An integrated community detection method and system based on weighted hybrid bipartite graph

Abstract

The present invention provides an integrated community detection method based on a weighted hybrid bipartite graph and a system thereof, comprising: constructing a node-community hybrid bipartite graph based on the operation results of an existing community detection algorithm; weighting the hybrid bipartite graph based on a measure of community reliability to obtain a weighted hybrid bipartite graph, and the weighted hybrid bipartite graph is used for integrated community detection. The present invention utilizes the integration of multiple community detection results to construct a bipartite graph, and performs a weighting process with low complexity. Compared with the prior art, the present invention has significant advantages in terms of running time and accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of community detection, and in particular relates to an integrated community detection method and a system thereof based on a weighted hybrid bipartite graph. Background Art

[0002] Ensemble community detection is mainly developed to address the uncertainty in a single community detection algorithm. It draws on the ideas of ensemble clustering to generate stable results from a set of partitions provided by a community detection algorithm with higher randomness. Ensemble methods are widely used in clustering because they can concentrate the advantages of different individual algorithms to produce stable and accurate results. There are also some studies on ensemble methods in the field of community detection, but the existing algorithms have the following main problems: The method based on consensus clustering, LF consensus, only focuses on the co-occurrence relationship of nodes. Since the relationship between each pair of nodes needs to be accessed, the constructed consistency matrix is ​​very dense. In addition, its repeated iteration of its own process leads to a high time complexity and cannot be applied to large networks. Summary of the invention

[0003] To solve the above technical problems, the present invention proposes an integrated community detection method and system based on a weighted hybrid bipartite graph. A bipartite graph is constructed by integrating multiple community detection results, and a low-complexity weighting process is performed. Compared with the existing technology, the present invention has significant advantages in running time and accuracy.

[0004] On the one hand, to achieve the above-mentioned purpose, the present invention provides an integrated community detection method based on a weighted hybrid bipartite graph, comprising:

[0005] Based on the community detection algorithm, a hybrid bipartite graph of nodes and communities is constructed;

[0006] Based on the measure of community reliability, the mixed bipartite graph is weighted to obtain a weighted mixed bipartite graph, and the integrated community detection is performed using the weighted mixed bipartite graph.

[0007] Optionally, constructing the hybrid bipartite graph of nodes-communities includes:

[0008] Running the community detection algorithm on the original network several times to obtain several network partitions, and putting the several network partitions into the same set to obtain an integration of the network partitions;

[0009] The hybrid bipartite graph is constructed based on the affiliation of network nodes to communities in the ensemble.

[0010] Optionally, after constructing the hybrid bipartite graph, the method further includes: modeling the nodes and communities in the original network as vertices in the bipartite graph, thereby generating a lossless representation of the community partition integration.

[0011] Optionally, the measure of community reliability includes:

[0012] Calculating the similarity between each community and other communities in the ensemble;

[0013] Based on the similarity, the local unreliability of each community is divided;

[0014] Based on the local unreliability, obtaining the global unreliability of each community;

[0015] Based on the global unreliability, the reliability of each community in the ensemble is obtained.

[0016] Optionally, weighting the mixed bipartite graph includes: weighting each edge on the mixed bipartite graph, wherein the weight is the reliability of the community connected by the edge in the integration.

[0017] Optionally, the community detection algorithm includes: a modularity-based method, an information theory-based method, a label propagation method, and a physical model-based method.

[0018] On the other hand, to achieve the above-mentioned purpose, the present invention also provides an integrated community detection system based on a weighted hybrid bipartite graph, comprising: a construction module, a weighting module and a detection module;

[0019] The building module is used to build a node-community hybrid bipartite graph based on a community detection algorithm;

[0020] The weighting module is used to weight the mixed bipartite graph based on the measure of community reliability to obtain a weighted mixed bipartite graph;

[0021] The detection module performs the integrated community detection using the weighted mixed bipartite graph.

[0022] Optionally, the process of constructing the hybrid bipartite graph of nodes and communities includes:

[0023] Running the community detection algorithm on the original network several times to obtain several network partitions, and putting the several network partitions into the same set to obtain an integration of the network partitions;

[0024] The hybrid bipartite graph is constructed based on the affiliation of network nodes to communities in the ensemble.

[0025] Optionally, the metric module is used for community reliability-based metric including:

[0026] Calculating the similarity between each community and other communities in the ensemble;

[0027] Based on the similarity, the local unreliability of each community is divided;

[0028] Based on the local unreliability, obtaining the global unreliability of each community;

[0029] Based on the global unreliability, the reliability of each community in the ensemble is obtained.

[0030] Compared with the prior art, the present invention has the following advantages and technical effects:

[0031] The present invention introduces an integrated method framework based on a hybrid bipartite graph, which lays the foundation for the algorithm's advantage in time complexity. The constructed bipartite graph is highly sparse, and has high time efficiency when running a community detection method to divide it. The community reliability is defined based on the information entropy of the community in the integration. The reliability is a relative measure that is only related to the basic division generated by the base algorithm, but has nothing to do with the topological structure of the original network. Based on this, the edges between nodes and communities in the hybrid bipartite graph are weighted to ensure the stability and accuracy of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0033] Figure 1 This is a flow chart of an integrated community detection method based on a weighted mixed bipartite graph according to Embodiment 1 of the present invention;

[0034] Figure 2 It is a schematic diagram of an example of HBGR in Example 1 of the present invention;

[0035] Figure 3 This is a schematic diagram of the NMI value comparison results of the integrated community detection method of Example 1 of the present invention on an LFR network with 1000 nodes;

[0036] Figure 4 This is a schematic diagram of the NMI value comparison results of the integrated community detection method of Example 1 of the present invention on an LFR network with 5000 nodes;

[0037] Figure 5 This is a schematic diagram of the comparison results of the running time of three integrated community detection methods in Example 1 of the present invention;

[0038] Figure 6 It is a schematic diagram of the Q value comparison results of the integrated community detection method of Example 1 of the present invention on a labeled real network;

[0039] Figure 7 It is a schematic diagram of the Q value comparison results of the integrated community detection method of Example 1 of the present invention on a real network without labels;

[0040] Figure 8 This is a schematic diagram of the structure of an integrated community detection system based on a weighted mixed bipartite graph according to Example 2 of the present invention. DETAILED DESCRIPTION

[0041] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0042] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0043] Example 1

[0044] This embodiment first introduces a representation method for community partitioning integration, which uses a mixed bipartite graph to characterize the affiliation of nodes to communities in multiple community partitions. Then, the reliability of each community is defined, and the mixed bipartite graph is weighted using the reliability. On this basis, an integrated community detection method WHBG-CD based on weighted mixed bipartite graph is proposed, and a simple example is used to illustrate the process of WHBG-CD. Finally, the time complexity of the algorithm is theoretically analyzed.

[0045] like Figure 1 As shown, this embodiment provides an integrated community detection method based on a weighted mixed bipartite graph, including:

[0046] Based on the existing community detection algorithm, a hybrid bipartite graph of nodes and communities is constructed;

[0047] Based on the measure of community reliability, the mixed bipartite graph is weighted to obtain a weighted mixed bipartite graph, and the integrated community detection is performed using the weighted mixed bipartite graph.

[0048] Furthermore, constructing a node-community hybrid bipartite graph includes:

[0049] First, run the community detection algorithm on the original network (original input network) several times to generate several network partitions, which are placed in the same set as an integration of network partitions. According to the affiliation of network nodes to communities in the integration, a node-community mixed bipartite graph is constructed. Among them, in the mixed bipartite graph, the nodes and communities in the original network are modeled as vertices in the bipartite graph, generating a lossless representation of the community partition integration. Existing community detection algorithms include: modularity-based methods, information theory-based methods, label propagation methods, and physical model-based methods. The four algorithms are run simultaneously several times to obtain the comprehensive results.

[0050] In this embodiment, the method of integrated hybrid bipartite graph representation (HBGR) specifically includes:

[0051] Given a graph G<N,E> , we can use a set Γ=P 1 , P 2 , ...P m To represent the integration of multiple community detection results of graph G. Each P c (c=1,...,m) all represent a community division, which can be used To represent, k is the partition P c The number of communities generated. The integration Γ can also be written as: The assignment of nodes to communities can be represented by a binary association matrix A. The rows of A correspond to the nodes of the graph G, and the columns of A correspond to the communities in the set Γ. A(i, j) represents the affiliation of node i to community j. If i is in j, then A(i, j) = 1, otherwise A(i, j) = 0.

[0052] Hybrid Bipartite Graph Representation HBGR (Hybrid Bipartite Graph Representation) constructs a bipartite graph BG<V,W> ——For the convenience of description, the nodes in BG are called vertices.

[0053] V=V C ∪V N , where V C Contains t vertices, each vertex corresponds to a community in the integration; V N Contains n vertices, each vertex represents a node in N, that is, a node in the original graph G.

[0054] W is defined as follows: if vertices i and j are both communities or nodes, W(i, j) = 0; otherwise, if node i belongs to community j, W(i, j) = W(j, i) = 1; if not, W(i, j) = W(j, i) = 0. W can be written in the form of formula 1:

[0055]

[0056] like Figure 2 FIG. 1 shows an example of HBGR, which includes two different partitions of the same network and shows the constructed HBGR.

[0057] Although the node set of HBGR not only includes all nodes in G, but also includes each community in the set Γ as a vertex, due to its special structure, the time complexity of constructing it is actually not high, only O(n×t), where n is the total number of nodes in G and t is the total number of communities in Γ. When t<<n, this complexity is much smaller than the O(n×t) time complexity of constructing the consistency matrix in LF consensus. 2 ) is much smaller.

[0058] Furthermore, the measurement method of community reliability includes: calculating the similarity between each community in the ensemble and other communities; dividing the local unreliability of each community based on the similarity; obtaining the global unreliability of each community based on the local unreliability; and obtaining the reliability of each community in the ensemble based on the global unreliability.

[0059] In this embodiment, community reliability is defined as:

[0060] For a given community in the ensemble, this embodiment defines the community reliability as the amount of specific information the ensemble has about the community. A reliable community is the community that has been separated the least number of times in other partitions in the ensemble, that is, the most stable community. Ignoring the reliability of the community may cause the ensemble method to be affected by low-quality communities, so this paper calculates the reliability of each community and uses it as the weight of the mixed bipartite graph.

[0061] The steps of calculating community reliability are divided into four steps. The first step is to calculate the similarity between each community and other communities. Since the communities in each partition are non-overlapping, this embodiment selects the simple and efficient Jaccard coefficient as the measure of community similarity. The similarity between two hard partitions is calculated by formula 2:

[0062]

[0063] The value range is [0,1].

[0064] The second step is to estimate a local unreliability for each community. The unreliability (or reliability) referred to in this embodiment is a relative indicator, which only comes from the integration and statistics of multiple community division results, without using any information related to the original network topology. Given an integration of community divisions, this embodiment defines the community reliability as follows: The reliability of a community is determined by how much information about the community is contained in the entire integration. Reliable communities often appear multiple times in different divisions, rather than being separated in other divisions. This also reflects its "stable" nature. The "instability" of a community means that it is of low quality, and there is reason to assume that they will affect the performance of the integration algorithm. Therefore, this embodiment calculates the stability of each community and uses it as the edge weight of the mixed bipartite graph.

[0065] Community About the division of P v The unreliability of P v How many about Therefore, we can use the information of P v Every community in The information entropy of the similarity between is used to estimate it. According to information theory, the information entropy of a discrete random variable can be estimated by formula 3:

[0066]

[0067] Given a community and a partition P v , we can define With P v Every community in The normalized similarity is Calculated by formula 4:

[0068]

[0069] where n v YesP v The number of communities in YesP v The lth community in is the similarity obtained by formula 2.

[0070] To obtain About P v The similarity of Substituting into equation 3, we get equation 5:

[0071]

[0072] The third step is to calculate the community's global unreliability based on the community's unreliability to each partition. Assume that each basic partition in the ensemble is independent of each other (each basic partition is generated independently without considering other basic partitions). So, The unreliability relative to the integrated Γ can be obtained by The unreliability of the m basic partitions in Γ is summed up, and this step is expressed by equation 6:

[0073]

[0074] Each basic partition P j ∈Γ, Calculate according to formula 5.

[0075] The fourth step is to calculate the reliability of each community in the integration based on the unreliability of the community. The purpose of this embodiment is to calculate a weight for each community in the mixed bipartite graph so that the weight of the reliable community is greater than that of the unreliable community. Because the reliability of the community is opposite to the unreliability, the unreliability can be converted into its reliability by any non-negative decreasing transformation function. For the purpose of weight normalization, this embodiment uses a negative exponential transformation so that the value range of the converted reliability falls between (0, 1]. The reliability is specifically calculated by formula 7:

[0076]

[0077] In this embodiment, the overall process of the community detection algorithm based on the weighted hybrid bipartite graph is divided into: running the base algorithm to generate a community partitioning integration, constructing a hybrid bipartite graph representation, calculating the community reliability, weighting the hybrid bipartite graph, and re-dividing the hybrid bipartite graph.

[0078] Specifically: using M community detection algorithms As input, each al m Run K times with different node orders, and the community structure generated by each run can be expressed as Each Integrated into the same set, called Γ, can be expressed as Γ = {P 1 , P 2 , ...P P}, a total of P = M × K community structures, Γ is the "ensemble". Then, the affiliation relationship between the nodes and the community in the ensemble is used to construct a hybrid bipartite graph. Next, the reliability is calculated for each community, and then each edge is weighted on the hybrid bipartite graph, and the weight is the reliability of the community connected by the edge.

[0079] For community detection algorithms In order to ensure the heterogeneity and diversity of the generated partitions, this embodiment selects several existing community detection algorithms based on different ideas, including: (1) Modularity-based methods: CNM and Louvain. (2) Information theory-based method Infomap (3) Label propagation method (LPA). (4) Physical model-based method Spinglass. For the redivision of mixed bipartite graphs, since they have a relatively obvious community structure, algorithms that are not targeted at bipartite graphs can also be used for division. This embodiment selects Infomap, which has relatively excellent comprehensive performance, as the redivision algorithm.

[0080] Time complexity analysis of the community detection method based on weighted mixed bipartite graph in this embodiment:

[0081] Assume that the original input network is G<V,E> , n = |V| is the number of nodes in the network, M is the number of base algorithms, K is the number of iterations of each base algorithm, is the average size of the community partitions output by the base algorithm. The step of constructing a mixed bipartite graph takes The algorithm calculates the reliability of each community. The step with the highest time complexity is to calculate the normalized similarity between each pair of communities. The time complexity of this step is Real networks are generally very sparse, and the number of potential communities is much smaller than the number of nodes.

[0082] In summary, the time complexity of the entire algorithm is Smaller than LF consensus's O(n 2 ). In addition, the bipartite graph constructed by WHBG-CD is highly sparse, and the time efficiency of running the community detection algorithm to divide it is higher than the dense graph constructed by LF consensus, which is also a major factor affecting the overall time efficiency of the algorithm.

[0083] This embodiment also uses normalized mutual information NMI, adjusted Rand index ARI, and modularity Q as evaluation indicators to verify the community detection method based on weighted mixed bipartite graph proposed in the present invention. Among them, for artificial networks with embedded community structures, this embodiment uses NMI to measure the accuracy of its algorithm operation; for real networks with known community structures, in order to prevent the results from being biased by using only one metric, ARI is used as a supplement in addition to NMI, and the two indicators are combined for comparison. Both NMI and ARI can explain the degree of match between two communities; the larger the value of NMI or ARI, the better the match between the community structure output by the algorithm and the actual community structure. For real networks with unknown community structures, Q is used to measure the quality of the community structure detected by the algorithm.

[0084] A total of six community detection methods were used as comparison algorithms, namely: modularity optimization method Louvain (Lo), label propagation algorithm LPA), information theory-based method Infomap, physical model-based method Spinglass, hierarchical clustering-based method CNM, and random walk-based method Walktrap, to verify the improvement of the integrated algorithm proposed in this paper on the performance of the algorithm running alone. In addition, since WHBG-CD was proposed for LF consensus, LFconsensus was used as a baseline for comparison in the experiment. Louvain, LPA, Spinglass, CNM, and Walktrap are all implemented in igraph, and Infomap uses the open source implementation of the original author of the algorithm. For the Louvain and LPA algorithms with greater randomness, the average of 100 running results is taken. The algorithm was executed on a laptop equipped with a 3.0GHz Intel Core i5 processor.

[0085] Comparative Experiments on Artificial Networks

[0086] By controlling the parameters of the LFR benchmark program, artificial networks with different statistical properties can be generated. This example uses a parameter configuration similar to that in LF consensus to generate four groups of artificial networks, each of which takes the same values ​​for the following parameters: degree distribution index τ1 = 2, community size distribution index τ2 = 3, maximum degree k max =50. By setting different n, c and μ are used to generate four different networks. The specific parameters are listed in Table 1.

[0087]

[0088] Table 1

[0089] like Figure 3The figure shows the NMI values ​​of several algorithms running on two sets of artificial networks, where the confusion coefficient μ gradually increases from 0.0625 to 0.875, with a step size of 0.0625. The base algorithm settings of WHBG-CD are: Louvain, LPA and Infomap. As the confusion coefficient μ increases, the community structure of the network tends to be blurred, and the detection results of each algorithm have declined. The NMI of almost all algorithms drops sharply in the interval of μ∈[0.5,0.6875], indicating that when μ>0.5, the community structure of the LFR benchmark network under this set of parameter settings is already highly blurred. When μ>0.75, the NMI of the three algorithms, Louvain, LF consensus, and CNM, increases unnaturally with the increase of μ, which further indicates that when μ is close to 1, the recognizability of the community structure in the LFR network is not large. When μ<0.5, the NMI of all algorithms is very considerable, and the WHBG-CD algorithm is the best among them. The NMI of the WHBG-CD algorithm drops sharply to 0 when μ=0.75, indicating that it is not suitable for detecting networks with highly ambiguous community structures. It can be observed that at this time, the NMI of the base algorithms Infomap and LPA are both equal to 0. The recorded community division results show that Infomap and LPA both identify the entire network as a large community, which seriously affects the topological characteristics of the hybrid bipartite graph used in the process of extracting consensus, causing all nodes to be connected to the same community many times, making the edge distribution of the constructed hybrid bipartite graph very uniform, resulting in a highly ambiguous community structure, which in turn causes the entire hybrid bipartite graph to be easily divided into a large community. When the number of nodes remains unchanged, the increase in the size of the embedded community will have a certain impact on the performance of the algorithm. Louvain and Spinglass perform better in identifying large communities, while the performance of Infomap and WHBG-CD is less affected by changes in community size. When μ is in the interval [0.5625,0.6875], regardless of the size of the community, the performance of WHBG-CD is much higher than that of the best base algorithm Infomap, and at the same time higher than another integrated algorithm-LF consensus.

[0090] like Figure 4 As shown in the figure, as the number of nodes in the network increases, the NMI values ​​of most algorithms decrease overall, but the decreasing trend is roughly the same as when the number of network nodes is equal to 1000. In the range of μ<0.6875, after extracting the consensus of Infomap, Louvain, and LPA, the WHBG-CD algorithm still maintains the best position in NMI, which is improved compared with LF consensus and higher than the best Infomap among non-integrated algorithms.

[0091] This embodiment also verifies the improvement of the WHBG-CD algorithm in operating efficiency on a set of LFR benchmark networks with specially set parameters, where only the number of nodes and the maximum number of communities are changed in the network parameters, n gradually increases from 1000 to 10000, with a step size of 1000; the maximum number of communities c max =n / 10, and the other parameters are fixed, namely: τ1=2, τ2=3, k max =50, c min =10, μ=0.3. The parameter K of WHBG-CD is set to 5. In order to compare the running speeds of similar algorithms, this embodiment compares two other ensemble community detection algorithms: LF consensus and Fast consensus.

[0092] like Figure 5 As shown in Figure 1, the time results of three algorithms, WHBG-CD, LF consensus, and Fast consensus, running on a set of artificial networks of increasing size are shown. Among them, Fast consensus is an improvement on LF consensus.

[0093] Comparative experiments on real networks

[0094] In addition to the artificial network with embedded community structure, this example also uses real-world network data to evaluate the algorithm, which is more challenging than artificial networks. The experiment mainly uses real networks with community labels, supplemented by real networks without community labels. The statistical data of each network in this chapter is listed in Table 2.

[0095] Table 2

[0096]

[0097] Real network with community labels

[0098] Four classic real networks are used: Karate, Dolphins, Polbooks, and Football. WHBG-CD uses Louvain, LPA, and Infomap as the base algorithms. The adjusted Rand coefficient ARI and normalized mutual information NMI are used to evaluate the algorithm performance and make a comprehensive comparison. The results are shown in Figure 6 shown.

[0099] Figure 6The results of comparative experiments on four real networks are shown. The comparative algorithms include Louvain (Lo), LPA (Lp), Infomap (I), CNM (C), Spinglass (S), LF consensus (Lc) and WHBG-CD (W). It can be seen that the performance of the WHBG-CD algorithm in the Karate network is better than that of other algorithms, and the corresponding ARI and NMI values ​​are 0.72 and 0.71 respectively. According to the literature records, the actual community structure of the Dolphins network can be two or four communities. This embodiment adopts the case of four. It can be seen that the two indicators of the WHBG-CD algorithm in the Dolphins network are significantly higher than those of other comparative algorithms, which are 0.92 and 0.87 respectively; the best among the comparative algorithms is Infomap, and its NMI and ARI are 0.86 and 0.81 respectively. The evaluation indicators of the WHBG-CD algorithm in the Football network are also the best. It can be seen that the NMI of the comparative algorithms are all high, indicating that the community structure of the Football network is obvious. The Polbooks network represents the book co-purchase relationship during the US presidential election, which can be divided into three communities according to the buyers' political inclinations. The NMI values ​​of the five standard community detection algorithms are close. In terms of NMI alone, WHBG-CD is the best, followed by LPA; the combined metric of the WHBG-CD algorithm is also the best.

[0100] comprehensive Figure 6 The results show that the WHBG-CD algorithm can obtain better results in four real networks by evaluating the quality of community division using normalized mutual information NMI, adjusted Rand coefficient ARI or a combination of the two.

[0101] Real network without community labels

[0102] A larger scale but unlabeled real network was selected for comparative experiments to verify the true effectiveness of the WHBG-CD algorithm. The networks used are Email, Powergrid, Astrophysics, Netscience and Yeast, with the number of nodes ranging from thousands to tens of thousands. Since the data set is unlabeled, the evaluation indicator is modularity Q. The comparative algorithms include Infomap based on information theory, label propagation algorithm LPA, Walktrap based on random walk, and CNM and Louvain based on modularity optimization. Among them, the Louvain algorithm and the CNM algorithm generally produce results with higher modularity because their optimization targets are modularity Q. Therefore, the two algorithms are used as comparison benchmarks, and they are not added to the base algorithm family of WHBG-CD. Only Infomap, LPA and Walktrap are taken as the base algorithms of WHBG-CD.

[0103] from Figure 7 It can be seen that after integrating the base algorithm, WHBG-CD can obtain a modularity slightly higher than the base algorithm. If the algorithm is evaluated by modularity alone, Louvain achieves the best results on all five data sets. Due to the resolution limitation problem when evaluating algorithms with modularity Q, the maximum modularity may cause the algorithm to miss the best potential community structure (this can be seen from the comparative analysis of artificial networks). Therefore, a high modularity Q can only indicate that the community structure detected by the algorithm is of high quality and is only suitable for reference. Figure 7 The results show that WHBG-CD can also obtain high-quality communities on larger real networks.

[0104] Example 2

[0105] like Figure 8 As shown, this embodiment provides an integrated community detection system based on a weighted hybrid bipartite graph, including: a construction module, a weighting module and a detection module;

[0106] The building module is used to construct a node-community hybrid bipartite graph based on the community detection algorithm;

[0107] The weighting module is used to weight the mixed bipartite graph based on the measure of community reliability to obtain the weighted mixed bipartite graph;

[0108] The detection module uses weighted mixed bipartite graphs for ensemble community detection.

[0109] Furthermore, the process of constructing a node-community hybrid bipartite graph includes:

[0110] Run the community detection algorithm on the original network several times to obtain several network partitions, and put the several network partitions into the same set to obtain the integration of network partitions;

[0111] Based on the affiliation of network nodes to communities in the ensemble, a hybrid bipartite graph is constructed.

[0112] Furthermore, the metrics module is used for community reliability-based metrics including:

[0113] Calculate the similarity between each community in the ensemble and other communities;

[0114] Based on the similarity, the local unreliability of each community is divided;

[0115] Based on the local unreliability, obtain the global unreliability of each community;

[0116] Based on the global unreliability, the reliability of each community in the ensemble is obtained.

[0117] Example 3

[0118] The community detection algorithm aims to divide the community structure of complex networks and obtain high-quality community division structures. According to the divided community structure, many practical applications can be realized. Friend recommendation, product recommendation, short video recommendation, etc. are the most popular application directions in the current big data era. This embodiment uses friend recommendation as an example to introduce the application process of the community detection algorithm in friend recommendation:

[0119] Based on the LF consensus algorithm, the WHBG-CD algorithm aims to solve the obvious defects. First, it uses the integration of multiple community detection results to construct a hybrid bipartite graph. Second, it defines the community reliability according to the amount of specific information about the community in the integration. Finally, it performs a low-complexity weighting process on the bipartite graph according to the community reliability. The process of applying the WHBG-CD algorithm in friend recommendation is as follows:

[0120] 1. The WHBG-CD algorithm is improved on the basis of the LF consensus algorithm. During the execution of the algorithm, only the structural information of the entire complex network is used. The extracted information is placed in the complex network, nodes are used to represent individual users, and edges are used to represent friend relationships, so as to obtain the input data for executing the algorithm.

[0121] 2. Execute the WHBG-CD algorithm on the constructed hybrid bipartite graph. First, run the base algorithm to generate an ensemble of community structures, construct a hybrid bipartite graph to represent this ensemble, and use the information in the ensemble to calculate the community reliability, using the reliability as the edge weight in the hybrid bipartite graph. Finally, use the community detection algorithm to repartition the hybrid bipartite graph to obtain the community partition result.

[0122] 3. According to the community division results, each user has a set of division results, which is compared with the set of the user's current friends, and the difference between the two sets is taken as the content recommended by the user's friends. The WHBG-CD algorithm accurately refines the content recommended by friends.

[0123] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. An integrated community detection method based on weighted mixed bipartite graph, characterized in that: include: Based on the community detection algorithm, a hybrid bipartite graph of nodes and communities is constructed; Constructing the hybrid bipartite graph of nodes and communities includes: Running the community detection algorithm on the original network several times to obtain several network partitions, and putting the several network partitions into the same set to obtain an integration of the network partitions; constructing the hybrid bipartite graph based on the affiliation of the network nodes to the communities in the integration; Based on a measure of community reliability, weighting the mixed bipartite graph to obtain a weighted mixed bipartite graph, and using the weighted mixed bipartite graph to perform the integrated community detection; The measures of community reliability include: Calculate the similarity between each community in the ensemble and other communities; the expression is: Based on the similarity, the local unreliability of each community is divided; the expression is: Based on the local unreliability, the global unreliability of each community is obtained; the expression is: Based on the global unreliability, the reliability of each community in the ensemble is obtained; the expression is:

2. The integrated community detection method based on weighted mixed bipartite graph according to claim 1, characterized in that: After constructing the hybrid bipartite graph, the method further includes: modeling the nodes and communities in the original network as vertices in the bipartite graph, thereby generating a lossless representation of the community partition integration.

3. The integrated community detection method based on weighted mixed bipartite graph according to claim 1, characterized in that: Weighting the mixed bipartite graph includes: weighting each edge on the mixed bipartite graph, wherein the weight is the reliability of the community connected by the corresponding edge in the integration.

4. The integrated community detection method based on weighted mixed bipartite graph according to claim 1, characterized in that: The community detection algorithm includes: a method based on modularity, a method based on information theory, a label propagation method and a method based on a physical model.

5. An integrated community detection system based on weighted hybrid bipartite graph, characterized in that: include: Building module, weighting module and detection module; The building module is used to build a node-community hybrid bipartite graph based on a community detection algorithm; The process of constructing the hybrid bipartite graph of nodes and communities includes: Running the community detection algorithm on the original network several times to obtain several network partitions, and putting the several network partitions into the same set to obtain an integration of the network partitions; constructing the hybrid bipartite graph based on the affiliation of the network nodes to the communities in the integration; The weighting module is used to weight the mixed bipartite graph based on the measure of community reliability to obtain a weighted mixed bipartite graph; The measures of community reliability include: Calculate the similarity between each community in the ensemble and other communities; the expression is: Based on the similarity, the local unreliability of each community is divided; the expression is: Based on the local unreliability, the global unreliability of each community is obtained; the expression is: Based on the global unreliability, the reliability of each community in the ensemble is obtained; the expression is: The detection module performs the integrated community detection using the weighted mixed bipartite graph.

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