CN110910261A - Network community detection countermeasure enhancement method based on multi-objective optimization - Google Patents

Network community detection countermeasure enhancement method based on multi-objective optimization Download PDF

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CN110910261A
CN110910261A CN201911014807.XA CN201911014807A CN110910261A CN 110910261 A CN110910261 A CN 110910261A CN 201911014807 A CN201911014807 A CN 201911014807A CN 110910261 A CN110910261 A CN 110910261A
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network
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population
reconnection
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宣琦
周嘉俊
王金焕
陈丽红
俞山青
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Zhejiang University of Technology ZJUT
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Abstract

A network community detection countermeasure enhancement method based on multi-objective optimization comprises the following steps: s1: loading a network; s2, detecting the community to obtain the community structure; s3: defining a candidate reconnection edge rule; s4: searching an optimal network reconnection strategy by using a genetic algorithm, and specifically comprising the following operation steps: 4.1) initializing a population; 4.2) selecting the roulette mode; 4.3) fixing the crossing rate to carry out crossing operation; 4.4) carrying out mutation operation by fixing the mutation rate; 4.5) keeping the elite; 4.6) judging a termination condition; s5: obtaining optimal individual from the last generation population, and reconnecting the network
Figure DDA0002245357030000011
Enhanced network
Figure DDA0002245357030000012
To pair
Figure DDA0002245357030000013
Community detection to obtain new community divisions
Figure DDA0002245357030000014
The invention utilizes the excellent global search capability and robustness of the genetic algorithm, can find the optimal network reconnection strategy on the whole network, gives consideration to the maximum modularity improvement and the optimal detection resolution, and greatly improves the performance of the community detection algorithm.

Description

Network community detection countermeasure enhancement method based on multi-objective optimization
Technical Field
The invention relates to the field of network science and data mining, in particular to a network community detection countermeasure enhancement method based on multi-objective optimization.
Background
The community structure of the complex network is another important network topology attribute besides the basic statistical characteristics of small worlds, no scale and the like. A number of empirical studies have shown that many networks are heterogeneous, i.e. complex networks are not a large collection of nodes of identical nature randomly connected together, but a combination of many types of nodes. There are more connections between nodes of the same type and relatively fewer connections between nodes of different types. The subgraph formed by defining nodes satisfying the same type and edges between the nodes is called a community in the network.
Since Girvan and Newman proposed GN algorithms based on edge numbers (reference [1]: Girvan M, Newman M EJ. Community structure in social and biological networks [ J ]. Proceedings of the national academy of sciences,2002,99(12):7821 7826. Girvan M, Newman M E J, social networks and community structures in biological networks, Proceedings of the national academy of sciences,2002,99(12):7821-7826.) the community in complex networks was discovered to be a focus of research in the field of network science, researchers from various fields of biology, physics, computers, etc. brought about many novel ideas and algorithms and applied to specific problems in various fields of science. For example, social circles are formed by clustering users with common interests in a social network by using community detection; the biological field utilizes community detection to analyze protein interaction mechanisms; the logistics field uses community detection to normalize regional distribution and shortest paths, and efficient and accurate distribution is achieved.
However, various network community detection algorithms, while being optimized in terms of accuracy and speed, are still limited by the topology of the network itself, and face many challenges. The presence of counterattacks (ref [2]: Dai H, Li H, Tian T, et. Adversal attack on graph structured data [ J ]. arXiv preprint arXiv:1806.02371,2018. i.e. Dai H, Li H, Tian T, etc., counterattacks on graph structure data, arXiv preprint Xiv:1806.02371,2018.) affects both the network structure and the associated algorithms. The network has a great deal of noise and loss, so that a great deal of deviation occurs in the analysis of the network; the anti-attack layer aiming at network clustering is endless, and the performance of the community detection algorithm is also seriously influenced. In addition, the accuracy of community detection results is also affected by the data missing problem caused by nature or human. For example, social relationships in the real world cannot be fully embodied on internet social platforms; the website privacy protection measures enable the data volume acquired by the crawler to have access limit; the industrial production data often has a large number of defects due to the limitations of experimental conditions and the like.
In summary, relatively few studies are currently conducted on how to improve the detection performance of the community detection algorithm on antagonistic and deficient data.
Disclosure of Invention
Aiming at the difficulties in the prior art, the invention innovatively provides a network community detection countermeasure enhancement concept, optimizes the connection of edges in a network community through a genetic algorithm, enhances the structure of the network community, adaptively adjusts the resolution of the community detection algorithm and finally improves the performance of the algorithm.
In order to solve the technical problems, the invention provides the following technical scheme:
a network community detection countermeasure enhancement method based on multi-objective optimization comprises the following steps:
s1: loading a network
Figure BDA0002245357010000021
Wherein
Figure BDA0002245357010000022
Denotes the set of nodes in the network, ∈ { e ═ eiI 1.., m represents the set of edges in the network,
Figure BDA0002245357010000023
representing a real community division of the network;
s2: method of detecting community using selection
Figure BDA0002245357010000024
Carrying out community detection on the network to obtain the community division of the original network
Figure BDA0002245357010000025
S3: and defining a candidate reconnection edge rule. For a target node vi，
Figure BDA0002245357010000026
A set of neighboring nodes that represent it,
Figure BDA0002245357010000027
represents a set of its non-neighboring nodes,
Figure BDA0002245357010000028
representing nodes v after community detectioniThe community being distributed. The candidate reconnection side rule is determined by the predicted community number and the real community number, and when the predicted community number is equal to the real community number, the intra-community addition and inter-community deletion are effective; when the number of the predicted communities is smaller than the number of the real communities, the deletion of the extra communities is effective; additional inter-community bordering is also effective when the number of predicted communities is greater than the number of actual communities. The candidate reconnected edge rule formula is as follows:
Figure BDA0002245357010000029
s4: searching an optimal network reconnection scheme by using a genetic algorithm, wherein the operation steps are as follows:
4.1) population initialization: according to designRandomly generating an initial population by the coding mode
Figure BDA00022453570100000210
The population size is fixed;
4.2) individual selection: calculating the fitness value of each individual in the population, and screening the parental individuals by using a roulette mode, wherein the probability of each individual being selected is proportional to the fitness value:
Figure BDA00022453570100000211
4.3) intersection: according to step 4.2), the two selected parents have a certain cross probability
Figure BDA00022453570100000212
Performing cross operation to form two new individuals;
4.4) mutation: the individuals in the population obtained in the step 4.3) have a certain mutation probability
Figure BDA00022453570100000213
Carrying out mutation operation;
4.5) Elite preservation: replacing the worst 20% of the children with the best 20% of the parents;
4.6) termination conditions: judging whether the termination condition of the genetic algorithm is met or not, if not, changing the newly generated offspring population into the parent population, and repeating the steps 4.2) -4.6), otherwise, terminating the algorithm;
s5: obtaining the optimal individual from the last generation population, namely obtaining the optimal network reconnection strategy through genetic algorithm search, and applying the optimal network reconnection strategy to the network
Figure BDA0002245357010000031
In the network after enhancement
Figure BDA0002245357010000032
Wherein epsilon*＝ε+εmodIs the edge set of the reconnected network. To pair
Figure BDA0002245357010000033
Community division for community detection and acquisition
Figure BDA0002245357010000034
Further, in the step 4.1), the encoding method is as follows: each individual can be represented by a chromosome, each chromosome being represented by a truncated fragment epsilondelAnd the bordered fragment εaddThe length of the edge deletion and edge addition segments respectively represents the number of the deleted and added edges and is respectively composed of two sampling rates βd,βaControlling the upper limit of the quantity, wherein each gene position represents a one-time side operation.
In the step 4.2), the design of the fitness function comprehensively considers the modularity and the clustering number, wherein the modularity is used for measuring the community structure strength of the network clustering algorithm partition result,
Figure BDA0002245357010000035
larger values indicate greater strength of community structure; the cluster number is used for adjusting the cluster resolution, and the fitness function formula is as follows:
Figure BDA0002245357010000036
the modularity formula is as follows:
Figure BDA0002245357010000037
where m denotes the number of consecutive edges in the network, AijAn adjacency matrix, k, representing the networki,kjRespectively representing the values of the nodes i, j, ci,cjRepresents the community, δ (c), to which the node i, j belongsi,cj) Is the kronecker delta function.
In the step 4.3), the crossing mode is multipoint crossing, and the two segments of the same chromosome type are crossed by the cross probability
Figure BDA0002245357010000039
And controlling whether to perform the crossover operation.
In the step 4.4), mutation is carried out by mutation probability
Figure BDA0002245357010000038
And controlling that each gene position has a certain probability of mutation, and the edge corresponding to the current gene position is randomly replaced under an updating rule during mutation.
The technical conception of the invention is as follows: network community detection countermeasure enhancement is considered an optimization problem. Through excellent global search capability and robustness of a genetic algorithm, an optimal network reconnection scheme is searched on the whole network, and maximum modularity improvement and optimal community detection resolution are considered.
The invention has the beneficial effects that: the network reconnection strategy for the network community detection enhancement task based on the genetic algorithm can better optimize the network structure, so that the structural strength of the target network community is obviously improved, and the community detection algorithm can obtain better community detection effect on the optimized network.
Drawings
FIG. 1 is a flowchart of a multi-objective optimization-based network community detection countermeasure enhancement method according to the present invention.
Fig. 2 is a graph showing the enhancement effect of the present invention on two original networks and two corresponding antagonistic networks when NMI and ARI are used as evaluation indexes.
FIG. 3 is a chromosome map of the present invention.
Detailed Description
The following detailed description of embodiments of the invention is provided in connection with the accompanying drawings.
Referring to fig. 1 to 3, a network community detection countermeasure enhancement method based on multi-objective optimization, in this embodiment, an empty hand club network data set is used, and the selected community detection method is a Louvain algorithm (reference [3]: Blondel V D, Guillaume J L, Lambliotte R, et al. fast underfolding of communications in large networks [ J ]. Journal of static mechanics: the entity and experience, 2008(10): P10008. Blondel V D, Guillame J. fast evolution of communities on large networks, Journal of static mechanics: the entity and experience, 2008 (2008 ) (10): P10008.)
In this embodiment, a network community detection countermeasure enhancement method based on multi-objective optimization includes the following steps:
s1: loading a network
Figure BDA0002245357010000041
Wherein
Figure BDA0002245357010000042
Denotes the set of nodes in the network, { (0,1), (0,2), (32,33) } denotes the set of edges in the network,
Figure BDA0002245357010000043
representing a real community division of the network;
s2: carrying out community detection on the network by using the selected community detection method Louvain algorithm to obtain the community division of the original network
Figure BDA0002245357010000044
S3: and defining a candidate reconnection edge rule. For a target node vi，
Figure BDA0002245357010000045
A set of neighboring nodes that represent it,
Figure BDA0002245357010000046
represents a set of its non-neighboring nodes,
Figure BDA0002245357010000047
representing nodes v after community detectioniThe distributed communities and the candidate reconnection side rule are determined by the predicted community number and the real community number, and when the predicted community number is equal to the real community number, the intra-community addition and inter-community deletion are effective; when the number of the predicted communities is smaller than the number of the real communities, the deletion of the extra communities is effective; when in useWhen the number of the predicted communities is larger than the number of the real communities, extra adding edges among the communities are also effective, and the formula of the candidate reconnection edge rule is as follows:
Figure BDA0002245357010000048
s4: searching an optimal network reconnection scheme by using a genetic algorithm, wherein the operation steps are as follows:
4.1) population initialization: randomly generating an initial population according to a designed coding mode
Figure BDA0002245357010000049
The population size is 120;
4.2) individual selection: calculating the fitness value of each individual in the population, and screening the parental individuals by using a roulette mode, wherein the probability of each individual being selected is proportional to the fitness value:
Figure BDA0002245357010000051
4.3) intersection: according to the step 4.2), the two selected parent individuals carry out cross operation with a certain cross probability of 0.8 to form two new individuals;
4.4) mutation: carrying out mutation operation on the individuals in the population obtained in the step 4.3) according to a certain mutation probability of 0.02;
4.5) Elite preservation: replacing the worst 20% of the children with the best 20% of the parents;
4.6) termination conditions: setting an upper limit of an evolution algebra as a termination condition, judging whether iteration _ num is 1000 or not, if the condition is not met, changing a newly generated offspring population into a parent population, and repeating the steps 4.2) -4.6), otherwise, terminating the algorithm;
s5: obtaining the optimal individual from the last generation population, namely obtaining the optimal network reconnection strategy through genetic algorithm optimization, and applying the optimal network reconnection strategy to the network
Figure BDA0002245357010000052
In (1), is enhancedLatter network
Figure BDA0002245357010000053
Wherein epsilon*＝ε+εmodIs the edge set of the reconnected network. To pair
Figure BDA0002245357010000054
Community division for community detection and acquisition
Figure BDA0002245357010000055
Further, in the step 4.1), the encoding mode is shown in FIG. 1, each individual can be represented by a chromosome, and each chromosome is represented by a deletion fragment epsilondelAnd the bordered fragment εaddThe length of the edge deletion and edge addition segments respectively represents the number of the deleted and added edges and is respectively composed of two sampling rates βd,βaThe upper limit of the control quantity is specifically set to βd＝0.2,βaEach gene position represents a one-sided operation, 3.0.
In the step 4.2), the design of the fitness function comprehensively considers the modularity and the clustering number, wherein the modularity is used for measuring the community structure strength of the network clustering algorithm partition result,
Figure BDA0002245357010000056
larger values indicate greater strength of community structure; the cluster number is used for adjusting the cluster resolution, and the fitness function formula is as follows:
Figure BDA0002245357010000057
the modularity formula is as follows:
Figure BDA0002245357010000058
where m denotes the number of consecutive edges in the network, AijAn adjacency matrix, k, representing the networki,kjRespectively representing the values of the nodes i, j, ci,cjRepresents the community, δ (c), to which the node i, j belongsi,cj) Is the kronecker delta function.
In the step 4.3), the crossing mode is multipoint crossing, and whether the crossing operation is carried out between the two segments with the same chromosome type is controlled by a crossing probability of 0.8.
In the step 4.4), mutation is controlled by a mutation probability of 0.02, each gene position has a certain probability of mutation, and an edge corresponding to the current gene position is randomly replaced under an update rule during mutation.
Enhanced network obtained by the invention
Figure BDA0002245357010000061
And detecting the community structure by using a Louvain algorithm, and verifying the enhancement effect.
FIG. 2 shows parameter settings (in the same embodiment)
Figure BDA0002245357010000063
βa＝3.0、βd0.2), carrying out community structure optimization on the two original networks and the corresponding antagonistic networks to obtain the network
Figure BDA0002245357010000064
And (4) displaying two evaluation indexes of the standardized mutual information NMI and the adjusted landed coefficient ARI after the community detection. The enhanced network has a stronger community structure compared with the original network, and the community detection algorithm has a better community detection effect on the enhanced network.
The normalized mutual information NMI is used for measuring the similarity of two clustering results, and the formula is as follows:
Figure BDA0002245357010000065
Figure BDA0002245357010000066
where H (X) represents the information entropy of the predicted clustering result, and H (X | Y) represents the conditional entropy, i.e., the amount of information needed to obtain partition X given partition Y.
The invention provides a confrontation enhancement method aiming at a network community detection task based on genetic algorithm optimization and innovatively. The present invention is to be considered as illustrative and not restrictive. It will be understood by those skilled in the art that various changes, modifications and equivalents may be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (4)

1. A multi-objective optimization-based network community detection countermeasure enhancement method is characterized by comprising the following steps:
s1: loading a network
Figure FDA0002245354000000011
Wherein
Figure FDA0002245354000000012
Denotes the set of nodes in the network, ∈ { e ═ eiI 1.., m represents the set of edges in the network,
Figure FDA0002245354000000013
representing a real community division of the network;
s2: method of detecting community using selection
Figure FDA0002245354000000014
Carrying out community detection on the network to obtain the community division of the original network
Figure FDA0002245354000000015
S3: defining candidate reconnection edge rule for one target node vi，
Figure FDA0002245354000000016
A set of neighboring nodes that represent it,
Figure FDA0002245354000000017
represents a set of its non-neighboring nodes,
Figure FDA0002245354000000018
representing nodes v after community detectioniThe distributed community and candidate reconnection edge rule formula is as follows:
Figure FDA0002245354000000019
s4: searching an optimal network reconnection scheme by using a genetic algorithm, wherein the operation steps are as follows:
4.1) population initialization: randomly generating an initial population according to a designed coding mode
Figure FDA00022453540000000110
The population size is fixed;
4.2) individual selection: calculating the fitness value of each individual in the population, and screening the parental individuals by using a roulette mode, wherein the probability of each individual being selected is proportional to the fitness value:
Figure FDA00022453540000000111
4.3) intersection: according to step 4.2), the two selected parents have a certain cross probability
Figure FDA00022453540000000112
Performing cross operation to form two new individuals;
4.4) mutation: the individuals in the population obtained in the step 4.3) have a certain mutation probability
Figure FDA00022453540000000113
Carrying out mutation operation;
4.5) Elite preservation: replacing the worst 20% of the children with the best 20% of the parents;
4.6) termination conditions: judging whether the termination condition of the genetic algorithm is met or not, if not, changing the newly generated offspring population into the parent population, and repeating the steps 4.2) -4.6), otherwise, terminating the algorithm;
s5: obtaining the optimal individual from the last generation population, namely obtaining the optimal network reconnection strategy through genetic algorithm search, and applying the optimal network reconnection strategy to the network
Figure FDA0002245354000000021
In the network after enhancement
Figure FDA0002245354000000022
Wherein epsilon*＝ε+εmodIs the edge set of the reconnected network. To pair
Figure FDA0002245354000000023
Community division for community detection and acquisition
Figure FDA0002245354000000024
2. The multi-objective optimization-based network community detection countermeasure enhancement method of claim 1, wherein: in the step 3), the candidate reconnection side rule is determined by the predicted community number and the real community number, and when the predicted community number is equal to the real community number, the intra-community addition side and the inter-community deletion side take effect; when the number of the predicted communities is smaller than the number of the real communities, the deletion of the extra communities is effective; additional inter-community bordering is also effective when the number of predicted communities is greater than the number of actual communities.
3. The multi-objective optimization-based network community detection countermeasure enhancement method of claim 1 or 2, wherein: in the step 4.1), the encoding mode is as follows: each individual can be represented by a chromosome, each chromosome being represented by a truncated fragment epsilondelAnd the bordered fragment εaddTwo parts, the lengths of the edge deletion and edge addition segments are respectivelyRepresenting the number of deleted, added edges, respectively, by two sample rates βd,βaControlling the upper limit of the quantity, wherein each gene position represents a one-time side operation.
4. The multi-objective optimization-based network community detection countermeasure enhancement method of claim 3, wherein: in the step 4.2), the design of the fitness function comprehensively considers the modularity and the clustering number, wherein the modularity is used for measuring the community structure strength of the network clustering algorithm partition result,
Figure FDA0002245354000000025
larger values indicate greater strength of community structure; the cluster number is used for adjusting the cluster resolution, and the fitness function formula is as follows:
Figure FDA0002245354000000026
the modularity formula is as follows:
Figure FDA0002245354000000027
where m denotes the number of consecutive edges in the network, AijAn adjacency matrix, k, representing the networki,kjRespectively representing the values of the nodes i, j, ci,cjRepresents the community, δ (c), to which the node i, j belongsi,cj) Is the kronecker delta function.
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