Group search method and device based on maximum clique search on uncertain graph
By constructing an initial graph and performing vertex filtering and search operations, the accuracy problem of searching for uncertain social user groups was solved, enabling efficient retrieval of social user groups and improving the accuracy and efficiency of content push.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INSTITUTE OF TECHNOLOGY (SHENZHEN) (INSTITUTE OF SCIENCE AND TECHNOLOGY INNOVATION HARBIN INSTITUTE OF TECHNOLOGY SHENZHEN)
- Filing Date
- 2026-02-03
- Publication Date
- 2026-06-26
AI Technical Summary
The lack of existing technologies for searching social user groups based on uncertain data on relationships between social users leads to inaccurate inferences about the correlations between social users.
By constructing an initial graph, invalid vertices are deleted based on vertex neighbor probability sorting and heuristic solution selection, generating an intermediate subgraph, and performing multiple search operations in the intermediate subgraph to determine the social user groups in the target subgraph, where the product of the association probability between any two social users in the target subgraph is greater than a preset value.
It enables efficient searching of social user groups in uncertain social networks, improves the accuracy and efficiency of content push, and ensures that the probability of association between social users in a group is higher than a preset threshold.
Smart Images
Figure CN121639201B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for finding communities based on the search for the largest community on an uncertain graph. Background Technology
[0002] The relevance between social users in social networks can provide important reference information for content delivery. Generally, pushing content of interest to closely related social user groups can produce higher delivery effectiveness. Current technologies determine the relevance between social users based on deterministic data, such as whether two users follow each other or have mutual comments and likes. However, in practical applications, the relationships between social users may not be directly displayed but require inference. For example, two social users may not follow each other, but their engagement with similar content can be used to infer a relationship between them.
[0003] The data obtained through this reasoning is uncertain, and in the existing technology, there is no technical solution to search for social user groups based on uncertain correlation data between social users. Summary of the Invention
[0004] This invention provides a method and apparatus for searching social user groups based on the search of the largest clique on an uncertain graph, in order to solve the deficiency in the prior art that there is no correlation data between social users based on uncertainty to search for social user groups, and to realize the search for social user groups based on correlation data between social users based on uncertainty.
[0005] This invention provides a method for finding a clique based on the search for the maximum clique on an uncertain graph, comprising:
[0006] Obtain an initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users.
[0007] The existence probabilities of all neighboring edges of a vertex in the initial graph are sorted in descending order to determine a reference value for each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value.
[0008] In the initial graph, delete the vertices whose reference values are not greater than the heuristic solution values to obtain the vertex set corresponding to the heuristic solution values, and determine the intermediate subgraph based on the vertex set.
[0009] The process involves traversing each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, a target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices, and the product of the probabilities of all edges is greater than a preset probability value. In each search operation, the first selected set is initialized to a vertex in the intermediate subgraph, and the first candidate set is initialized to the set of neighboring vertices of the vertex added to the first selected set. Vertices in the first candidate set corresponding to this search operation are added to the first selected set in sequence, and the first candidate set is updated to the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. The candidate subgraph is determined based on the first selected set and the first candidate set.
[0010] The target social user groups in the social network to be processed are determined based on the target subgraph.
[0011] According to the present invention, a community search method based on maximum clique search on an uncertain graph, before deleting vertices in the initial graph whose corresponding reference values are not greater than the heuristic solution values to obtain the vertex set corresponding to the heuristic solution values, includes:
[0012] Select the vertex with the largest first reference value as the first seed node, initialize the second selected set to include the first seed node, and initialize the second candidate set to include the neighbor nodes of the first seed node in the initial graph.
[0013] Repeat the following steps until the second candidate set is empty, and take the second selected set when the second candidate set is empty as the first heuristic solution set, and take the number of vertices in the first heuristic solution set as the value of the heuristic solution with the smallest value:
[0014] Move the vertex with the highest candidate probability in the second candidate set from the second candidate set to the second selected set;
[0015] Update the candidate probability of each vertex in the second candidate set with respect to the second selected set. If the candidate probability of a vertex in the second candidate set is lower than the probability threshold, then delete the vertex from the second candidate set.
[0016] The candidate probability of a vertex relative to the set is the product of the existence probabilities of the vertex and the neighboring edges of each vertex in the set.
[0017] The process of determining the intermediate subgraph based on the vertex set includes:
[0018] The graph consisting of the set of vertices corresponding to the heuristic solution with the smallest numerical value is taken as the intermediate subgraph.
[0019] According to the present invention, a method for finding a community based on the search for the maximum community on an uncertain graph, wherein determining the candidate subgraph based on the first selected set and the first candidate set includes:
[0020] Based on the candidate subgraph with the largest current number of vertices, determine the current lower limit value of the number of vertices;
[0021] Based on the lower limit of the number of vertices and the number of vertices in the first selected set, the number of vertices to be added is determined;
[0022] Based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added, vertices in the first candidate set are deleted.
[0023] If the first candidate set is empty after the deletion operation, then the graph corresponding to the current first selected set is determined to be the candidate subgraph.
[0024] According to the present invention, a method for finding a community based on the search for the maximum clique on an uncertain graph includes the following steps before determining the candidate subgraph based on the first selected set and the first candidate set:
[0025] Based on the set of vertices corresponding to the largest heuristic solution value, determine the second heuristic solution set;
[0026] Based on the number of vertices in the second heuristic solution set, determine the lower limit value of the number of vertices;
[0027] The larger of the first heuristic solution set and the second heuristic solution set is taken as a candidate subgraph.
[0028] According to the present invention, a community search method based on maximum clique search on an uncertain graph includes deleting vertices in the first candidate set based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added, comprising:
[0029] Vertices x in the first candidate set that satisfy the following conditions will be deleted:
[0030] ;
[0031] in, For the first selected set, for The product of the existence probabilities of all corresponding edges. For the set of vertices that include the vertices to be added, The number of vertices to be added. The value of is the first in the intermediate subgraph. The product of the probabilities of each edge. For the vertices in the first candidate set The candidate probabilities related to the first selected set, As vertices Maximum edge probability Power of 1 The preset probability value is [value].
[0032] According to the present invention, a community search method based on maximum clique search on an uncertain graph, wherein each time a vertex from the first candidate set is added to the first selected set, includes:
[0033] Determine the upper bound of the existence probability of the graph formed by the vertices of the first selected set after adding the number of vertices to be supplemented from the first candidate set to the first selected set;
[0034] If the upper bound of the existence probability is less than the preset probability value, then the current search operation ends and the next search operation is executed.
[0035] The present invention also provides a clique search apparatus based on maximum clique search on an uncertain graph, comprising:
[0036] An initial graph construction module is used to obtain an initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users.
[0037] The reference value determination module is used to sort the existence probabilities of all neighboring edges of the vertices in the initial graph in descending order and determine the reference value of each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value.
[0038] The graph reduction module is used to delete vertices in the initial graph whose corresponding reference values are not greater than the heuristic solution values, to obtain a set of vertices corresponding to the heuristic solution values, and to determine an intermediate subgraph based on the vertex set.
[0039] The graph search module is used to traverse each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations and the intermediate subgraph, the target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices and the product of the existence probabilities of all edges is greater than the preset probability value. In each search operation, the first selected set is initialized to a vertex in the intermediate subgraph, and the first candidate set is initialized to the set of neighboring vertices of the vertex added to the first selected set. In the first candidate set corresponding to this search operation, vertices are added to the first selected set in sequence, and the first candidate set is updated to the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. The candidate subgraph is determined based on the first selected set and the first candidate set.
[0040] The target social user group determination module is used to determine the target social user group in the social network to be processed based on the target subgraph.
[0041] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement any of the above-described methods for finding a community based on the maximum community search on an uncertain graph.
[0042] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-described community search methods based on maximum community search on uncertain graphs.
[0043] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements any of the above-described methods for finding a community based on the maximum community search on an uncertain graph.
[0044] The present invention provides a method and apparatus for finding communities based on maximum clique search on uncertain graphs. This involves converting social network data, including the probability of associations between social users, into an initial graph. Vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of edges in the initial graph reflects the probability of associations between social users. Then, the existence probabilities of all neighboring edges of a vertex in the initial graph are sorted in descending order. A reference value is determined for each vertex in the initial graph; the reference value is the maximum m value that ensures the product of the existence probabilities of the vertex's first m neighboring edges is not less than a preset probability value. Vertices with reference values not greater than the heuristic solution value are deleted from the initial graph, resulting in a vertex set corresponding to the heuristic solution value. An intermediate subgraph is determined based on this vertex set, thus reducing the number of useless vertices and edges in the initial graph. The algorithm reduces the number of vertices and then performs multiple search operations on the resulting intermediate subgraph. Each search operation is based on a vertex in the intermediate subgraph. After traversing all vertices in the intermediate subgraph, candidate subgraphs are obtained, leading to the target subgraph with the largest number of vertices. In the target subgraph, there is an edge between any two distinct vertices, and the product of the probabilities of all edges is greater than a preset probability value. Based on this target subgraph, the target social user group with the largest number of vertices in the social network can be identified. The product of the association probabilities of all social user pairs in this group is greater than the preset probability value. The association probability of a social user pair is the probability that there is a relationship between the two social users included in the pair. In other words, there is a high probability of association between any two social users in the target social user group. This method enables the search of social user groups based on uncertain association data between social users. Attached Figure Description
[0045] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0046] Figure 1 This is a flowchart illustrating the community search method based on maximum community search on an uncertain graph provided by the present invention.
[0047] Figure 2 This is a schematic diagram of the preprocessing process of the initial graph in the community search method based on the maximum clique search on an uncertain graph provided by the present invention.
[0048] Figure 3 This is a flowchart illustrating the process of determining the vertex set corresponding to the heuristic solution in the community search method based on maximum clique search on uncertain graphs provided by this invention. Figure 1 .
[0049] Figure 4 This is a flowchart illustrating the process of determining the vertex set corresponding to the heuristic solution in the community search method based on maximum clique search on uncertain graphs provided by this invention. Figure 2 .
[0050] Figure 5 This is a flowchart illustrating the backtracking solution stage in the community search method based on maximum community search on uncertain graphs provided by this invention.
[0051] Figure 6 This is a schematic diagram of the recursive search process in the community search method based on the maximum community search on an uncertain graph provided by the present invention.
[0052] Figure 7 This is a schematic diagram of the structure of the group search device based on the maximum group search on the uncertain graph provided by the present invention.
[0053] Figure 8 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation
[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0055] The following is combined Figures 1-6 The present invention describes a community search method based on maximum clique search on uncertain graphs, such as... Figure 1 As shown, the method includes the following steps:
[0056] S110. Obtain the initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to the social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users.
[0057] S120. Sort the existence probabilities of all neighboring edges of the vertices in the initial graph in descending order, and determine the reference value of each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than the preset probability value.
[0058] S130. Delete the vertices whose reference values are not greater than the heuristic solution values in the initial graph to obtain the vertex set corresponding to the heuristic solution values, and determine the intermediate subgraph based on the vertex set.
[0059] S140. Traverse each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, determine the target subgraph with the largest number of vertices. In the target subgraph, there is an edge between any two different vertices and the product of the existence probabilities of all edges is greater than a preset probability value. In each search operation, initialize the first selected set as a vertex in the intermediate subgraph and initialize the first candidate set as the set of neighboring vertices of the vertex added to the first selected set. In the first candidate set corresponding to this search operation, add vertices to the first selected set in sequence and update the first candidate set to the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. Determine the candidate subgraph based on the first selected set and the first candidate set. The first candidate set corresponding to this search operation is the neighboring vertices of the vertex added to the first selected set in this search operation.
[0060] S150. Determine the target social user groups in the social network to be processed based on the target subgraph.
[0061] The method provided by this invention converts social network data, including the probability of associations between social users, into an initial graph. Vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of edges in the initial graph reflects the probability of associations between social users. Then, the existence probabilities of all neighboring edges of a vertex in the initial graph are sorted in descending order. A reference value is determined for each vertex in the initial graph; the reference value is the maximum m value that ensures the product of the existence probabilities of the vertex's first m neighboring edges is not less than a preset probability value. Vertices with reference values not greater than the heuristic solution value are deleted from the initial graph, resulting in a vertex set corresponding to the heuristic solution value. An intermediate subgraph is determined based on this vertex set, thus reducing useless vertices and edges in the initial graph. Furthermore, after reduction... Multiple search operations are performed on the obtained intermediate subgraph. Each search operation is based on a vertex in the intermediate subgraph. After traversing all vertices in the intermediate subgraph, candidate subgraphs are obtained, and then the target subgraph with the largest number of vertices is obtained. In the target subgraph, there is an edge between any two different vertices, and the product of the probabilities of all edges is greater than a preset probability value. In this way, based on the target subgraph, the target social user group with the largest number of vertices in the social network can be obtained. The product of the association probabilities of all social user pairs in this social user group is greater than the preset probability value. The association probability of a social user pair is the probability that there is an association relationship between the two social users included in the social user pair. That is to say, there is a high probability of association between any social users in the target social user group. This realizes the search for social user groups based on the association data between social users with uncertainty.
[0062] The method provided by this invention identifies a target social user group within a social network to be processed. This target social user group, identified by the method, possesses the following characteristics: the product of the association probabilities of all social user pairs within the group is greater than a preset probability value; the association probability of a social user pair is the probability that there is an association relationship between the two social users included in the pair. Based on these characteristics, it is clear that the probability of an association relationship between any two social users within this group is not less than the preset probability value. Therefore, by setting a preset probability value, the method provided by this invention can identify the largest social user group where the probability of an association relationship between any two social users is not less than the preset probability value, thereby improving the efficiency of content delivery.
[0063] Relationships between social users can arise from mutual acquaintance or shared interest in the same content. Based on the probability of these relationships, the probability of edges existing within the social network to be processed can be determined. For example, if the probability of a relationship between social user A and social user B is 50%, then the probability of an edge connecting the nodes corresponding to social user A and social user B in the initial graph is also 50%. This correspondence allows us to obtain the initial graph corresponding to the social network to be processed.
[0064] The initial graph is an uncertain graph. To facilitate the subsequent explanation, the relevant concepts of uncertain graphs will be defined below.
[0065] Uncertainty graph It is a triple ,in It is a picture The vertex set, It is a picture edge set, This is for each edge Assigning a function with probability of existence. This means that each edge has... The probability exists in the graph In the graph, the probability of the existence of each edge is independent. Given an uncertain graph... subgraph , making and ,but Existence The probability is:
[0066]
[0067] group It refers to a set of vertices such that from Subgraph exported from To form a complete graph, that is, for They all A maximum clique is a clique with the most vertices. In an uncertain graph, according to the formula above, a clique... The probability of it existing on an uncertain graph is If a group probability of existence Then it is called a -group.
[0068] Furthermore, given a vertex and a group ,group The probability is:
[0069] ;
[0070] If each vertex has its clique information pre-maintained product of connection probabilities The probability of a new candidate set can be quickly calculated during the backtracking solution stage of the method provided in this invention. Here, Known as the vertex About the group The candidate probability. When a new vertex... Join the group At that time, the new candidate probabilities are updated as follows:
[0071] ;
[0072] The method provided by this invention aims to address the uncertainty graph corresponding to the social network to be processed. (i.e., the initial graph) and a preset probability value ,turn up One of the largest - This allows us to identify the largest social user group from the social networks to be processed.
[0073] The method provided in this application preprocesses the initial graph after it has been determined to obtain an intermediate subgraph.
[0074] After obtaining the initial graph, the existence probabilities of the neighboring edges of the vertices in the initial graph are first sorted in descending order to determine the reference value of each vertex. A vertex's neighboring edge refers to the edge between two neighboring vertices, and the existence probability of an edge between a vertex and its neighboring vertex is greater than 0. In the method provided by this invention, the reference value of each vertex is first calculated; this reference value can also be referred to as... Degree. In calculating the vertex of Spend At that time, for the vertex Sort all adjacent edges in descending order of their existence probability to obtain the sequence. ,satisfy Then from Start incrementing, find the largest integer. Make the former product of probabilities of the edges ,Should The value is The significance of this measurement lies in... Belongs to a certain size of - If it is a group, then it must be in harmony with the rest of the group. The vertices are connected, and this The product of the existence probabilities of each edge is not less than ;and That's right The maximum number of neighbors that can be connected under this constraint can therefore be used as... Location - An upper bound on the group size. This calculation can be performed on... Complete within the time limit ( (where is the degree of the vertex), applicable to large-scale graphs.
[0075] In one possible implementation, before deleting vertices in the initial graph whose reference values are not greater than the heuristic solution value, and obtaining the vertex set corresponding to the heuristic solution value, the following steps are included:
[0076] Select the vertex with the largest first reference value as the first seed node, initialize the second selected set to include the first seed node, and initialize the second candidate set to include the neighbor nodes of the first seed node in the initial graph.
[0077] Repeat the following steps until the second candidate set is empty, and take the second selected set when the second candidate set is empty as the first heuristic solution set. Take the number of vertices in the first heuristic solution set as the heuristic solution with the smallest value:
[0078] Move the vertex with the highest candidate probability in the second candidate set to the second selected set;
[0079] Update the candidate probability of each vertex in the second candidate set with respect to the second selected set. If the candidate probability of a vertex in the second candidate set is lower than the probability threshold, then remove the vertex from the second candidate set.
[0080] The candidate probability of a vertex relative to the set is the product of the existence probabilities of the vertex and the neighboring edges of each vertex in the set.
[0081] Determining intermediate subgraphs based on vertex sets includes:
[0082] The graph consisting of the set of vertices corresponding to the heuristic solution with the smallest numerical value is used as the intermediate subgraph.
[0083] like Figure 2 As shown, in this implementation, the first step is to calculate the vertex's... The degree is then used to find a heuristic solution using a degree-based heuristic algorithm, and then the uncertain graph is reduced to... The kernel method removes useless vertices and edges from the graph, and finally uses a kernel-based approach. The kernel's heuristic algorithm attempts to obtain a better heuristic solution.
[0084] like Figure 3 As shown, in this implementation, a vertex is first selected as the seed point. Initialize the selected set Candidate set , Represents seed point Neighboring nodes in the initial graph. Then repeat the following steps: In Select the vertex with the highest candidate probability. join in and will Updated to At the same time, for Each vertex Update its relative to the current The candidate probability. If the candidate probability of a vertex is lower than the threshold... Then take it from Removed from the middle. This process continues until... Empty, final This is the heuristic solution. For degree-based heuristic algorithms, the seed point is the entire graph. The largest vertex Heuristic solutions The number of vertices included is the minimum value of the heuristic solution. .
[0085] Subsequently, execution Nuclear decomposition with pruned original image Wherein, the k-kernel is a maximal subset of vertices in the derived subgraph whose degree is not less than k. The kernel is the source of each vertex in the subgraph. A maximal subset of vertices with degree no less than k. The current heuristic solution is the minimum value. The goal is to find a size of at least 1. of -Group. According to - Properties of a clique, where any vertex In the original image The degree must be no less than (Because there are in the group) For each vertex, v needs to connect the remaining vertices. (One). Therefore, any Degree less than The vertex cannot appear in a larger one. - It can be safely deleted within the group. The method provided in this application uses a similar approach. - An iterative stripping strategy for kernel decomposition, pre-calculating all possible... Nuclear power is used in subsequent processes, and its flowchart is as follows: Figure 4 As shown: Initialization Repeatedly scan all vertices in the graph; if a vertex exists... satisfy If it is not found, it is removed from the graph and all its remaining neighbors are recalculated. Degree (due to the reduction of adjacent sides, its) (degree); when it no longer exists in the graph Degree less than When the vertex is reached, it indicates The kernel, i.e., the set of vertices, has been formed.
[0086] In this implementation, since only the following is concerned... The core can be directly from The stripping process begins, skipping computations of lower-order kernels to accelerate preprocessing.
[0087] As can be seen, based on the above process, we can start with the smallest heuristic solution value, and each heuristic solution value will generate a corresponding set of vertices. (kernel), and use the subgraph corresponding to the vertex set with the smallest heuristic solution value as the intermediate subgraph. .
[0088] exist On top of that, further operation based on The heuristic construction of the kernel follows the same process as the aforementioned degree-based method, the only difference being the choice of the seed point: it is no longer based on the global kernel. degree, but from Select a vertex from the list – this vertex belongs to the maximum non-empty list. nucleus (i.e.) The non-empty kernel with the largest value). Because The core implicitly requires its neighbors to also have sufficiently high [core values] during its construction. Therefore, the local region where the seed point is located is more likely to contain high-quality dense substructures, thus improving the quality of the heuristic solution. The obtained solution is denoted as... The lower bound of the output in the final preprocessing stage intermediate subgraph Updated to heuristic solution values The corresponding vertex set, and with and Entering the backtracking phase.
[0089] This invention provides a novel preprocessing workflow. This workflow defines... Degree is used as a measure of the potential for vertices to form dense subgraphs in an uncertain graph, and based on this, two complementary heuristic algorithms (degree-based and degree-based) are developed. (Core). This framework can not only automatically generate high-quality initial solutions as lower bounds, but also use these lower bounds to effectively modify the original graph. Nuclear decomposition and pruning reduce the scale of the problem at its source.
[0090] During the retrospective phase, such as Figure 5 As shown, the intermediate subgraphs are traversed sequentially. Each vertex in and with The derived subgraph formed by it and its neighbors As the search domain. In each search, the first selected set is used as the search domain. First candidate set The recursion is initiated, and the flowchart of the recursive algorithm is as follows: Figure 6 As shown. In the textual description and accompanying drawings of the method provided in this application, the symbols... This indicates the number of vertices included in the set within the symbol.
[0091] At each step of the recursion, a vertex from the first candidate set is added to the first selected set. Based on the first selected set and the first candidate set, candidate subgraphs are determined, specifically including:
[0092] Based on the candidate subgraph with the largest number of vertices, determine the lower limit of the current number of vertices;
[0093] The number of vertices to be added is determined based on the lower limit of the number of vertices and the number of vertices in the first selected set;
[0094] Based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added, vertices in the first candidate set are deleted.
[0095] If the first candidate set is empty after the deletion operation, then the graph corresponding to the current first selected set is determined as a candidate subgraph. If the newly generated candidate subgraph... If the intermediate subgraph has more vertices than the existing candidate subgraphs, then the intermediate subgraph is reduced to... nuclear.
[0096] Before determining candidate subgraphs based on the first selected set and the first candidate set, the following steps are included:
[0097] Determine the second heuristic solution set based on the set of vertices corresponding to the largest heuristic solution value;
[0098] Determine the lower limit of the number of vertices based on the number of vertices in the second heuristic solution set;
[0099] The larger corresponding subgraph in the first heuristic solution set and the second heuristic solution set is selected as a candidate subgraph.
[0100] In other words, the lower limit of the number of vertices at the beginning of the backtracking phase. The lower bound obtained during the preprocessing stage In this context, the subgraph corresponding to the second heuristic solution set can be considered a candidate subgraph. Furthermore, in one possible implementation, the first heuristic solution set can also be considered a candidate subgraph, and the first and second heuristic solution sets can be compared, retaining the larger corresponding subgraph as the candidate subgraph.
[0101] Based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added, vertices in the first candidate set are deleted, including:
[0102] Vertices in the first candidate set that satisfy the following conditions Delete:
[0103] ;
[0104] in, This is the first selected episode. for The product of the existence probabilities of all corresponding edges. For the set of vertices that include the vertices to be added, The value is taken from the front of the middle subgraph. The product of the probabilities of each edge. The number of vertices to be added. Vertices in the first candidate set The candidate probabilities of the first selected set are relevant. As vertices Maximum edge probability Power of 1 This is a preset probability value.
[0105] In each step of the recursion, the selected vertex... join in form Then, first update the first candidate set to and update The candidate probabilities of each vertex are then calculated. The pruning mechanism proposed in this invention is then applied: Let the current lower bound be... Then it is still necessary to start from Select at least vertices (if the current vertices) It has exceeded Alright, Only then can it surpass the current optimal solution. any vertex If it is to participate in the formation of a better solution, it must be in conjunction with... and those selected in the future who can form a group The rest All vertices are connected. Since the future vertices are unknown, the method provided in this application employs a conservative estimate: Let... ,use The highest edge probability The power as Upper bound of the probability of connection with future vertices At the same time, sort the top edges of the list using the aforementioned edges. Probability product estimation clique of the strips Upper bound of existence probability .then, The necessary condition for being able to participate in a better solution is:
[0106]
[0107] Equivalent to:
[0108]
[0109] like satisfy Then it is safe to get from Delete it. This calculation is performed dynamically on each recursive call, significantly reducing invalid branches.
[0110] Furthermore, to further improve the search efficiency of the method provided in this application, each time a vertex in the first candidate set is added to the first selected set, the process includes:
[0111] Determine the upper bound of the existence probability of the graph formed by adding the number of vertices to be added from the first candidate set to the first selected set;
[0112] If the upper bound of the probability is less than the preset probability value, then the current search operation ends and the next search operation is executed.
[0113] like Figure 5 and Figure 6 As shown, the method provided in this application estimates the upper bound of the existence probability of the first selected set after adding the number of vertices to be supplemented in the first candidate set to the first selected set, and evaluates whether the current candidate set has the potential to generate a feasible solution that is better than the current candidate subgraph.
[0114] Specifically, the coloring-based upper bound estimation algorithm is invoked to evaluate the vertices on which this search is based. The derived subgraph formed by it and its neighbors Does it possess the potential to generate feasible solutions better than the current lower bound? First, graph coloring is performed on the intermediate subgraph: a greedy coloring strategy is used to assign colors to vertices such that the two endpoints of any edge have different colors. Then, the vertices are grouped by color, and the vertex with the highest candidate probability in each color group is selected as the representative of that group. To further improve estimation accuracy, this invention introduces an explicit estimation of the probability of edges between selected vertices. Specifically, the algorithm pre-estimates the probability of edges between selected vertices. All edges in the set are sorted in descending order of probability. Let the current goal be to select from the candidate set. Selected from among vertices to expand Because a size of The complete graph contains There are 10 edges, so the algorithm takes the first edge after sorting. The product of the probabilities of the edges is denoted as... As the first candidate set by The upper bound of the probability of the existence of a clique composed of vertices.
[0115] In the calculation of the upper bound of staining, if the following is selected For each color class (corresponding to the number of vertices to be added), the new selected set is... The upper bound of the existence probability is estimated as:
[0116] ;
[0117] The first term represents the probability of the currently selected set, the second term is the product of the candidate probabilities of the representative vertices of each color class, and the third term estimates the upper bound on the probability that these newly added vertices will form complete connections with each other. Only when the calculated... Only then is it considered that the branch exists and a valid one has been found. If a cluster is found, proceed with the next recursive search; otherwise, prune the branch, stop the search based on the current vertex, and start the next search.
[0118] The method provided by this invention is the first to explicitly introduce the existence probability information of edges between candidate vertices in the upper bound estimation. By pre-sorting the edges in the local subgraph by probability and using combinatorial mathematics principles to estimate the upper probability limit of the formation of a complete graph among newly added vertices, a more compact and realistic probability upper bound is constructed than that of existing techniques. This mechanism is key to achieving efficient pruning and controlling the explosion of the search space.
[0119] In the first candidate set After deleting vertices in the array, if If empty, then If the current branch is the local optimum, and its size exceeds the global record, then update it, while simultaneously shrinking the intermediate subgraph to reduce unnecessary branches; if If the vertex is not empty, the improved upper bound algorithm described above is called again to determine whether to continue recursion. The entire backtracking process terminates after traversing all vertices, and the maximum value is output. -group.
[0120] This invention is the first to propose that, at each step of the backtracking process, not only the connection probability between the vertex and the currently selected set is considered, but also the future required number of vertices is taken into account to conservatively estimate the "potential contribution" of each vertex in the candidate set. By setting a dynamic probability threshold, vertices that cannot contribute to the formation of an effective set even in the most ideal circumstances are excluded. - Clique vertices are removed in advance, thus significantly simplifying the candidate set and reducing invalid computations.
[0121] The subgraph with the largest number of vertices in the candidate subgraph is selected as the target subgraph, and the social users corresponding to the vertices in the target subgraph form the target social user group.
[0122] The following describes the community search apparatus based on maximum clique search on uncertain graphs provided by the present invention. The community search apparatus described below can be referred to in correspondence with the community search method described above. Figure 7 As shown, the community search device based on maximum community search on uncertain graphs provided by the present invention includes:
[0123] The initial graph construction module 710 is used to obtain the initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to the social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users.
[0124] The reference value determination module 720 is used to sort the existence probabilities of all neighboring edges of the vertex in the initial graph in descending order and determine the reference value of each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than the preset probability value.
[0125] Graph reduction module 730 is used to delete vertices whose corresponding reference values are not greater than the heuristic solution values in the initial graph, to obtain the vertex set corresponding to the heuristic solution values, and to determine the intermediate subgraph based on the vertex set.
[0126] The graph search module 740 is used to traverse each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, the target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices and the product of the existence probabilities of all edges is greater than a preset probability value. In each search operation, the first selected set is initialized as a vertex in the intermediate subgraph, and the first candidate set is initialized as the set of neighboring vertices of the vertex added to the first selected set. In the first candidate set corresponding to this search operation, vertices are added to the first selected set in turn, and the first candidate set is updated as the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. The candidate subgraph is determined based on the first selected set and the first candidate set.
[0127] The target social user group determination module 750 is used to determine the target social user group in the social network to be processed based on the target subgraph.
[0128] Figure 8 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 8As shown, the electronic device may include: a processor 810, a communication interface 820, a memory 830, and a communication bus 840. The processor 810, communication interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute a community search method based on maximum clique search on an uncertain graph. This community search method includes: obtaining an initial graph corresponding to the social network to be processed, where vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of edges in the initial graph reflects the probability of association between social users; sorting the existence probabilities of all neighboring edges of a vertex in the initial graph in descending order, determining a reference value for each vertex in the initial graph, where the reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value; deleting vertices in the initial graph whose corresponding reference values are not greater than the heuristic solution value, obtaining a vertex set corresponding to the heuristic solution value, and determining intermediate sub-vertices based on the vertex set. The process involves traversing each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, a target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices, and the product of the probabilities of all edges is greater than a preset probability value. In each search operation, the first selected set is initialized with a vertex in the intermediate subgraph, and the first candidate set is initialized with the set of neighboring vertices of the vertex added to the first selected set. Vertices in the first candidate set corresponding to this search operation are added to the first selected set in sequence, and the first candidate set is updated to be the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. Based on the first selected set and the first candidate set, candidate subgraphs are determined. Based on the target subgraph, target social user groups in the social network to be processed are determined.
[0129] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0130] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the community search method based on maximum clique search on an uncertain graph provided by the above methods. The community search method based on maximum clique search on an uncertain graph includes: obtaining an initial graph corresponding to the social network to be processed, wherein the vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between social users; sorting the existence probabilities of all neighboring edges of a vertex in the initial graph in descending order, determining a reference value for each vertex in the initial graph, wherein the reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value; and deleting the corresponding reference value in the initial graph that is not greater than the heuristic value. The vertex with the heuristic solution value is used to obtain the vertex set corresponding to the heuristic solution value. An intermediate subgraph is determined based on the vertex set. Each vertex in the intermediate subgraph is traversed to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, the target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices and the product of the existence probabilities of all edges is greater than a preset probability value. In each search operation, the first selected set is initialized as a vertex in the intermediate subgraph, and the first candidate set is initialized as the set of neighboring vertices of the vertex added to the first selected set. Vertices in the first candidate set corresponding to this search operation are added to the first selected set in turn, and the first candidate set is updated as the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. A candidate subgraph is determined based on the first selected set and the first candidate set. The target social user group in the social network to be processed is determined based on the target subgraph.
[0131] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the community search method based on maximum clique search on an uncertain graph provided by the above methods. This community search method includes: obtaining an initial graph corresponding to the social network to be processed, where vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of edges in the initial graph reflects the probability of association between social users; sorting the existence probabilities of all neighboring edges of a vertex in the initial graph in descending order, determining a reference value for each vertex in the initial graph, where the reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value; and deleting vertices in the initial graph whose corresponding reference values are not greater than the heuristic solution value, thereby obtaining a heuristic solution value pair. The system first determines the corresponding vertex set and then identifies intermediate subgraphs based on this vertex set. It traverses each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from these search operations, it identifies the target subgraph with the largest number of vertices. In the target subgraph, there is an edge between any two distinct vertices, and the product of the probabilities of all edges is greater than a preset probability value. In each search operation, the system initializes the first selected set with a vertex from the intermediate subgraph and the first candidate set with the set of neighboring vertices of the vertex added to the first selected set. Vertices from the first candidate set corresponding to this search operation are sequentially added to the first selected set, and the first candidate set is updated to be the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. Based on the first selected set and the first candidate set, it identifies candidate subgraphs. Finally, based on the target subgraph, it identifies the target social user groups in the social network to be processed.
[0132] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.
[0133] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.
[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for finding a clique based on maximum clique search on an uncertain graph, characterized in that, include: Obtain an initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users. The existence probabilities of all neighboring edges of a vertex in the initial graph are sorted in descending order to determine a reference value for each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value. In the initial graph, vertices whose reference values are not greater than the heuristic solution value are deleted to obtain the vertex set corresponding to the heuristic solution value. An intermediate subgraph is determined based on the vertex set. After obtaining the vertex set corresponding to the current heuristic solution value, the current heuristic solution value is incremented by 1 to obtain the next heuristic solution value. The step of deleting vertices whose reference values are not greater than the heuristic solution value in the initial graph is repeated to obtain the vertex set corresponding to the heuristic solution value. When the node set in the initial graph is an empty set, the largest heuristic solution value is obtained. The process involves traversing each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, a target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices, and the product of the probabilities of all edges is greater than a preset probability value. In each search operation, the first selected set is initialized to a vertex in the intermediate subgraph, and the first candidate set is initialized to the set of neighboring vertices of the vertex added to the first selected set. Vertices in the first candidate set corresponding to this search operation are added to the first selected set in sequence, and the first candidate set is updated to the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. The candidate subgraph is determined based on the first selected set and the first candidate set. Based on the target subgraph, the target social user groups in the social network to be processed are determined; Before deleting vertices in the initial graph whose reference values are not greater than the heuristic solution value, and obtaining the vertex set corresponding to the heuristic solution value, the process includes: Select the vertex with the largest first reference value as the first seed node, initialize the second selected set to include the first seed node, and initialize the second candidate set to include the neighbor nodes of the first seed node in the initial graph. Repeat the following steps until the second candidate set is empty, and take the second selected set when the second candidate set is empty as the first heuristic solution set, and take the number of vertices in the first heuristic solution set as the value of the heuristic solution with the smallest value: Move the vertex with the highest candidate probability in the second candidate set from the second candidate set to the second selected set; Update the candidate probability of each vertex in the second candidate set with respect to the second selected set. If the candidate probability of a vertex in the second candidate set is lower than the probability threshold, then delete the vertex from the second candidate set. The candidate probability of a vertex relative to the set is the product of the existence probabilities of the vertex and the neighboring edges of each vertex in the set. The process of determining the intermediate subgraph based on the vertex set includes: The graph consisting of the set of vertices corresponding to the heuristic solution with the smallest numerical value is taken as the intermediate subgraph.
2. The community search method based on maximum community search on an uncertain graph according to claim 1, characterized in that, The step of determining the candidate subgraph based on the first selected set and the first candidate set includes: Based on the candidate subgraph with the largest current number of vertices, determine the current lower limit value of the number of vertices; Based on the lower limit of the number of vertices and the number of vertices in the first selected set, the number of vertices to be added is determined; Based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added, vertices in the first candidate set are deleted. If the first candidate set is empty after the deletion operation, then the graph corresponding to the current first selected set is determined to be the candidate subgraph.
3. The community search method based on maximum community search on an uncertain graph according to claim 2, characterized in that, Before determining the candidate subgraph based on the first selected set and the first candidate set, the process includes: Based on the set of vertices corresponding to the largest heuristic solution value, determine the second heuristic solution set; Based on the number of vertices in the second heuristic solution set, determine the lower limit value of the number of vertices; The larger of the first heuristic solution set and the second heuristic solution set is taken as a candidate subgraph.
4. The community search method based on maximum community search on an uncertain graph according to claim 2, characterized in that, The step of deleting vertices from the first candidate set based on the maximum edge probability of vertices in the first candidate set and the number of vertices to be added includes: Vertices x in the first candidate set that satisfy the following conditions will be deleted: ； in, For the first selected set, for The product of the existence probabilities of all corresponding edges. For the set of vertices that include the vertices to be added, The value of is the first in the intermediate subgraph. The product of the probabilities of each edge. The number of vertices to be added. For the vertices in the first candidate set The candidate probabilities related to the first selected set, As vertices Maximum edge probability Power of 1 The preset probability value is [value].
5. The community search method based on maximum community search on an uncertain graph according to claim 2, characterized in that, Each time a vertex from the first candidate set is added to the first selected set, the process includes: Determine the upper bound of the existence probability of the graph formed by the vertices of the first selected set after adding the number of vertices to be supplemented from the first candidate set to the first selected set; If the upper bound of the existence probability is less than the preset probability value, then the current search operation ends and the next search operation is executed.
6. A clique search device based on maximum clique search on an uncertain graph, characterized in that, The device includes: An initial graph construction module is used to obtain an initial graph corresponding to the social network to be processed. The vertices in the initial graph correspond to social users in the social network to be processed, and the existence probability of the edges in the initial graph reflects the probability that there is a relationship between the social users. The reference value determination module is used to sort the existence probabilities of all neighboring edges of the vertices in the initial graph in descending order and determine the reference value of each vertex in the initial graph. The reference value is the maximum m value that makes the product of the existence probabilities of the vertex's first m neighboring edges not less than a preset probability value. The graph reduction module is used to delete vertices in the initial graph whose reference values are not greater than the heuristic solution value, obtain the vertex set corresponding to the heuristic solution value, determine an intermediate subgraph based on the vertex set, and after obtaining the vertex set corresponding to the current heuristic solution value, increment the current heuristic solution value by 1 to obtain the next heuristic solution value, and re-execute the step of deleting vertices in the initial graph whose reference values are not greater than the heuristic solution value to obtain the vertex set corresponding to the heuristic solution value. When the node set in the initial graph is an empty set, the largest heuristic solution value is obtained. The graph search module is used to traverse each vertex in the intermediate subgraph to perform multiple search operations. Based on the candidate subgraphs obtained from the search operations, the target subgraph with the largest number of vertices is determined. In the target subgraph, there is an edge between any two different vertices and the product of the existence probabilities of all edges is greater than the preset probability value. In each search operation, the first selected set is initialized to a vertex in the intermediate subgraph, and the first candidate set is initialized to the set of neighboring vertices of the vertex added to the first selected set. Vertices in the first candidate set corresponding to this search operation are added to the first selected set in sequence, and the first candidate set is updated to the intersection of the set of neighboring vertices added to the first selected set and the first candidate set before the update. The candidate subgraph is determined based on the first selected set and the first candidate set. The target social user group determination module is used to determine the target social user group in the social network to be processed based on the target subgraph. Before deleting vertices in the initial graph whose reference values are not greater than the heuristic solution value, and obtaining the vertex set corresponding to the heuristic solution value, the process includes: Select the vertex with the largest first reference value as the first seed node, initialize the second selected set to include the first seed node, and initialize the second candidate set to include the neighbor nodes of the first seed node in the initial graph. Repeat the following steps until the second candidate set is empty, and take the second selected set when the second candidate set is empty as the first heuristic solution set, and take the number of vertices in the first heuristic solution set as the value of the heuristic solution with the smallest value: Move the vertex with the highest candidate probability in the second candidate set from the second candidate set to the second selected set; Update the candidate probability of each vertex in the second candidate set with respect to the second selected set. If the candidate probability of a vertex in the second candidate set is lower than the probability threshold, then delete the vertex from the second candidate set. The candidate probability of a vertex relative to the set is the product of the existence probabilities of the vertex and the neighboring edges of each vertex in the set. The process of determining the intermediate subgraph based on the vertex set includes: The graph consisting of the set of vertices corresponding to the heuristic solution with the smallest numerical value is taken as the intermediate subgraph.
7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the community search method based on maximum community search on an uncertain graph as described in any one of claims 1 to 5.
8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the community search method based on the maximum community search on an uncertain graph as described in any one of claims 1 to 5.
9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the community search method based on the maximum community search on an uncertain graph as described in any one of claims 1 to 5.