Polarization community detection method based on multilayer symbol network

Abstract

A polarization community detection method based on a multi-layer symbol network is characterized in that a single-layer symbol network is constructed for each community, nodes of the single-layer symbol network represent individuals in the community, positive sides among the nodes represent friendly relationships among the individuals, and negative sides among the nodes represent hostile relationships among the individuals; the interaction relationship among individuals in different communities is represented by cross-layer coupling edges, and the single-layer symbol networks are connected through the cross-layer coupling edges to form a multi-layer symbol network; initializing a multi-layer symbol network, independently dividing each node into a community, and calculating an initial value of the modularity of the multi-layer symbol network; carrying out community division again by taking the initial value of the modularity of the multilayer symbol network as an initial comparison reference, traversing and transferring all nodes in a loop iteration mode until the modularity of the multilayer symbol network reaches the maximum value through community division, completing community division, and obtaining a plurality of new communities as polarized communities; and calculating a polarity value of each new community, and judging the polarized communities based on the polarity values.

Description

Technical Field

[0001] The present invention belongs to the technical field of electrical data processing, and in particular relates to a polarization community detection method based on a multi-layer symbolic network. Background Art

[0002] In fields such as social networks and bioinformatics, accurate detection of polarized communities is crucial for understanding group behavior, information dissemination, and system function. Traditional methods are often based on single-layer network models (such as the Louvain algorithm and spectral clustering), identifying community structures through modularity optimization or local search.

[0003] In recent years, existing studies have advanced the research on polarization detection from different levels. However, existing methods are mostly targeted at single-layer networks and still have some shortcomings: First, the complex relationship networks in real society are multidimensional. For example, in discussions on public events, users will form differentiated position clusters due to different perspective dimensions (such as judgment of the nature of the event, attribution of responsibility, solution preferences, etc.), and single-layer network modeling is prone to semantic loss; second, polarization in symbolic networks is the result of the coupling of positive and negative edges. Existing single-layer detection methods lack a systematic modeling framework when balancing the cross-layer negative edge opposition and the intra-layer positive edge cohesion, which may lead to information loss in multi-layer networks, thereby affecting the accuracy of polarized community detection.

[0004] However, complex systems in reality generally exhibit multi-layered interactions. Single-layer models ignore cross-layer connections and sign relationships (positive and negative), leading to a loss of key information and a significant decrease in detection accuracy. For example, existing modularity metrics (such as Newman modularity) are not designed for multi-layer signed networks and cannot quantify the polarization characteristics of positive edge cohesion within a layer and negative edge confrontation between layers, resulting in insufficient robustness in complex network scenarios.

[0005] In the conference paper "Discovering Conflict Groups in Signed Networks" (Conference Name: NeurIPS, Publication Year: 2020), the authors studied the problem of detecting k conflict groups in signed networks. The premise is that each group is positively connected internally and negatively connected with the other k-1 groups. A notable feature of this problem is that they are not looking for a complete partition of the signed network, but rather allow a portion of nodes to remain neutral with respect to the conflict structure being sought. Therefore, this problem is different from previously studied problems such as correlation clustering and k-way partitioning. To solve the problem of conflict group discovery, the authors derive a new formulation in which each conflict group is naturally characterized by the solution of the maximum discrete Rayleigh quotient (MAX-DRQ) problem. The authors proposed two spectral methods to find approximate solutions to the MAX-DRQ problem and analyzed them theoretically. Experimental evaluation shows that compared with the state-of-the-art baseline methods, the method proposed in this paper can find higher quality solutions, is faster, and can recover the true conflict groups with higher accuracy.

[0006] While some of the aforementioned studies attempt to extend modularity to multi-layer networks, they fail to distinguish between the differential contributions of positive and negative edges to polarization and fail to address the dynamic balance between community cohesion and cross-layer antagonism in signed networks. Furthermore, while existing algorithms (such as MPBTV and DGFM3) support multi-layer networks, they rely on fixed parameters or ignore sign characteristics, making them difficult to adapt to the needs of polarized community detection in noisy environments. For example, while the LSPCD algorithm incorporates sign sensitivity, its single-layer framework fails to capture the reinforcing effect of cross-layer coupling on polarization, leading to increased misjudgment rates in scenarios such as public opinion analysis. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a polarization community detection method based on a multi-layer symbol network with high efficiency and high accuracy.

[0008] The technical solution adopted to solve the above technical problems is: a polarization community detection method based on a multi-layer symbol network, comprising the following steps:

[0009] Step 1. Build a multi-layer symbol network

[0010] A single-layer signed network is constructed for each community. The nodes of the single-layer signed network represent individuals in the community. Positive edges between nodes indicate friendly relationships between individuals, while negative edges between nodes indicate hostile relationships between individuals.

[0011] The interaction between individuals in different communities is represented by cross-layer coupling edges, and each single-layer symbolic network is connected through cross-layer coupling edges to form a multi-layer symbolic network;

[0012] Step 2. Initialize the multi-layer symbolic network. Divide each node into a community as the initial division and calculate the initial value of the modularity of the multi-layer symbolic network.

[0013] Step 3. Re-dividing the community using the initial value of the modularity of the multi-layer symbolic network as the initial comparison benchmark, traversing and transferring all nodes in a loop iterative manner until the community division makes the modularity of the multi-layer symbolic network reach the maximum value, completing the community division and obtaining multiple new communities as polarized communities;

[0014] Step 4. Calculate the polarity value of each new community and determine the polarized community based on the polarity value.

[0015] As a preferred technical solution, the multi-layer symbol network modularity Q is:

[0016]

[0017] Where, is the modularity of the rth single-layer community, s is the total number of single-layer communities, is the modularity of the lth cross-layer community, which is composed of the nth single-layer community and the mth single-layer community connected together, n∈[1,s], m∈[1,s], n≠m, and u is the total number of cross-layer communities.

[0018] As a preferred technical solution, the modularity of the rth single-layer community in step 2 is for:

[0019]

[0020] Where D r is the total degree of all nodes in the rth single-layer community, V r is the node set in the rth single-layer community, i r 、j r are two different nodes in the rth single-layer community, is the adjacency matrix, representing node i r 、j r If there are positive edges between is 1, otherwise 0; Represents node i r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node i r The number of connected coupling edges, Represents node j r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node j n The number of connected coupling edges;

[0021] The modularity of the lth cross-layer community for:

[0022]

[0023] Where, is the total degree of positive edges of all nodes in the nth single-layer community, i n 、j n are two different nodes in the nth single-layer community, V n is the set of nodes in the nth single-layer community, is the adjacency matrix, representing node i n 、j n If there are positive edges between is 1, otherwise 0; For node i n 、j nThe number of positive edges connecting to other nodes in the nth single-layer community, is the total degree of positive edges of all nodes in the mth single-layer community, i m 、j m are two different nodes in the mth single-layer community, V m is the node set in the mth single-layer community, is the adjacency matrix, representing node i m 、j m If there are positive edges between is 1, otherwise 0; For node i m 、j m The number of positive edges connecting to other nodes in the mth single-layer community, are the total positive edge degrees and negative edge degrees of all nodes in the l-th cross-layer community, respectively, p n is the node in the nth single-layer community in the lth cross-layer community, q m is the node in the mth single-layer community in the lth cross-layer community, is the adjacency matrix, representing the node p n ,q m If there is a negative edge between is 1, otherwise 0; for, for, is the adjacency matrix, representing the node p n ,q m If there are positive edges between is 1, otherwise it is 0; E coupled is the set of node pairs with coupled edges.

[0024] As a preferred technical solution, the method of traversing and transferring all nodes in a loop iterative manner is:

[0025] Step A1. Select a node in a certain order and try to transfer it from its current community to the community where its neighboring nodes are located. Calculate the change in modularity ΔQ of the multi-layer signed network before and after the transfer. If ΔQ > 0, accept the transfer, move the node to the new community, and update the community division; if ΔQ < 0, keep the node in the original community.

[0026] Step A2. Repeat step A1 until all nodes in the multi-layer symbol network are traversed;

[0027] Step A3. After completing a round of node traversal, check whether the modularity of the multi-layer symbolic network has reached the convergence condition. If not, restart the node traversal and continue to optimize the community division until the modularity of the multi-layer symbolic network reaches the convergence condition or the maximum number of iterations is reached.

[0028] As a preferred technical solution, selecting a node in a certain order refers to selecting in a random order or in a node number order.

[0029] As a preferred technical solution, the convergence condition in step A3 is: ΔQ≤t, where t is a set threshold.

[0030] The beneficial effects of the present invention are as follows:

[0031] The present invention constructs a multi-layer symbolic network structure to accurately quantify the polarization characteristics of positive edge cohesion within a layer and negative edge confrontation between layers, thereby avoiding information loss and significantly improving the accuracy of community detection. It solves the technical problem that traditional methods are mostly based on single-layer network models, which are prone to semantic loss and loss of key information.

[0032] This method uses a loop-based iterative approach to traverse and transfer all nodes. This strategy can quickly find the optimal community partitioning solution within a limited number of iterations. During each iteration, the change in modularity ΔQ of the multi-layer symbolic network before and after the transfer is calculated to determine whether the node should be transferred. This approach avoids complex global searches, reduces unnecessary computation, and improves detection efficiency.

[0033] The present invention considers factors such as the weight and quantity of various sign relationships (positive, negative, and coupled edges) during the detection process, resulting in a certain degree of robustness against noise. Even when there is a certain degree of error or uncertainty in the data, it can still accurately detect polarized communities. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a structural schematic diagram of the present invention.

[0035] Figure 2 It is a structural diagram of the cross-layer community.

[0036] Figure 3 It is a schematic diagram of a multi-layer symbolic network for students majoring in liberal arts and physiology.

[0037] Figure 4 This is a schematic diagram of polarized communities based on the detection of the thinking of liberal arts students and science students of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to the following embodiments.

[0039] The polarization community detection method based on a multi-layer signed network of this embodiment includes the following steps:

[0040] Step 1. Build a multi-layer symbol network

[0041] The step is to construct a single-layer symbolic network for each community. The nodes of the single-layer symbolic network represent individuals in the community. Positive edges between nodes represent friendly relationships between individuals, and negative edges between nodes represent hostile relationships between individuals. The interactive relationships between individuals in different communities are represented by cross-layer coupling edges. Each single-layer symbolic network is connected through cross-layer coupling edges to form a multi-layer symbolic network.

[0042] Step 2. Initialize the multi-layer symbolic network. Divide each node into a community as the initial division and calculate the initial value of the modularity of the multi-layer symbolic network.

[0043] Among them, the modularity Q of the multi-layer symbol network is:

[0044]

[0045] Where, is the modularity of the rth single-layer community, s is the total number of single-layer communities, is the modularity of the lth cross-layer community, the lth cross-layer community is composed of the nth single-layer community and the mth single-layer community, n∈[1,s], m∈[1,s], n≠m, u is the total number of cross-layer communities, as shown Figure 2 ,In the figure, the solid line indicates that the connection between two nodes is a positive edge, ,which is a friendly relationship; the dotted line indicates the connection ,is a negative edge, which is a hostile relationship.

[0046] The modularity of the rth single-layer community for:

[0047]

[0048] Where D r is the total degree of all nodes in the rth single-layer community, V r is the node set in the rth single-layer community, i r 、j r are two different nodes in the rth single-layer community, is the adjacency matrix, representing node i r 、j r If there are positive edges between is 1, otherwise 0; Represents node i r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node i r The number of connected coupling edges, Represents node j r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node j nThe number of connected coupling edges;

[0049] The modularity of the lth cross-layer community for:

[0050]

[0051] Where, is the total degree of positive edges of all nodes in the nth single-layer community, i n 、j n are two different nodes in the nth single-layer community, V n is the set of nodes in the nth single-layer community, is the adjacency matrix, representing node i n 、j n If there are positive edges between is 1, otherwise 0; For node i n 、j n The number of positive edges connecting to other nodes in the nth single-layer community, is the total degree of positive edges of all nodes in the mth single-layer community, i m 、j m are two different nodes in the mth single-layer community, V m is the node set in the mth single-layer community, is the adjacency matrix, representing node i m 、j m If there are positive edges between is 1, otherwise 0; For node i m 、j m The number of positive edges connecting to other nodes in the mth single-layer community, are the total positive edge degrees and negative edge degrees of all nodes in the l-th cross-layer community, respectively, p n is the node in the nth single-layer community in the lth cross-layer community, q m is the node in the mth single-layer community in the lth cross-layer community, is the adjacency matrix, representing the node p n ,q m If there is a negative edge between is 1, otherwise 0; for, for, is the adjacency matrix, representing the node p n ,q m If there are positive edges between is 1, otherwise it is 0; E coupled is the set of node pairs with coupled edges.

[0052] Step 3. Re-dividing the community using the initial value of the modularity of the multi-layer symbolic network as the initial comparison benchmark, traversing and transferring all nodes in a loop iterative manner until the community division makes the modularity of the multi-layer symbolic network reach the maximum value, completing the community division and obtaining multiple new communities;

[0053] Among them, the method of traversing and transferring all nodes in a loop iteration manner is:

[0054] Step A1. Select a node in the order of node number, or randomly, and try to transfer it from its current community to the community where its neighbor node is located. Calculate the change in modularity ΔQ of the multi-layer signed network before and after the transfer. If ΔQ > 0, accept the transfer, move the node to the new community, and update the community division; if ΔQ < 0, keep the node in the original community.

[0055] Step A2. Repeat step A1 until all nodes in the multi-layer symbol network are traversed;

[0056] Step A3. After completing a round of node traversal, check whether the modularity of the multi-layer symbol network has reached the convergence condition, that is, ΔQ≤t, t is the set threshold, t=10 -7 ,If the convergence condition is not met, the node traversal is restarted and the ,community division is continued to be optimized until the modularity of the ,multilayer symbolic network reaches the convergence condition or the maximum number of ,iterations is reached.

[0057] Step 4. Calculate the polarity value of each new community according to the following formula, and determine the polarized community based on the polarity value.

[0058]

[0059] Where, is the adjacency matrix, z is the number of nodes in the network, Represents node i z community belonging, Represents node j z ownership.

[0060] Next, the polarization community detection method based on the multi-layer symbolic network of the present invention is used to detect the polarization phenomenon in the thinking of liberal arts students and science students.

[0061] Based on the questions "Should the development of artificial intelligence prioritize technological ethics or technological efficiency?" and "Which is more academically valuable, qualitative or quantitative research?", this study was divided into two dimensions. The first dimension focused on the humanities and social sciences, emphasizing that "the development of artificial intelligence must prioritize technological ethics" and that "qualitative research has greater academic value." The second dimension, focusing on science and engineering, advocated that "artificial intelligence should prioritize technological efficiency" and that "quantitative research is more academically rigorous." 20 questions were asked on each dimension, for a total of 40 questions. A five-point Likert scale was then developed, with 1-5 representing "strongly disagree" to "strongly agree." Nineteen science students (numbered 1-19) and 19 liberal arts students (numbered 20-38) were selected to rate their responses. The resulting scores were averaged across each dimension to determine each student's opinion orientation, yielding a student's opinion orientation score for both dimensions.

[0062] like Figure 3 As shown in the figure, the liberal arts students and science students in the student group are regarded as a layer of symbolic network respectively, namely, a single-layer symbolic network for liberal arts and a single-layer symbolic network for science. Each layer of symbolic network contains a total of 19 students as nodes.

[0063] In each layer of the symbolic network, for any two students i r 、j r The positive and negative edges between them are determined by the comprehensive difference value. Specifically, the difference a1 between the two students' opinion tendency values ​​in the first dimension and the difference b1 between the two students' opinion tendency values ​​in the second dimension are weighted to obtain the comprehensive difference. Two thresholds T1 = 0.128 and T2 = 0.2 are set for the comprehensive difference value. When , it is considered that the views of the two students tend to be consistent, which is a relatively friendly relationship, and a positive edge is assigned; when Δ ij When it is >T2, it indicates that the two students have a large difference in views and tend to have a hostile relationship, and is assigned a negative edge; It is believed that the difference in views between the two is not enough to constitute an obvious friendly or hostile relationship, so no border will be assigned.

[0064] Cross-layer coupling edges represent the positive or negative interaction between any liberal arts student and a science student. The sign of the coupling edge is determined by the comprehensive difference between the liberal arts and science students connected by the coupling edge. The calculation method for the comprehensive difference value is the same as that of the layer-signed network, where the thresholds for the comprehensive difference value are T3 = 0.1 and T4 = 0.477. When the comprehensive difference between a liberal arts student and a science student is greater than T4, it indicates that the two students have significant differences in their views on the same issue, and a negative edge is assigned. When the comprehensive difference between a liberal arts student and a science student is less than T3, it indicates that the two students have a relatively small difference in their views on the same issue, and a positive edge is assigned. In other cases, no significant relationship is considered, and no edge is assigned.

[0065] Each liberal arts student and each science student is divided into a community as the initial division, with a total of 38 communities. Each community corresponds to a single-layer symbolic network, and the corresponding multi-layer symbolic network modularity Q = 0 is used as the initial value;

[0066] After traversing and transferring all nodes in a loop iteration, the community division is completed and 3 new communities are obtained as polarized communities, as shown in Table 1 and Figure 4 .

[0067] Among them, the polarity values ​​of community 1, community 2, and community 3 are 14.7692, 10.7143, and 15.1765, respectively.

[0068] Table 1. New community division results

[0069]

[0070] exist Figure 4 In the figure, pink lines represent negative edges, and darker lines represent positive edges. Community 1 represents a group that can transcend disciplinary boundaries and form comprehensive perspectives. Community 2 represents the polarized thinking of liberal arts students within this community, who tend to cling to their own disciplinary positions. Community 3 represents significant differences in perspectives between liberal arts and science students, necessitating that the university take measures to mitigate these differences and promote interdisciplinary integration and exchange.

Claims

1. A polarization community detection method based on a multi-layer symbolic network, characterized in that: The following steps are involved: Step 1. Build a multi-layer symbol network A single-layer signed network is constructed for each community. The nodes of the single-layer signed network represent individuals in the community. Positive edges between nodes indicate friendly relationships between individuals, while negative edges between nodes indicate hostile relationships between individuals. The interaction between individuals in different communities is represented by cross-layer coupling edges, and each single-layer symbolic network is connected through cross-layer coupling edges to form a multi-layer symbolic network; Step 2. Initialize the multi-layer symbolic network. Divide each node into a community as the initial division and calculate the initial value of the modularity of the multi-layer symbolic network. Step 3. Re-dividing the community using the initial value of the modularity of the multi-layer symbolic network as the initial comparison benchmark, traversing and transferring all nodes in a loop iterative manner until the community division makes the modularity of the multi-layer symbolic network reach the maximum value, completing the community division and obtaining multiple new communities as polarized communities; Step 4. Calculate the polarity value of each new community and determine the polarized community based on the polarity value.

2. The polarization community detection method based on a multi-layer symbol network according to claim 1, characterized in that: The modularity Q of the multi-layer symbol network is: Where, is the modularity of the rth single-layer community, s is the total number of single-layer communities, is the modularity of the lth cross-layer community, which is composed of the nth single-layer community and the mth single-layer community connected together, n∈[1,s], m∈[1,s], n≠m, and u is the total number of cross-layer communities.

3. The polarization community detection method based on a multi-layer signed network according to claim 2, characterized in that: The modularity of the rth single-layer community in step 2 for: Where D r is the total degree of all nodes in the rth single-layer community, V r is the node set in the rth single-layer community, i r 、j r are two different nodes in the rth single-layer community, is the adjacency matrix, representing node i r 、j r If there are positive edges between is 1, otherwise 0; Represents node i r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node i r The number of connected coupling edges, Represents node j r The number of positive edges and negative edges connecting to other nodes in the r-th single-layer community, Indicates the cross-layer network with node j n The number of connected coupling edges; The modularity of the lth cross-layer community for: Where, is the total degree of positive edges of all nodes in the nth single-layer community, i n 、j n are two different nodes in the nth single-layer community, V n is the set of nodes in the nth single-layer community, is the adjacency matrix, representing node i n 、j n If there are positive edges between is 1, otherwise 0; For node i n 、j n The number of positive edges connecting to other nodes in the nth single-layer community, is the total degree of positive edges of all nodes in the mth single-layer community, i m 、j m are two different nodes in the mth single-layer community, V m is the node set in the mth single-layer community, is the adjacency matrix, representing node i m 、j m If there are positive edges between is 1, otherwise 0; For node i m 、j m The number of positive edges connecting to other nodes in the mth single-layer community, are the total positive edge degrees and negative edge degrees of all nodes in the l-th cross-layer community, respectively, p n is the node in the nth single-layer community in the lth cross-layer community, q m is the node in the mth single-layer community in the lth cross-layer community, is the adjacency matrix, representing the node p n ,q m If there is a negative edge between is 1, otherwise 0; for, for, is the adjacency matrix, representing the node p n ,q m If there are positive edges between is 1, otherwise it is 0; E coupled is the set of node pairs with coupled edges.

4. The polarization community detection method based on a multi-layer symbolic network according to claim 1, characterized in that: The method of traversing and transferring all nodes in a loop iteration manner is: Step A1. Select a node in a certain order and try to transfer it from its current community to the community where its neighboring node is located. Calculate the change in modularity ΔQ of the multi-layer signed network before and after the transfer. If ΔQ > 0, accept the transfer, move the node to the new community, and update the community division. If ΔQ < 0, the node is retained in the original community; Step A2. Repeat step A1 until all nodes in the multi-layer symbol network are traversed; Step A3. After completing a round of node traversal, check whether the modularity of the multi-layer symbolic network has reached the convergence condition. If not, restart the node traversal and continue to optimize the community division until the modularity of the multi-layer symbolic network reaches the convergence condition or the maximum number of iterations is reached.

5. The polarization community detection method based on a multi-layer symbol network according to claim 4, characterized in that: Selecting a node in a certain order refers to selecting in a random order or in a node number order.

6. The polarization community detection method based on a multi-layer symbol network according to claim 4, characterized in that: The convergence condition in step A3 is: ΔQ≤t, where t is a set threshold.

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