence distribution of academic knowledge.

[0051] 2. This scheme uses the MDL optimization aggregation scheme to effectively integrate the core-periphery structures obtained by different methods to form a more representative and stable consensus structure. This method can not only better evaluate the influence of core papers in the academic citation network, but also provide more precise theoretical support for academic influence analysis, and provide a strong basis for the analysis and decision-making of academic research.

[0052] 3. This scheme calculates the uncertainty and reliability of each node set, determines the local aggregation weight, and aggregates multiple core-periphery structures in the literature citation network analysis into a more representative and robust consensus core-periphery structure; by combining Bayesian inference with the random block model, it can not only encode the prior knowledge in the literature citation network and enhance the model fitting ability, but also optimize the representation accuracy of the core-periphery structure through local weighted aggregation. This invention provides an important theoretical basis for the importance measurement of documents, the accurate identification of core documents, and the analysis of document influence.

[0053] In summary, the present invention proposes a Bayesian optimization driven literature citation network core-periphery random block model clustering aggregation method, which combines Bayesian prior and model minimum description length (MDL) optimization, can accurately identify core papers and peripheral papers in the literature citation network, reveal the dissemination path and influence distribution of academic knowledge, and the introduction of Bayesian prior improves the model's ability to handle data uncertainty and noise, while MDL optimization effectively avoids model overfitting and improves the robustness and generalization ability of the model. In addition, the clustering aggregation scheme aggregates multiple core-periphery structures into a comprehensive consensus structure by calculating the uncertainty and reliability of the node set, thereby improving the stability and accuracy of the analysis results.

[0054] Compared with existing methods, the present invention can more accurately reflect the overall characteristics of the literature citation network and the influence of core papers. The practical significance of the present invention lies in providing more precise theoretical support and tools for academic influence analysis, helping researchers to better understand the dynamics and trends of academic research, providing a strong basis for academic decision-making and resource allocation, and promoting the in-depth development of academic research and knowledge innovation. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is the overall flow chart of the present invention.

[0056] Figure 2 is a schematic diagram of the spoke model in the present invention;

[0057] Figure 3 It is a schematic diagram of the hierarchical model in the present invention;

[0058] Figure 4 The figure is a polymerization flow chart of the local weighted core-periphery structure in the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following Figure 1-4 It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0060] A core-periphery random block model clustering aggregation method for literature citation networks, such as Figure 1 As shown, the following steps are included:

[0061] S1. Define the literature citation network; give the definition of the literature citation network G(V, E), G(V, E) includes a set V consisting of N nodes and a set E consisting of M unweighted directed edges, where each unweighted directed edge represents a specific citation record of the document.

[0062] S2, constructing a core-periphery random block model of the literature citation network. In step S2, constructing a core-periphery random block model of the literature citation network includes the following steps:

[0063] S21: The model assumptions of the core-periphery random block model of the literature citation network are given, that is, the core nodes and peripheral nodes are assigned to different blocks, and based on the defined G(V, E) a given The corresponding adjacency matrix of the literature citation network of nodes is , Nodes are randomly assigned to M blocks;

[0064] S22: The block allocation vector D of length N represents the block allocation of nodes in the literature citation network, which is specifically expressed as , where the node is assigned to block s and is represented accordingly as ; The connection probability of any two nodes in G(V, E) is expressed by the matrix express, represents the probability of connecting a node in block s to a node in block t; in the core-periphery random block model of the reference network, the connection probability between two nodes depends on the block assignment matrix D and the block connection matrix ;

[0065] S23: Based on the Bayesian method, Combined with the prior probability of the block assignment vector D and the block connection matrix R, we get Formula 1: ;in, Symbols indicate proportions, Indicates that when the adjacency matrix is ​​observed Under the condition that the block allocation vector and block connection matrix The joint probability distribution of represents the prior distribution of the block allocation vector, represents the prior distribution of the block connectivity matrix, Indicates a given and Generate an adjacency matrix probability.

[0066] S3, build a hub-and-spoke model and a hierarchical model. The hub-and-spoke model in S3 is obtained by combining the two-block model with the core-periphery random block model of the literature citation network; the two-block model divides the network nodes into core blocks and peripheral blocks, and connects them through the block connection matrix A structural model that defines the probability of connection between nodes; in the hub-and-spoke model, network nodes are divided into two node sets: core nodes and peripheral nodes. The core nodes are connected to each other, the core nodes and some peripheral nodes are connected to each other, and the peripheral nodes are not connected to each other.

[0067] The core block of the hub-and-spoke model is encoded as , the peripheral block is encoded as ; The specific definition is and ( ),in, represents the connection probability of the internal nodes of the core block. In the hub-and-spoke model, , that is, the core nodes are fully connected, represents the connection probability between the core block and the peripheral block, represents the connection probability of the internal nodes of the peripheral block.

[0068] Figure 2 This is a schematic diagram of the hub-and-spoke model, in which the mutual connections between nodes in the core layer are the densest, while the number of connections between nodes in the peripheral layer opposite to the core layer and the core nodes is second, and the mutual connections between nodes in the peripheral layer are the sparsest.

[0069] The prior constraints of the block connection matrix R of the hub-and-spoke model are expressed by Formula 2 and Formula 3; Formula 2 is: ; Formula 3 is ;in, is an indicator function used to define the block connection matrix in the hub-and-spoke model The legal constraints Represents the block connectivity matrix The prior probability distribution of .

[0070] The hierarchical model in S3 is obtained by combining the k-core model with the core-periphery random block model of the literature citation network. In the hierarchical model, the network nodes are layered based on the k-core decomposition method, where the k-core represents the set of nodes in the network that are connected to at least other k nodes. The k-core decomposition method defines a k-shell hierarchy, where each layer of the k-shell consists of all nodes in the k-core, but does not include nodes in the (k + 1) core. The hierarchy gradually increases the connectivity from the outside to the inside. Figure 3 This is a schematic diagram of a hierarchical model. The nodes in the innermost first layer are most likely to be connected to the nodes in other layers, and the probability of nodes in other layers being connected to nodes in more peripheral layers is lower.

[0071] The prior constraints of the block connection matrix R of the hierarchical model are expressed by Formula 4 and Formula 5; Formula 4 is , Formula 5 is ;in, is an indicator function that ensures that the block connectivity matrix of the hierarchical model In line with its structural assumptions, Represents the block connectivity matrix The prior probability distribution of .

[0072] S4, using Bayesian reasoning to infer the core-periphery random block model of the literature citation network. In S4, using Bayesian reasoning to infer the core-periphery random block model of the literature citation network specifically includes the following sub-steps:

[0073] S41: Based on the Gibbs sampling idea, alternate sampling block allocation vector D and block connection matrix , that is, first fix the block allocation vector D and update the block connection matrix , and then fix the updated block connection matrix And further update the block allocation vector D.

[0074] S42: Gibbs sampling process node The most frequently allocated block s is used as the statistical block allocation, i.e. ; For two blocks s and t, two quantities are specified: the two quantities are specifically the number of edges that actually exist in the block and the maximum number of edges that can exist .

[0075] S43: According to and , the expectation of the edges from block s to other blocks in the core-periphery random block model of the literature citation network is expressed as , the expectation without edge connection is .

[0076] Posterior distribution of the core-periphery random block model of literature citation networks It is expressed by formula 6: ;in, Indicates that in a given block The connection probability Under the conditions, it was observed The probability of an edge, Representation Block The connection probability, Representation Block The number of potential unconnected edges, is an indicator function used to enforce a priori constraints on the hierarchical model.

[0077] S44: Using Markov Chain Monte Carlo simulation method based on Get the posterior distribution , randomly assign blocks to nodes in the literature citation network, and after a certain number of iterations, randomly select a node And update its block tag .

[0078] S45: Random sampling is used for Select its new block tag ,Right now , where L is the number of model layers; Reverse and get the new block allocation .

[0079] S46: According to the Metropolis-Hastings criterion, calculate the acceptance The probability is calculated by formula 7, which is: ;in, Represents the connectivity matrix in a given block and the adjacency matrix Under the condition of The posterior probability of and Respectively represent the old allocation Transfer to New Allocation The proposed distribution probability and the probability of reverse transition.

[0080] S5: Based on the principle of the minimum description length (MDL) of the model, the core-periphery random block model of the literature citation network is optimized and evaluated. Step S5 is as follows: the variation information (VI) metric is used to quantify the differences between different core-periphery structures, and the minimum description length (MDL) model is used to evaluate the fit and network feature representation ability of each core-periphery structure; the evaluation indicators of the core-periphery structure provided are as follows:

[0081] Select a node from the citation network , Belongs to the node collection The probability of is expressed by formula eight, which is: ,in and They are and the number of nodes contained in the literature citation network; define a length of A discrete random variable, The variables correspond to the core-periphery division The number of sets contained in ; discrete random variables The entropy of is expressed by formula nine, which is: ;

[0082] Given two different core-periphery node partitions and ,exist The node collection in correspond The node collection in ;Will In the division Belongs to the node set And in the division Belongs to the node set The joint probability distribution of is expressed by formula 10, which is ;in, Indicated in and It is divided into Also divided into The number of nodes;

[0083] Using mutual information (MI) to describe About the division Information; Select in the network , exist The uncertainty in ; and The MI value is expressed by Formula 11, which is: ;in, represents the amount of shared information between the two partitions. By subtracting the shared information from the total uncertainty, we get the difference between the two. Indicates that the node belongs to The cth set and Middle The joint probability of a set of Indicates that the node belongs to a partition The probability of the cth set in Indicates that the node belongs to a partition Middle The probability of a set;

[0084] Will and Considered as a division and division The uncertainty of the node set, Representation Division and division The known information shared in the network is used to calculate the sum of uncertainties and eliminate the influence of shared information to obtain the VI distance between different core-periphery node partitions. The value of the VI distance is expressed by Formula 12, which is: .

[0085] When using the minimum description length (MDL) model to evaluate the goodness of fit and network feature representation of each core-periphery structure, the evaluation of the core-periphery random block model is divided into the number of bits of the core-periphery random block model itself and the number of bits required by the core-periphery random block model to describe the network data, that is, ; The model length describing the network data is approximately expressed by Formula 13, which is: ;in, represents the minimum description length of the core-periphery random block model; represents the coding length of the model M, i.e. the number of bits required to describe the core-periphery random block model structure itself; Indicates that under a given model M, the encoding data block is allocated , block connection matrix , adjacency matrix The number of bits required; Indicates that a given block is allocated , connection matrix Under model M, the adjacency matrix The likelihood function of ;

[0086] Using Monte Carlo simulations in Get indivual The sample of the approximate model describes the integral of the length; the sum of the intervals between the samples obtained by sampling is 1, and the distribution probability of the intervals is consistent and randomly combined. Describe the sample ,Right now ;

[0087] Taking the logarithm of the core-periphery random block model description length, the core-periphery random block model description length is obtained as a formula, which is specifically expressed by Formula 14. Formula 14 is: ;in, ; Indicates that a given block is allocated and block connection matrix The log-likelihood function of the adjacency matrix A is Under a given model M, we observe the adjacency matrix A and the block assignment The joint probability of Indicates that under model M, block allocation The prior probability of .

[0088] S6: Structural aggregation of the core-periphery random block model of the literature citation network. Figure 4The flowchart of local weighted core-periphery structure aggregation is presented. The uncertainty and reliability of each node set are calculated to determine the local aggregation weight, so that multiple core-periphery structures in literature citation network analysis can be aggregated into a more representative and robust consensus core-periphery structure.

[0089] In step S6, the core-periphery random block model of the literature citation network is subjected to structural aggregation, including estimating the uncertainty of the core-periphery structure in each core-periphery partition using the concept of information entropy, specifically:

[0090] Given a set of nodes Core and Periphery Division ,in and Respectively represent all node sets and core-periphery partition sets, , ; for The uncertainty is taken into account How do the nodes in Calculate from formula 15 Each node in The node collection in The distribution of , formula 15 is: ;in, Indicates that it belongs to the node set at the same time and division A subset of The number of nodes; Indicates belonging to a set The number of nodes.

[0091] Further distribution for The uncertainty of is specifically expressed by Formula 16, which is: ;in, Is a collection of nodes and division A subset of distribution ratio.

[0092] Introducing the core-periphery structure into the calculation of uncertainty ,get For the core-periphery partition set Uncertainty , expressed by Formula 17, Formula 17 is: ;in, Represents a node collection In the division local uncertainty in Indicates the kth core peripheral partition The minimum description length.

[0093] In step S6, the core-periphery random block model of the literature citation network is structured and aggregated, including using the ensemble-driven clustering index (ECI) to represent the reliability of each node set; given the core-periphery partition set and , There are a total of Core periphery partition, node set of It is expressed by formula 18, which is: ; Among them, the parameters To balance the instability The impact of growth, Represents a node collection The combined uncertainty in the core-periphery partition set P.

[0094] Based on the global diversity and local reliability of the core-periphery structure, a local weighted core-periphery structure aggregation method based on bipartite graph is proposed. The nodes in the literature citation network, the core node set and the peripheral node set are all taken as nodes of the bipartite graph. Indicators and core-periphery division Combined.

[0095] Define a bipartite graph ,in , represents all nodes, S represents the union of the core node set and the peripheral node set, and W represents The weight matrix of the edges between two different sets of nodes in , .

[0096] Nodes belonging to different sets and The edge weight between The definition of is shown in Formula 19: ;

[0097] Calculate the degree matrix U of the nodes in the bipartite graph. The elements in the matrix ; According to the degree matrix U and weight Calculate the normalized weight matrix , and find out The length k feature matrix ;Will Each row of is normalized to unit length, Each row of is the k-dimensional embedding of a node in the bipartite graph. K-means is used to cluster the nodes. Nodes in the same part of the clustering result are considered to belong to the same set, and the partition result of the bipartite graph is obtained. The partition result of the bipartite graph corresponds to the consensus core-periphery structure after aggregation.

[0098] S7: Obtain influential documents, i.e. core nodes.

[0099] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present invention. Those skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A literature citation network core-periphery random block model clustering method, characterized in that: The following steps are involved: S1. Define the literature citation network; give the definition of the literature citation network G(V, E), G(V, E) includes a set V consisting of N nodes and a set E consisting of M unweighted directed edges, where each unweighted directed edge represents a specific citation record of the document; S2, constructing a core-periphery random block model of literature citation network; S3, construct hub-and-spoke model and hierarchical model; S4, using Bayesian inference to infer the core-periphery random block model of the literature citation network; S5: Based on the principle of minimum description length of the model, the core-periphery random block model of the literature citation network is optimized and evaluated; S6: Structural aggregation of the core-periphery random block model of the literature citation network; S7: Obtain influential documents, i.e. core nodes.

2. The document citation network core-periphery random block model clustering method according to claim 1, characterized in that: The construction of the core-periphery random block model of the literature citation network in step S2 includes the following steps: S21: The model assumptions of the core-periphery random block model of the literature citation network are given, that is, the core nodes and peripheral nodes are assigned to different blocks, and based on the defined G(V, E) a given The corresponding adjacency matrix of the literature citation network of nodes is , Nodes are randomly assigned to M blocks; S22: The block allocation vector D of length N represents the block allocation of nodes in the literature citation network, which is specifically expressed as , where the node is assigned to block s and is represented accordingly as ; The connection probability of any two nodes in G(V, E) is expressed by the matrix express, represents the probability of connecting a node in block s to a node in block t; in the core-periphery random block model of the reference network, the connection probability between two nodes depends on the block assignment matrix D and the block connection matrix ; S23: Based on the Bayesian method, with the block allocation vector D and the block connection matrix The prior probability is connected to get formula 1: ;in, Symbols indicate proportions, Indicates that when the adjacency matrix is ​​observed Under the condition that the block allocation vector and block connection matrix The joint probability distribution of represents the prior distribution of the block allocation vector, represents the prior distribution of the block connectivity matrix, Indicates a given and Generate an adjacency matrix probability.

3. The document citation network core-periphery random block model clustering method according to claim 2 is characterized in that: The hub-and-spoke model in S3 is obtained by combining the two-block model with the core-periphery random block model of the literature citation network; the two-block model divides the network nodes into core blocks and peripheral blocks, and connects them through the block connection matrix A structural model that defines the probability of connections between nodes; in the hub-and-spoke model, network nodes are divided into two sets of nodes: core nodes and peripheral nodes. Core nodes are connected to each other, core nodes are connected to some peripheral nodes, and peripheral nodes are not connected to each other. The core block of the hub-and-spoke model is encoded as , the peripheral block is encoded as ; The specific definition is and ( ),in, represents the connection probability of the internal nodes of the core block. In the hub-and-spoke model, , that is, the core nodes are fully connected, represents the connection probability between the core block and the peripheral block, represents the connection probability of the internal nodes of the peripheral block; The prior constraints of the block connection matrix R of the hub-and-spoke model are expressed by Formula 2 and Formula 3: Formula 2 is: ; Formula 3 is ;in, is an indicator function used to define the block connection matrix in the hub-and-spoke model The legal constraints Represents the block connectivity matrix The prior probability distribution of .

4. The document citation network core-periphery random block model clustering method according to claim 3 is characterized in that: The hierarchical model in S3 is obtained by combining the k-core model with the core-periphery random block model of the literature citation network. In the hierarchical model, the network nodes are layered based on the k-core decomposition method, where the k-core represents the set of nodes in the network that are connected to at least k other nodes. The prior constraints of the block connection matrix R of the hierarchical model are expressed by Formula 4 and Formula 5; Formula 4 is , Formula 5 is ;in, is an indicator function that ensures that the block connectivity matrix of the hierarchical model In line with its structural assumptions, Represents the block connectivity matrix The prior probability distribution of .

5. The document citation network core-periphery random block model clustering method according to claim 4 is characterized by: In S4, Bayesian reasoning is used to infer the core-periphery random block model of the literature citation network, which specifically includes the following sub-steps: S41: Based on the Gibbs sampling idea, alternate sampling block allocation vector D and block connection matrix , that is, first fix the block allocation vector D and update the block connection matrix , and then fix the updated block connection matrix And further update the block allocation vector D; S42: Gibbs sampling process node The most frequently allocated block s is used as the statistical block allocation, i.e. ; For two blocks s and t, two quantities are specified: the two quantities are specifically the number of edges that actually exist in the block and the maximum number of edges that can exist ; S43: According to and , the expectation of the edges from block s to other blocks in the core-periphery random block model of the literature citation network is expressed as , the expectation without edge connection is ; Posterior distribution of the core-periphery random block model of literature citation networks It is expressed by formula 6: ;in, Indicates that in a given block The connection probability Under the conditions, it was observed The probability of an edge, Representation Block The connection probability, Representation Block The number of potential unconnected edges, is an indicator function used to enforce a priori constraints on the hierarchical model; S44: Using Markov Chain Monte Carlo simulation method based on Get the posterior distribution ; Randomly allocate blocks to nodes in the literature citation network. After a certain number of iterations, randomly select a node And update its block tag ; S45: Random sampling is used for Select its new block tag ,Right now , where L is the number of model layers; Reverse and get the new block allocation ; S46: According to the Metropolis-Hastings criterion, calculate the acceptance The probability is calculated by formula 7, which is: ;in, Represents the connectivity matrix in a given block and the adjacency matrix Under the condition of The posterior probability of and Respectively represent the old allocation Transfer to New Allocation The proposed distribution probability and the probability of reverse transition.

6. The document citation network core-periphery random block model clustering method according to claim 5, characterized in that: Step S5 specifically includes: using variation information metrics to quantify the differences between different core-periphery structures, and using the minimum description length model to evaluate the fit and network feature representation capabilities of each core-periphery structure; the evaluation indicators of the core-periphery structure provided are as follows: Select a node from the citation network , Belongs to the node collection The probability of is expressed by formula eight, which is: ,in and They are and the number of nodes contained in the literature citation network; define a length of A discrete random variable, The variables correspond to the core-periphery division The number of collections contained in ; Discrete random variables The entropy of is expressed by formula nine, which is: ; Given two different core-periphery node partitions and ,exist The node collection in correspond The node collection in ;Will In the division Belongs to the node set And in the division Belongs to the node set The joint probability distribution of is expressed by formula 10, which is ;in, Indicated in and It is divided into Also divided into The number of nodes; Using mutual information to describe About the division Information; Select in the network , exist The uncertainty in ; and The MI value is expressed by Formula 11, which is: ;in, represents the amount of shared information between the two partitions. By subtracting the shared information from the total uncertainty, we get the difference between the two. Indicates that the node belongs to The cth set and Middle The joint probability of a set of Indicates that the node belongs to a partition The probability of the cth set in Indicates that the node belongs to a partition Middle The probability of a set; Will and Considered as a division and division The uncertainty of the node set, Representation Division and division The known information shared in the network is used to calculate the sum of uncertainties and eliminate the influence of shared information to obtain the VI distance between different core-periphery node partitions. The value of the VI distance is expressed by Formula 12, which is: .

7. The document citation network core-periphery random block model clustering method according to claim 6, characterized in that: When using the minimum description length model to evaluate the goodness of fit and network feature representation of each core-periphery structure, the evaluation of the core-periphery random block model is divided into the number of bits of the core-periphery random block model itself and the number of bits required by the core-periphery random block model to describe the network data, that is, ; The model length describing the network data is approximately expressed by Formula 13, which is: ;in, represents the minimum description length of the core-periphery random block model; represents the coding length of the model M, i.e. the number of bits required to describe the core-periphery random block model structure itself; Indicates that under a given model M, the encoding data block is allocated , block connection matrix , adjacency matrix The number of bits required; Indicates that a given block is allocated , connection matrix Under model M, the adjacency matrix The likelihood function of ; Using Monte Carlo simulations in Get indivual The sample of the approximate model describes the integral of the length; the sum of the intervals between the samples obtained by sampling is 1, and the distribution probability of the intervals is consistent and randomly combined. Describe the sample ,Right now ; Taking the logarithm of the core-periphery random block model description length, the core-periphery random block model description length is obtained as a formula, which is specifically expressed by Formula 14. Formula 14 is: ;in, ; Indicates that a given block is allocated and block connection matrix The log-likelihood function of the adjacency matrix A is Under a given model M, we observe the adjacency matrix A and the block assignment The joint probability of Indicates that under model M, block allocation The prior probability of .

8. The document citation network core-periphery random block model clustering method according to claim 7, characterized in that: In step S6, the core-periphery random block model of the literature citation network is subjected to structural aggregation, including estimating the uncertainty of the core-periphery structure in each core-periphery partition using the concept of information entropy, specifically: Given a set of nodes Core and Periphery Division ,in and Respectively represent all node sets and core-periphery partition sets, , ; for The uncertainty is taken into account How do the nodes in Calculate from formula 15 Each node in The node collection in The distribution of , formula 15 is: ;in, Indicates that it belongs to the node set at the same time and division A subset of The number of nodes; Indicates that it belongs to a set The number of nodes; Further distribution for The uncertainty of is specifically expressed by Formula 16, which is: ;in, Is a collection of nodes and division A subset of The distribution ratio of Introducing the core-periphery structure into the calculation of uncertainty ,get For the core-periphery partition set Uncertainty , expressed by Formula 17, Formula 17 is: ;in, Represents a node collection In the division local uncertainty in Indicates the kth core peripheral partition The minimum description length.

9. The document citation network core-periphery random block model clustering method according to claim 8, characterized in that: In step S6, the core-periphery random block model of the literature citation network is subjected to structural aggregation, including using an integrated driven clustering index to represent the reliability corresponding to each node set; given the core-periphery partition set and , There are a total of Core periphery partition, node set of It is expressed by formula 18, which is: ; Among them, the parameters To balance the instability The impact of growth, Represents a node collection The combined uncertainty in the core-periphery partition set P; Based on the local weighted core-periphery structure aggregation method of bipartite graph, the nodes in the literature citation network, the core node set and the peripheral node set are all taken as the nodes of the bipartite graph. Indicators and core-periphery division Combined; Define a bipartite graph ,in , represents all nodes, S represents the union of the core node set and the peripheral node set, and W represents The weight matrix of the edges between two different sets of nodes in , ; Nodes belonging to different sets and The edge weight between The definition of is shown in Formula 19: ; Calculate the degree matrix U of the nodes in the bipartite graph. The elements in the matrix ; According to the degree matrix U and weight Calculate the normalized weight matrix , and find out The length k feature matrix ;Will Each row of is normalized to unit length, Each row of is the k-dimensional embedding of a node in the bipartite graph. K-means is used to cluster the nodes. Nodes in the same part of the clustering result are considered to belong to the same set, and the partition result of the bipartite graph is obtained. The partition result of the bipartite graph corresponds to the consensus core-periphery structure after aggregation.

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