Dynamic expansion and optimization overlapped community detection method

Abstract

The invention discloses a dynamically expanded and optimized overlapping community detection method. The method comprises the following steps: 1, selecting a core community: randomly selecting a non-overlapping community from existing non-overlapping community division results as an initial core community oci; step 2, key parameters are calculated based on the scale of a core community oci: step 3, community expansion: in each cycle of the expansion process, candidate nodes are found and unique nodes with the highest overlapping community attribution degree are absorbed, and community boundaries are expanded step by step; step 4, community contraction: in each cycle of the contraction process, firstly calculating the purity of each node, evaluating the stability of the nodes in the community, and then removing a node which has the lowest purity and is not in the core community; and 5, repeating community expansion-contraction until the overlapping degree reaches a certain threshold value, and obtaining a final overlapping community division result. According to the method, a real community boundary can be identified more accurately, and the interpretability and practicability of community division in a complex network are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of complex network analysis, and in particular to a dynamically expanded and optimized overlapping community detection method. Background Art

[0002] With the development of complex network theory, community detection, as an important technique for revealing latent groups within network structures, has been widely applied in fields such as social networks, biological networks, recommender systems, and precision marketing. Traditional community detection methods are mostly based on non-overlapping partitioning, which divides network nodes into several non-overlapping communities, with each node belonging to only one community. Such methods have achieved good results in many application scenarios, but in real complex networks, nodes often have multiple affiliations. For example, in social networks, a user may participate in multiple interest groups simultaneously, and in marketing scenarios, a customer may exhibit behavioral preferences for multiple product categories. Therefore, accurately identifying the overlapping community structure of nodes in a network has become a research priority.

[0003] This phenomenon has prompted researchers to propose a variety of overlapping community detection algorithms, such as those based on label propagation and seed expansion. These methods can, to a certain extent, mine the multiple community structures of nodes, but there is still room for improvement in terms of the flexibility of modeling complex overlapping relationships and the control mechanism of structural purity:

[0004] The granularity of the expansion starting point is low, resulting in insufficient structural stability: Some methods use a single seed node as the starting point and expand the node to form a community. This low-granularity starting point may lead to unstable initial structures and be susceptible to local network noise. There is a lack of overlap detection methods that use larger structural units (such as complete communities) as the starting point;

[0005] Lack of contraction mechanism: Many expansion methods only perform node absorption during community formation, but ignore the identification and removal of mistakenly absorbed nodes, resulting in blurred community boundaries and affecting the accuracy and interpretability of detection results.

[0006] Poor parameter adaptability: Existing methods often use a fixed expansion scale or number of iterations, lacking a dynamic parameter adaptation mechanism for different community sizes or network structures, making it difficult to ensure the versatility and stability of the method.

[0007] For example, the "Global Overlapping Community Detection Method for Social Networks Based on Clique Expansion and Quadratic Optimization" (Grant Announcement No. CN110750732B, Application Publication No. CN110750732A), filed by Huazhong University of Science and Technology, uses a strategy of expansion based on maximal cliques as the initial structure. While this strategy improves the compactness of the starting structure, the large number and dense distribution of maximal cliques can easily lead to high overlap between the initial structures, increasing the complexity of subsequent optimization. Existing methods still lack a highly structured and controllable expansion mechanism based on the skeleton of salient communities. Summary of the Invention

[0008] In order to overcome the above technical problems, the purpose of the present invention is to propose a dynamically expanded and optimized overlapping community detection method, and combine it with an overlapping community detection method with dual evaluation of structural attribution and purity, which helps to more accurately identify the real community boundaries and improve the interpretability and practicality of community division in complex networks.

[0009] The technical solution adopted in the present invention is:

[0010] A dynamically extended and optimized overlapping community detection method includes the following steps:

[0011] Step 1: Core community selection, randomly select non-overlapping communities from the existing non-overlapping community division results as the initial core community oc i , to ensure the diversity of algorithm initialization;

[0012] Step 2: Dynamic calculation of parameters based on core community oc i Key parameters for scale calculation:

[0013] Step 3: Community expansion. In each cycle of the expansion process, find candidate nodes and absorb the unique node with the highest overlapping community affiliation, gradually expanding the community boundary.

[0014] Step 4: Community contraction. In each cycle of the contraction process, the purity of each node is first calculated to evaluate the stability of the node in the community. Then, a node with the lowest purity that is not in the core community is removed.

[0015] Step 5: Repeat the community expansion-contraction until the overlap reaches a certain threshold, and obtain the final overlapping community division result.

[0016] The dynamically expanded and optimized overlapping community detection method proposed in this paper is primarily applicable to real-world network datasets with naturally overlapping structures, such as complex social networks, academic collaboration networks, and biomolecular interaction networks. For example, in social network datasets (e.g., Facebook), users may participate in multiple interest groups or communities simultaneously, resulting in highly overlapping community structures; in academic collaboration networks (e.g., DBLP), an author may belong to multiple research directions or academic teams simultaneously, resulting in significant overlap; and in user-item bipartite graphs in online content recommendation systems, users are often active across interest groups, also exhibiting a significant overlapping structure.

[0017] The core community selection step in step 1 includes:

[0018] Step 1.1: Obtain non-overlapping community division results through any non-overlapping community detection algorithm;

[0019] Step 1.2: Randomly select a community as the initial core community oc i .

[0020] In step 2, there are three key parameters:

[0021] Expand candidate scale adjustment parameter ks=|oc i | / ks′, where ks′ is the preset scaling factor;

[0022] Extension times kex=ks / kex′, where kex′ is a preset proportional coefficient;

[0023] The number of contractions kcon=ks / kcon′, where kcon′ is a preset proportional coefficient and satisfies kcon>kex.

[0024] In step 3:

[0025] Candidate nodes are nodes in the current core community's adjacent node set that have not yet been absorbed by any identified community, or that have been absorbed by other communities but have direct edge connections to the current community. These nodes have direct connections to the current community in the network topology and have potential structural relevance. By selecting the nodes with the highest degree of belonging among the candidate nodes for absorption, we can achieve stable expansion of the community structure and avoid the introduction of redundant nodes.

[0026] The community expansion step in step 3 includes:

[0027] Step 3.1: Collect core community oc i All neighbor nodes of form a candidate set NE;

[0028] Step 3.2: Calculate the relationship between each node in NE and oc i The number of connected edges of the midpoint node. The calculation formula for the number of connected edges is:

[0029] Conn(v j ,oc i )=|Γ(v j )∩oc i |

[0030] Where Γ(v j ) represents node v j The neighbor set of , |·| represents the size of the set;

[0031] Step 3.3: Select ks nodes with the highest number of connected edges to form the candidate set CA;

[0032] Step 3.4: Calculate the relationship between each node in CA and oc i The overlapping community affiliation degree OCA(v j ,oc i ), the calculation formula is:

[0033]

[0034] Among them, Γ(v j ) represents node v j The neighbor node set of |oc i | indicates community oc i The size of D(v i ,v j ) represents node v i and v j the distance between them;

[0035] Step 3.5: Add the node with the highest degree of belonging to the overlapping community in the candidate set CA to the core community oc i ;

[0036] Step 3.6: Repeat steps 3.1 to 3.5 for a total of kex times to complete the community expansion process.

[0037] The community shrinking step in step 4 includes:

[0038] Step 4.1: oc i Each node v in j , calculate its purity (v j ), the calculation formula is:

[0039]

[0040] Among them, I(v j ) is the node v j In the community oc i Maximum internal degree (i.e., the number of edges connected to nodes within the community), E max (vj ) is the largest external community with node v j The number of edges, c in (v j ) is the node v j The clustering coefficient of

[0041] Step 4.2: Remove OCs that do not belong to the core community i And the node v with the smallest purity value j ;

[0042] Step 4.3: Repeat steps 4.1 to 4.2 for a total of kcon times to complete the community contraction process.

[0043] Beneficial effects of the present invention:

[0044] The present invention provides a method for detecting overlapping communities with dynamic expansion and optimization. The method first obtains the initial non-overlapping community division results using any non-overlapping community detection algorithm, and randomly selects a core community from it based on a set selection mechanism to ensure the diversity of algorithm initialization. Subsequently, according to the scale of the core community, key parameters such as the expansion scale, the number of expansions, and the number of contractions are dynamically calculated to adapt to the evolution needs of communities with different structural characteristics. In the community expansion stage, by collecting neighboring nodes outside the core community, combined with the number of connected edges and the overlapping community belongingness index, nodes with a higher correlation with the core community are selected and gradually incorporated into the community to achieve orderly expansion of the community boundary. In the community contraction stage, by calculating the purity index of the node, the nodes that do not belong to the core community and have the lowest purity are removed, thereby enhancing the structural stability of the community. Using an iterative optimization framework, the dynamic adjustment of the community boundary is achieved through the alternating execution of expansion-contraction operations, and finally the community division result with a clear overlapping structure is output.

[0045] This method addresses the problems of traditional overlapping community detection methods, such as poor starting point structural stability, difficulty in removing misabsorbed nodes, and insufficient parameter adaptability. By introducing a dynamic expansion and contraction mechanism driven by core communities, it achieves the orderly evolution of community boundaries and enhanced structural purity. It can more accurately identify the multiple affiliations of nodes, effectively improving the clarity, stability, and interpretability of community partitioning results in complex networks. In practical applications, this method can help social network analysis more accurately identify key users across communities and optimize cross-domain interest mining in recommendation systems, providing efficient and reliable technical support for complex network analysis in areas such as social network analysis and intelligent recommendation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a process diagram of the overlapping community detection method of the present invention.

[0047] Figure 2It is a schematic diagram of overlapping community detection in combination with a specific implementation case of the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] A dynamically expanded and optimized overlapping community detection method. As used herein, a "community" refers to a subset of nodes in a complex network that exhibits a relatively high degree of connectivity and typically shares common attributes, functions, or behavioral patterns. In social networks, communities can represent groups of users with similar interests or close relationships; in biological networks, communities may correspond to functionally related protein or gene modules; and in citation networks, communities can represent collections of literature with consistent research themes. Communities can overlap, meaning that some nodes may participate in multiple communities simultaneously, reflecting the complexity of nodes' multiple roles or relationships.

[0050] Therefore, effectively identifying overlapping community structures in networks is not only a core issue in network science research, but also an important foundation for a wide range of applications, including social behavior analysis, recommendation systems, public opinion recognition, and bioinformatics analysis. This paper, by improving the extended starting point structure, introducing a community boundary contraction mechanism, and designing a parameter adaptation strategy, provides a more robust and practical solution for identifying community structures in these practical scenarios.

[0051] The following is a specific embodiment of the application of the present invention in a product recommendation system.

[0052] An e-commerce platform currently has a behavioral network graph of tens of thousands of users (e.g., edges formed by co-browsing, likes, purchases, and comments). The goal is to identify user groups with overlapping interests or behavioral patterns to enable targeted advertising and marketing strategy development. The application process for precision marketing using OCNSE is as follows:

[0053] Step 1: The core community selection process includes:

[0054] Step 1.1: Use the Louvain algorithm to divide the entire platform user behavior network into non-overlapping communities and identify multiple interest communities, such as "digital products," "mother and baby products," and "travel and travel."

[0055] Step 1.2: Based on the size of the community, randomly select a larger community as the initial core community oc i, for example, select the "Travel and Travel" community (including 2,000 users);

[0056] Ensuring that you start with a group with highly concentrated interests and a stable size will help subsequent expansion converge to the real user interest circle and avoid the local noise impact that may be caused by starting from a single point.

[0057] Step 2: Dynamic calculation of parameters, selected oc i Containing 2000 users, the preset proportional coefficients are calculated based on the core community size: ks′=20, kex′=5, kcon′=2, then: ks=2000 / 20=100 (expanded candidate size), kex=100 / 5=20 (expanded times), kcon=100 / 2=50 (contracted times, satisfying kcon>kex);

[0058] Parameters are dynamically adjusted with the size of the community to ensure that expansion and contraction operations are neither too radical nor too conservative, adapting to the structural characteristics of different communities and improving the flexibility and stability of the algorithm.

[0059] Step 3: The process steps for community expansion include:

[0060] Step 3.1: Collect core community oc i All with v j The set of other users with direct connections forms the candidate set NE. For example, if user A browses the "travel" page and pays attention to "digital products" at the same time, he / she will be included in the candidate set;

[0061] Step 3.2: Calculate v for each user in NE j With oc i The number of connected edges of users in the , the calculation formula of the number of connected edges is:

[0062] Conn(v j ,oc i )=|Γ(v j )∩oc i |

[0063] Where Γ(v j ) indicates user v j The neighbor set of v in the user behavior network j There are other users with direct connections, core community oc i All users in the group, that is, the 2000 users currently confirmed in the "Travel and Travel" group, |·| represents the size of the group;

[0064] Step 3.3: Select ks users with the highest number of connected edges to form the candidate set CA, ensuring that the newly joined users have strong connections with the core community;

[0065] Step 3.4: Considering the community size, candidate user activity and community interaction, calculate the interaction between each user in CA and oc i The overlapping community affiliation degree OCA(v j ,oc i ), the calculation formula is:

[0066]

[0067] Among them, Γ(v j ) indicates user v j The neighbor user set of |oc i | indicates community oc i The size of D(v i ,v j ) indicates user v i and v j the distance between them;

[0068] Step 3.5: Add the users with the highest overlapping community affiliation in the candidate set CA to the core community oc i ;

[0069] Step 3.6: Add the user with the highest OCA value in each iteration, and perform 20 iterations in total to form preliminary overlapping communities.

[0070] Each round of iteration will j ,oc i )The largest user joined the community, and it expanded for 20 rounds in total, forming an initial overlapping community that covers users who "browse travel and digital content at the same time."

[0071] Step 4: The process of community contraction includes:

[0072] Step 4.1: For each oc i For users in , calculate their purity (v j ), the calculation formula is:

[0073]

[0074] Among them, I(v j ) is user v j In the community oc i Maximum internal degree (i.e., the number of edges connected to nodes within the community), E max (v j ) is the largest external community and user v j The number of edges, c in (v j ) is user v j The clustering coefficient of

[0075] Step 4.2: Remove OCs that do not belong to the core community i And the node v with the smallest purity value j ;

[0076] Step 4.3: Perform 50 iterations to filter out marginal noise users.

[0077] Remove users with the lowest purity who do not belong to the initial core community, filter out noise and marginal users, and perform 50 rounds of iterations.

[0078] The final stable overlapping community division results are obtained, such as the target group of "those who are interested in digital products and frequently browse travel content". Through the method of the present invention, the platform can accurately identify overlapping user groups and implement cross-category targeted advertising (such as pushing outdoor drones, travel power banks, etc.) for young users who like both "travel" and "digital products", thereby increasing the click-through rate of advertisements and reducing the degree of user disgust.

[0079] like Figure 1 As shown in the figure, the overlapping community detection method proposed in the present invention is divided into three stages. First, the user behavior network is preliminarily divided by a non-overlapping community detection method (such as the Louvain algorithm) to obtain the basic community structure. Then, in the expansion and contraction stages, adjacent users with similar behaviors are gradually introduced based on the core community, and then the noise nodes on the edge of the community are removed through the purity screening mechanism, and finally the overlapping community division result is obtained, which allows users to belong to multiple communities at the same time.

[0080] Figure 2 The present invention is demonstrated in conjunction with a specific embodiment in a product recommendation system. The flowchart on the left shows the entire process from inputting the user network to iteratively optimizing and outputting community results. The schematic diagram on the right reflects the application effect of the algorithm in actual marketing. For example, it successfully identifies a user group that is interested in both "travel" and "digital" at the same time, enabling the platform to accurately push cross-category advertisements such as outdoor drones and travel power banks to this overlapping group, thereby increasing click-through rate and improving user experience.

Claims

1. A dynamically extended and optimized overlapping community detection method, characterized in that: The following steps are included: Step 1: Core community selection, randomly select non-overlapping communities from the existing non-overlapping community division results as the initial core community oc i ; Step 2: Dynamic calculation of parameters based on core community oc i Key parameters for scale calculation: Step 3: Community expansion. In each cycle of the expansion process, find candidate nodes and absorb the unique node with the highest overlapping community affiliation, gradually expanding the community boundary. Step 4: Community contraction. In each cycle of the contraction process, the purity of each node is first calculated to evaluate the stability of the node in the community. Then, a node with the lowest purity that is not in the core community is removed. Step 5: Repeat the community expansion-contraction until the overlap reaches a certain threshold, and obtain the final overlapping community division result.

2. A dynamically extended and optimized overlapping community detection method according to claim 1, characterized in that: The core community selection step in step 1 includes: Step 1.1: Obtain non-overlapping community division results through any non-overlapping community detection algorithm; Step 1.2: Randomly select a community as the initial core community oc i .

3. The method for dynamically expanding and optimizing overlapping community detection according to claim 1, wherein: In step 2, there are three key parameters: Expand candidate scale adjustment parameter ks=|oc i | / ks′, where ks′ is the preset scaling factor; Extension times kex=ks / kex′, where kex′ is a preset proportional coefficient; The number of contractions kcon=ks / kcon′, where kcon′ is a preset proportional coefficient and satisfies kcon>kex.

4. The method for dynamically expanding and optimizing overlapping community detection according to claim 1, wherein: In step 3: Candidate nodes refer to the set of nodes in the adjacent node set of the current core community that have not been absorbed by any identified community, or have been absorbed by other communities but have direct edge connections with the current community.

5. The method for dynamically expanding and optimizing overlapping community detection according to claim 1, wherein: The community expansion step in step 3 includes: Step 3.1: Collect core community oc i All neighbor nodes of form a candidate set NE; Step 3.2: Calculate the relationship between each node in NE and oc i The number of connected edges of the midpoint node. The calculation formula for the number of connected edges is: Conn(v j ,oc i )=|Γ(v j )∩oc i | Where Γ(v j ) represents node v j The neighbor set of , |·| represents the size of the set; Step 3.3: Select ks nodes with the highest number of connected edges to form the candidate set CA; Step 3.4: Calculate the relationship between each node in CA and oc i The overlapping community affiliation degree OCA(v j ,oc i ), the calculation formula is: Among them, Γ(v j ) represents node v j The neighbor node set of |oc i | indicates community oc i The size of D(v i ,v j ) represents node v i and v j the distance between them; Step 3.5: Add the node with the highest degree of belonging to the overlapping community in the candidate set CA to the core community oc i ; Step 3.6: Repeat steps 3.1 to 3.5 for a total of kex times to complete the community expansion process.

6. The method for dynamically expanding and optimizing overlapping community detection according to claim 1, characterized in that: The community shrinking step in step 4 includes: Step 4.1: oc i Each node v in j , calculate its purity (v j ), the calculation formula is: Among them, I(v j ) is the node v j In the community oc i Maximum internal degree (i.e., the number of edges connected to nodes within the community), E max (v j ) is the largest external community with node v j The number of edges, c in (v j ) is the node v j The clustering coefficient of Step 4.2: Remove OCs that do not belong to the core community i And the node v with the smallest purity value j ; Step 4.3: Repeat steps 4.1 to 4.2 for a total of kcon times to complete the community contraction process.

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