Influence maximization method based on artificial fish school

Abstract

The invention discloses an influence maximization method based on an artificial fish school, and belongs to the technical field of complex network analysis. Step 1, identifying an initial community; dividing a network with n nodes into M communities by using a Louvain algorithm; 2, comparing the number of nodes of each divided community with a threshold value theta, and taking the nodes in the communities greater than the threshold value theta as candidate seed nodes; step 3, selecting seed nodes from the candidate seeds by using an artificial fish school initialization algorithm based on degree centrality, and initializing the artificial fish school; 4, performing iterative optimization on the artificial fishes by using three artificial fish school behaviors, namely a foraging behavior, a clustering behavior and a rear-end collision behavior, for the initialized artificial fish school, so that the EDV value of the artificial fishes is maximum; and step 5, finding out an artificial fish vector with the maximum EDV value from all the artificial fishes after iteration, namely a group of optimal seed nodes. According to the method, community division of the network, an artificial fish school initialization method based on degree centrality and an artificial fish school algorithm are combined, so that the efficiency of the algorithm is improved, and the influence of influence overlapping during seed node selection is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network analysis, and in particular relates to an influence maximization method based on artificial fish swarms. Background Art

[0002] The problem of maximizing influence is one of the important contents of complex network research. It selects a fixed-size set of nodes so that the information spread by these nodes can influence as many other nodes in the network as possible. The research on maximizing influence is widely used in many fields such as social network analysis, marketing, public health and rumor control. At present, the algorithms for solving the problem of maximizing influence can be roughly divided into five categories, namely, greedy strategy-based algorithms, centrality-based algorithms, random sampling-based methods, community partition-based algorithms and meta-heuristic algorithms. The greedy strategy-based algorithm has high accuracy, but high time complexity, and is still very time-consuming when dealing with large-scale complex networks. The centrality-based algorithm is based on various centrality indicators and has high time efficiency, but it is easy to produce influence overlap, and the performance varies greatly on different networks, and there is a monotonicity problem. The random sampling-based algorithm solves the problem of time-consuming Monte Carlo simulation through sampling methods, and has an approximately linear time complexity, but the sampling results may be biased, which affects the accuracy. The community partition-based algorithm uses the community structure to simplify the node influence evaluation process and improve the efficiency of the algorithm. However, community partitioning methods may not fully consider the structure of the entire network because they focus on local community structures and may ignore the connections and interactions between communities. Metaheuristic techniques have shown remarkable effectiveness in solving complex optimization challenges. The biggest advantage of using metaheuristic algorithms is that you can avoid running Monte Carlo simulations. It also has the advantages of wide applicability, efficient global search capabilities, flexibility and adjustability, and strong adaptability to different network structures and propagation models. In general, the current influence maximization methods are not only highly complex, but also affected by the overlap of seed nodes. Summary of the invention

[0003] In order to overcome the above technical problems, the purpose of the present invention is to provide an influence maximization method based on artificial fish swarms. First, the Louvain algorithm is used to divide the network into communities. Secondly, communities larger than a threshold are selected and the nodes therein are used as candidate seed nodes, thereby reducing the time complexity of seed node selection. Next, an artificial fish initialization strategy based on degree centrality is proposed, which not only improves the convergence speed of the algorithm but also reduces the impact of influence overlap.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] An influence maximization method based on artificial fish swarms comprises the following steps;

[0006] Step 1: Identify the initial community; use the Louvain algorithm to divide the network with n nodes into M communities;

[0007] Step 2: Compare the number of nodes in each divided community with the threshold θ, and take the nodes in the community with a value greater than the threshold θ as candidate seed nodes;

[0008] Step 3: Use an artificial fish swarm initialization algorithm to select seed nodes from candidate seeds and initialize the artificial fish swarm;

[0009] Step 4: Use three artificial fish school behaviors, namely, foraging behavior, swarming behavior and tail-chasing behavior, to iteratively optimize the artificial fish after initialization, so as to maximize the EDV value of the artificial fish;

[0010] Step 5: From all the artificial fish at the end of the iteration, find the artificial fish vector with the largest EDV value, which is a set of optimal seed nodes.

[0011] In step 2, the number of nodes in the divided community needs to be compared with the threshold θ, and the nodes in the community with a number greater than the threshold θ are taken as candidate seed nodes. The threshold θ is calculated as follows:

[0012]

[0013] The threshold θ represents the average size of the community in the entire network. i represents the i-th community set of the partition, Represents C i The number of nodes in the community.

[0014] In step 3, N artificial fish vectors are initialized, each artificial fish vector X i Initialized to k nodes. The selection method for each artificial fish vector k nodes is: find the three nodes with the largest degree from the candidate node set obtained by community division, and randomly select a node to join X i , and remove the node and its first-order neighbor nodes from the candidate nodes. This approach reduces the overlap of influence. Next, continue to select the three nodes with the largest degree from the remaining nodes and randomly select a node to join X i , and so on, k nodes are selected. The same method is used to select the remaining N-1 artificial fish vectors.

[0015] In step 4, three artificial fish school behaviors, namely, foraging behavior, swarming behavior and tail-chasing behavior, are used to iteratively optimize the artificial fish vector. The specific steps of the three artificial fish optimizations are as follows:

[0016] Step 4.1: Foraging behavior; the current state of the artificial fish is Xi , in the original algorithm, X i It is necessary to find a position within the field of view and move a distance within Step. In order to adapt to the influence maximization algorithm, a formula for calculating the distance between two artificial fish vectors is designed:

[0017] Distance(X1,X2)=k-|X1∩X2|

[0018] X1 and X2 are two artificial fish vectors. The above formula means the number of different nodes between the two vectors. Therefore, when the foraging behavior searches for candidate seed nodes, the specific operation of the moving Step is to move the artificial fish vector X i The Step(Step≤Visual) nodes with the smallest median and the candidate seed node set are not in X i Step nodes in the grid are randomly selected for replacement to determine the EDV value. Visual represents the visual range of the artificial fish. If Y j >Y i , the artificial fish moves to this position. i =EDV(X i ). Similarly, Y j Represents the artificial fish vector X after replacement j EDV value, Y i Represents X i After trying trynumber times, if the condition is still not met, the random behavior is executed, that is, the Step nodes with the smallest degree are randomly replaced.

[0019] Step 4.2: Grouping behavior; suppose the current state of the artificial fish is X i , the number of partners n that explore their neighborhood f ,In order to count the artificial fish within a certain neighborhood, the definition formula of the artificial fish set within the K-distance neighborhood is:

[0020] N(X,K)={X′|Distance(X,X′)≤K}

[0021] N(X,K) is called the set of artificial fish in the K-distance neighborhood of X, and X′∈N(X,K) is called a neighbor of X, which is a k-dimensional vector. f is selected from N artificial fish, so n f =|(X i ,Visual)|. If <δ, (0<δ<1), δ is the crowding factor, indicating that the partner center has more food and is not too crowded, and select n f The center position of the neighbors X cIn order to calculate the center position of the artificial fish, a new center position calculation formula is proposed, which is suitable for the calculation of network nodes. Therefore, the calculation formula of the center position is:

[0022]

[0023] The Most operator represents taking the nodes with the largest cumulative number among the m artificial fishes to form a vector X c That is, select the center position X of the neighborhood node c Then, if Y c >Y i , then X c Instead of X i , in order to find the local optimum.

[0024] Step 4.3: Tail-chasing behavior; Tail-chasing behavior is a behavior of chasing the most active partner among the nearby partners. In the optimization algorithm, it can be understood as the process of moving towards the best partner nearby. Suppose the current state of the artificial fish is X i , explore its neighborhood N(X i ,Visual) The best neighbor X in state max If Y max >Y i , and X max The number of partners in the neighborhood of f ,satisfy Indicates X max There are more food nearby and it is not too crowded, then X max Instead of X i , in order to achieve local optimization.

[0025] Step 4.4: The expected influence value (EDV) is used to effectively estimate the influence spread range of the seed node. The calculation formula is as follows:

[0026]

[0027] S is the set of seed nodes, v is the first-order neighbor of the seed node excluding the seed node, p represents the activation probability, and r(v) represents the number of edges between node v and the nodes in the set S.

[0028] Beneficial effects of the present invention:

[0029] Aiming at the problem of maximizing influence in complex networks, the present invention introduces artificial fish swarm optimization into the influence maximization research for the first time. It uses three kinds of artificial fish group search behaviors, namely foraging behavior, clustering behavior and tail-chasing behavior, to perform local and global optimization, so that the EDV value is maximized, and finally a group of seed nodes with the best propagation power are found. First, the network is divided into communities using the Louvain algorithm; second, communities greater than the threshold are selected, and the nodes therein are used as candidate seed nodes to improve the time efficiency of the algorithm. Then, an artificial fish initialization strategy based on degree centrality is proposed, which not only improves the convergence speed but also reduces the overlap of influence. Finally, a new distance metric and a new center position metric method are proposed, which are used to calculate the distance between seed sets and the center position of a group of seed node sets, respectively. While ensuring the accuracy of influence, the time cost is limited, so that the accuracy and time efficiency of the algorithm are well balanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is the overall process of the influence maximization method of the present invention.

[0031] Figure 2 This is the artificial fish initialization process of the influence maximization method of the present invention.

[0032] Figure 3 This is the foraging behavior optimization process of the influence maximization method of the present invention.

[0033] Figure 4 This is the clustering behavior optimization process of the influence maximization method of the present invention.

[0034] Figure 5 This is the optimization process of the tailgating behavior of the influence maximization method of the present invention.

[0035] Figure 6 It is a process schematic diagram of the influence maximization method of the present invention. DETAILED DESCRIPTION

[0036] In the embodiments of the present invention, the specific implementation process of the technical solution is clearly described by means of diagrams. The diagrams include the process of dividing communities, initializing artificial fish swarms, optimizing artificial fish swarms, and selecting seed nodes. It should be clear that the technical solutions described in the embodiments of the present invention only represent some embodiments, not all embodiments. All other embodiments that can be obtained by ordinary technicians in this field without performing creative work are within the scope of protection of the present invention.

[0037] Therefore, the present invention, through detailed description and illustration, shows the technical personnel an innovative influence maximization method based on artificial fish swarm. The method combines the community division of the network, the artificial fish swarm initialization based on degree centrality and the artificial fish swarm algorithm, which not only improves the efficiency of the algorithm, but also reduces the influence of influence overlap when selecting seed nodes.

[0038] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0039] An influence maximization method based on artificial fish swarms comprises the following steps;

[0040] Step 1: Identify the initial community; use the Louvain algorithm to divide the network with n nodes into M communities;

[0041] Step 2: The number of nodes in each divided community needs to be compared with the threshold θ, and the nodes in the community with a value greater than the threshold θ are taken as candidate seed nodes. The calculation of the threshold θ is as follows:

[0042]

[0043] The threshold θ represents the average size of the community in the entire network. i represents the i-th community set of the partition, Represents C i Number of nodes in the community

[0044] In step 3: Initialize N artificial fish vectors, each artificial fish vector X i Initialized to k nodes. The selection method for each artificial fish vector k nodes is: find the three nodes with the largest degree from the candidate node set obtained by community division, and randomly select a node to join X i , and remove the node and its first-order neighbor nodes from the candidate nodes. This approach reduces the overlap of influence. Next, continue to select the three nodes with the largest degree from the remaining nodes and randomly select a node to join X i , and so on, k nodes are selected. The same method is used to select the remaining N-1 artificial fish vectors.

[0045] Step 4: Use three artificial fish school behaviors, foraging behavior, swarming behavior, and tail-chasing behavior, to iteratively optimize the artificial fish vector. The specific steps for the three artificial fish optimizations are as follows:

[0046] Step 4.1: Foraging behavior; the current state of the artificial fish is X i , in the original algorithm, X i It is necessary to find a position within the field of view and move a distance within Step. In order to adapt to the influence maximization algorithm, a formula for calculating the distance between two artificial fish is designed:

[0047] Distance(X1,X2)=k-|X1∩X2|

[0048] X1 and X2 are two artificial fish vectors. The above formula means the number of different nodes between the two vectors. Therefore, when the foraging behavior searches for candidate seed nodes, the specific operation of the moving Step is to move the artificial fish vector X i The Step(Step≤Visual) nodes with the smallest median and the candidate seed node set are not in X i Step nodes in the grid are randomly selected for replacement to determine the EDV value. Visual represents the visual range of the artificial fish. If Y j >Y i , the artificial fish moves to this position. i =EDV(X i ). Similarly, Y j Represents the artificial fish vector X after replacement j EDV value, Y i Represents X i After trying trynumber times, if the condition is still not met, the random behavior is executed, that is, the Step nodes with the smallest degree are randomly replaced.

[0049] Step 4.2: Grouping behavior; suppose the current state of the artificial fish is X i , the number of partners n that explore their neighborhood f ,In order to count the artificial fish within a certain neighborhood, the definition formula of the artificial fish set within the K-distance neighborhood is:

[0050] N(X,K)={X′|Distance(X,X′)≤K}

[0051] N(X,K) is called the set of artificial fish in the K-distance neighborhood of X, and X′∈N(X,K) is called a neighbor of X, which is a k-dimensional vector. f is selected from N artificial fish, so n f =|(X i ,Visual)|. If (0<δ<1), δ is the crowding factor, indicating that the partner center has more food and is less crowded, and select n f The center position of the neighbors X c In order to calculate the center position of the artificial fish, a new center position calculation formula is proposed, which is suitable for the calculation of network nodes. Therefore, the calculation formula of the center position is:

[0052]

[0053] The Most operator represents taking the nodes with the largest cumulative number among the m artificial fishes to form a vector X c That is, select the center position X of the neighborhood node c Then, if Y c >Y i , then X c Instead of X i , in order to find the local optimum.

[0054] Step 4.3: Tail-chasing behavior; Tail-chasing behavior is a behavior of chasing the most active partner among the nearby partners. In the optimization algorithm, it can be understood as the process of moving towards the best partner nearby. Suppose the current state of the artificial fish is X i , explore its neighborhood N(X i ,Visual) The best neighbor X in the state max , if Y max >Y i , and X max The number of partners in the neighborhood of f ,satisfy Indicates X max There are more food nearby and it is not too crowded, then X max Instead of X i , in order to achieve local optimization.

[0055] Step 4.4: The expected influence value (EDV) is used to effectively estimate the influence spread range of the seed node. The calculation formula is as follows:

[0056]

[0057] S is the set of seed nodes, v is the first-order neighbor of the seed node excluding the seed node, p represents the activation probability, and r(v) represents the number of edges between node v and the nodes in the set S.

[0058] Step 5: From all the artificial fish at the end of the iteration, find the artificial fish vector with the largest EDV value, which is a set of optimal seed nodes.

Claims

1. A method for maximizing influence based on artificial fish swarms, characterized in that: The steps include: Step 1: Identify the initial community; The Louvain algorithm is used to divide a network with n nodes into M communities; Step 2: Compare the number of nodes in each divided community with the threshold θ, and take the nodes in the community with a value greater than the threshold θ as candidate seed nodes; Step 3: Use an artificial fish swarm initialization algorithm to select seed nodes from candidate seeds and initialize the artificial fish swarm; Step 4: Use three artificial fish school behaviors, namely, foraging behavior, swarming behavior and tail-chasing behavior, to iteratively optimize the artificial fish after initialization, so as to maximize the EDV value of the artificial fish; Step 5: From all the artificial fish at the end of the iteration, find the artificial fish vector with the largest EDV value, which is a set of optimal seed nodes. In step 2, the number of nodes in the divided community needs to be compared with the threshold θ, and the nodes in the community that are greater than the threshold θ are taken as candidate seed nodes. The threshold θ is calculated as follows: The threshold θ represents the average size of the community in the entire network. i represents the i-th community set of the partition, Represents C i The number of nodes in the community. In step 3, N artificial fish vectors are initialized, each artificial fish vector X i Initialized to k nodes. The selection method for each artificial fish vector k nodes is: find the three nodes with the largest degree from the candidate node set obtained by community division, and randomly select a node to join X i , and remove the node and its first-order neighbor nodes from the candidate nodes. This approach reduces the overlap of influence. Next, continue to select the three nodes with the largest degree from the remaining nodes and randomly select a node to join X i , and so on, k nodes are selected. The same method is used to select the remaining N-1 artificial fish vectors. In step 4, three artificial fish school behaviors, foraging behavior, grouping behavior and tail-chasing behavior, are used to iteratively optimize the artificial fish vector, and finally the EDV value is calculated. The specific steps are: Step 4.1: Foraging behavior; The current state of the artificial fish is X i , in the original algorithm, X i It is necessary to find a position within the field of view and move a distance within Step. In order to adapt to the influence maximization algorithm, a formula for calculating the distance between two artificial fish vectors is designed: Distance(X1,X2)=k-|X1∩X2| X1 and X2 are two artificial fish vectors. The above formula means the number of different nodes between the two vectors. Therefore, when the foraging behavior searches for candidate seed nodes, the specific operation of the moving Step is to move the artificial fish vector X i The Step(Step≤Visual) nodes with the smallest median and the candidate seed node set are not in X i Step nodes in the grid are randomly selected for replacement to determine the EDV value. Visual represents the visual range of the artificial fish. If Y j >Y i , the artificial fish moves to this position. i =EDV(X i ). Similarly, Y j Represents the artificial fish vector X after replacement j EDV value, Y i Represents X i After trying trynumber times, if the condition is still not met, the random behavior is executed, that is, the Step nodes with the smallest degree are randomly replaced. Step 4.2: Grouping behavior; suppose the current state of the artificial fish is X i , the number of partners n that explore their neighborhood f ,In order to count the artificial fish within a certain neighborhood, the definition formula of the artificial fish set within the K-distance neighborhood is: N(X,K)={X′|Distance(X,X′)≤X} N(X,K) is called the set of artificial fish in the K-distance neighborhood of X, and X′∈N(X,K) is called a neighbor of X, which is a k-dimensional vector. f is selected from N artificial fish, so n f =|(X i ,Visual)|. If <δ, (0<δ<1), δ is the crowding factor, indicating that the partner center has more food and is not too crowded, and select n f The center position of the neighbors X c In order to calculate the center position of the artificial fish, a new center position calculation formula is proposed, which is suitable for the calculation of network nodes. Therefore, the calculation formula of the center position is: The Most operator represents taking the nodes with the largest cumulative number among the m artificial fishes to form a vector X c That is, select the center position X of the neighborhood node c Then, if Y c >Y i , then X c Instead of X i , in order to find the local optimum. Step 4.3: Tail-chasing behavior; Tail-chasing behavior is a behavior of chasing the most active partner among the nearby partners. In the optimization algorithm, it can be understood as the process of moving towards the best partner nearby. Suppose the current state of the artificial fish is X i , explore its neighborhood N(X i ,Visual) The best neighbor X in the state max If Y max >Y i , and X max The number of partners in the neighborhood of f ,satisfy Indicates X max There are more food nearby and it is not too crowded, then X max Instead of X i , in order to achieve local optimization. Step 4.4: The expected influence value (EDV) is used to effectively estimate the influence spread range of the seed node. The calculation formula is as follows: S is the set of seed nodes, v is the first-order neighbor of the seed node excluding the seed node, p represents the activation probability, and r(v) represents the number of edges between node v and the nodes in the set S.

Images