CN104657442B - Multiple target community discovery method based on Local Search - Google Patents
Multiple target community discovery method based on Local Search Download PDFInfo
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Abstract
The invention discloses a kind of multiple target community discovery method based on Local Search, available for network function analysis and structures visualization, devise and increase faster Local Search direction, local neighborhood and neighborhood are defined based on network characteristicses, the time complexity of Local Search is reduced using the method for calculating target function increment size.The present invention organically combines the local search approach and traditional evolutionary search method, being capable of the multi-level community structure of significantly more efficient analysis.
Description
Technical field
The invention belongs to complex network technical field, specifically, is related to multi-level community structure in a kind of complex network
It was found that method, available for network function analysis and structures visualization.
Background technology
Community discovery method in complex network is for understanding that the function of network and the structure of visual network etc. are heavy to closing
Will.As a rule, a community is a subset of the set of all individual compositions in network, and the individual in the subset is based on certain
Attribute is completely embedded, and is connected with the individual outside subset sparse.
Found through the literature search to prior art, most of community discovery method is divided into heuristic and most
Optimization method.Heuristic is typically based on intuitively to observe and divided by performing some heuristic rules to obtain community, but
It is that this kind of method is generally deficient of accurate description to network overall situation community structure feature.Optimal method advises community discovery problem
Divide combinatorial optimization problem into, community structure is found by optimizing the object function of description certain property of community.Traditional method
Optimize single object function, the community structure for reacting single community characteristics can only be obtained.In order to portray community from multiple angles
Structure, Pizzuti et al. in 2012《IEEE Transactions on Evolutionary Computation》Upper hair
Table article " A multiobjective genetic algorithm to find communities in complex
Networks ", propose disposably to find a variety of community structures by optimizing multiple object functions.In order to optimize on network simultaneously
Two object functions, Community Score (community scores) and Community Fitness (community health degree),
Pizzuti et al. extensions devise a kind of multi-objective genetic algorithm MOGA-Net.This method since initial community structure population,
The new community populations of formation such as crossover operation, mutation operation are carried out to original population, according to two object functions in original population
With outstanding individual is selected in new population, form new sub- population and carry out follow-on evolution.Evolved through excessive wheel, in population
The community structure that community structure representated by individual will increasingly meet two object functions and define.The essence of this method is based on losing
Pass principle, there is stronger ability of searching optimum, can in community division space fast positioning to the preferable region of quality.So
And the method lacks effective local search ability, it is easy to before optimal community structure is searched, from a quality compared with
Another region is jumped in good region.Therefore, this method is unfavorable for the effective community structure for finding near-optimization.Pin of the present invention
To this problem, fast local search process is integrated in multi-target evolution community discovery method, effectively finds complex network
In multi-level community structure.
The content of the invention
It is weak in order to solve multiple target community discovery method local search ability, it can not effectively find lacking for optimal community structure
Point, calculated the invention provides multi-level community structure discovery method in a kind of complex network, and by multi-target evolution community discovery
Method and local search approach organically integrate to form a more effective accurately multi-level community structure discovery method.
In order to solve the above technical problems, embodiments of the invention provide a kind of multiple target community discovery based on Local Search
Method, comprise the following steps：
S1, the adjacency matrix A for establishing network to be analyzed, it is that all nodes of network carry out serial number, numbers since 1.
Build square matrices A；Elements A in matrixijThere is side to be connected between node corresponding to 1 representative, for node corresponding to 0 representative
Between side is not present；
S2, two object functions IntraQ and InterQ for building community discovery,
Wherein, X be network certain community division, C be community division in some community, lCRepresent inside community C
The quantity on side, m represent the total side number of network；
Wherein, kCThe total number of degrees of community's C interior joints are represented, the number of degrees of node represent the side number with node adjacency；
S3, initialization Web Community division population：
Described step S3, it is specially：
S31, division individual in community's is encoded using community's label coding method, that is, dividing individual has N number of position, and wherein N is net
Network node total number, each one node of position correspondence, the value of each opening position represent community's label of its corresponding node, had
All nodes of identical community's label belong to same community, setting Population Size SD, setting Evolution of Population iterations Gmax,
Initialize population algebraically g=0；
S32, generation SDIndividual identical community division, a part of node, Jiang Qishe are randomly selected in being divided in each community
Area's label assigns its all adjacent node, so as to be randomized each community's division, generates SDIndividual various community's division conduct
Initial population B0。
S4, global search Web Community division space and more new communities division population；
Described step S4, it is specially：
S41, non-dominant relation is defined according to two target function values of individual, an individual dominates another individual and represented
The individual, better than another individual, colony B is found out according to non-dominant relation on object functiongIn all non-dominant individuals, it is non-
Dominate a part of individual that individual represents best in colony.Define crowding distance and weigh community division individual position residing in colony
The density put, the more sparse individual more representative and diversity in present position, is more suitable for generating more preferable individual, by crowded
The S before descending selectionDIndividual non-dominant individual forms non-dominant population, replicates the non-dominant outside non-dominant population of population generation,
For retaining the excellent individual in the population；
S42, crossover operation is carried out to non-dominant population, the division of Liang Ge communities is randomly choosed from non-dominant population as friendship
The father's individual for pitching operation, randomly chooses a node, and same operation is carried out to two father's individuals：Find out institute in father's individual
Have and the node has the individual of identical community's label, and corresponding is assigned in another individual by their community's label
Body, two father's individual intersections generate two son individuals, repeat the processSecondary, all newly-generated sub- group of individuals are into cross-community
Divide population；
S43, mutation operation is carried out to cross-community division population, each division divided to cross-community in population is carried out
Variation, to each node in division, assigns its community's label to its all neighbor node with mutation probability, generates new variation
Individual, the individual of all new variations and the individual Composition Variation community division population not made a variation.
S5, Local Search community division space and more new communities division population；
Described step S5, it is specially：
S51, select the two initial kinds of outside non-dominant population and variation community division population respectively as Local Search
Group, find out the non-dominant population that all non-dominant individuals in each initial population form Local Search respectively；
S52, calculate Local Search direction vector for each non-dominant division in two non-dominant populations, the direction of search to
Measure ωPNIt is as follows for the approximate normal line vector of community division individual position in purpose-function space, calculation formula：
Wherein, π=f2(X1)-f2(X2)+f1(X2)-f1(X1),f1And f2Two target letters of community's division are represented respectively
Number, X1And X2It is the division of the X communities that two adjacent in purpose-function space, direction approximation corresponds to the ladder that object function increases
Spend direction；
S53, setting Local Search maximum iteration MI, for each non-dominant community's Definition of Division local neighborhood and neighbour
Domain, local neighborhood are defined as moving the set for community's division composition that some node is formed into its adjacent community, and neighborhood is
The union of its all local neighborhood, newly more excellent is searched for using network structure in the local neighborhood of each community division and neighborhood
Elegant community's division replaces original community to divide, and concrete operations form division phase to calculate some node motion to neighbours community
For the increment of the object function caused by former division in the direction of search, the maximum neighbours of increment are selected to draw in local neighborhood
Divide and replace original division, the process is repeated to each node, community's division optimal in neighborhood is found, in two non-dominant kinds
The process is repeated on group MI times, forms two sub- populations of Local Search.
Two S6, combination sub- populations of Local Search, generate population B of future generationg, population algebraically g=g+1 is set, if g ＜
Gmax, then return to step S4, otherwise carries out step S7；
S7, find out final community's division population BgIn all non-dominant communities divisions, calculate each non-dominant community
The community's number and modularity of division, multi-level community's partition structure is analyzed according to community's number and modularity.
Described step S7, it is specially：Find out final community's division population BgIn all non-dominant communities divisions, meter
The community's number and modularity Q of each non-dominant community's division are calculated, modularity Q calculation formula is as follows：
Wherein, lCRepresent the quantity on the side inside community C；kCRepresent the total number of degrees of community's C interior joints；M represents that network is total
Side number.Module angle value is bigger, represents that community's intensity of division is bigger, is divided in population and selected from community according to community's number and modularity
Select and analyze multi-level community's partition structure.
The invention has the advantages that：
Local search approach is incorporated in traditional multi-target evolution community algorithm, the part for enhancing community space is searched
Suo Nengli, population is set to converge to significant multi-level community structure faster；The local search approach used is each individual
The suitable direction of search is set and defines local domain and field, and local searching strategy of the use based on network structure, with showing
Local search approach in some evolution communities algorithm is compared, and population can converge to faster stablizes outstanding community structure.
Brief description of the drawings
Fig. 1 is the direction of search schematic diagram for the Local Search that the present invention designs.
Fig. 2 is the performance comparison figure when present invention integrates Local Search and unconformity Local Search.
Fig. 3 is the performance comparison figure between of the invention and multiple existing methods.
Fig. 4 is the schematic diagram of the present invention one real network of analysis.
Embodiment
To make the technical problem to be solved in the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and tool
Body embodiment is described in detail.
The embodiments of the invention provide a kind of multiple target community discovery method based on Local Search, comprise the following steps：
Step 1, the adjacency matrix of network to be analyzed is established.Serial number is carried out for all nodes of network, numbers and is opened from 1
Begin.Build square matrices A, its elements AijFor 1 expression node i and node j between undirected side be present, for 0 represent node it
Between side is not present.
Step 2, two object functions IntraQ and InterQ of community discovery are built, for calculating community's division population
Target function value.Object function IntraQ is：
Wherein, X be network certain community division, C be community division in some community, lCRepresent inside community C
The quantity on side, m represent the total side number of network.The object function calculates all community's internal edges in community's division and accounts for all sides of network
Ratio.The value is bigger, represents that the connection of community's internal edges is closer.
Object function InterQ is：
Wherein, kCThe total number of degrees of community's C interior joints are represented, the number of degrees of node represent the side number with node adjacency；The target
Function calculates 1 and subtracts the quadratic sum that community's internal node number of degrees in community's division account for the total number of degrees ratio of network.The value is bigger, represents
Connected between community more sparse.
Step 3, Web Community division population is initialized.Using community's label coding method coding community's division individual, that is, draw
Individual is divided to have N number of position, wherein N is that network node is total, and each one node of position correspondence, the value of each opening position represents
Community's label of its corresponding node, all nodes with identical community's label belong to same community.Set Population Size SD,
Set Evolution of Population iterations Gmax, initialization population algebraically g=0.
Generate SDIndividual identical community division, randomly selects a part of node in being divided in each community, its community is marked
Label assign its all adjacent node, so as to be randomized each community's division, generate SDIndividual various community's division is as initial
Population B0。
Step 4, global search Web Community division space and more new communities division population.According to two target letters of individual
Numerical value defines non-dominant relation, an individual dominate another individual represent the individual be better than on object function it is another each and every one
Body.Colony B is found out according to non-dominant relationgIn all non-dominant individuals, non-dominant individual represents a best part in colony
Individual.Define the density that crowding distance weighs community division individual present position in colony, the more sparse individual in present position
More representative and diversity, it is more suitable for generating more preferable individual, S before choosing by crowding distance descendingDIndividual non-dominant individual
Form non-dominant population.The non-dominant outside non-dominant population of population generation is replicated, for retaining the excellent individual in the population.
Crossover operation is carried out to non-dominant population, the division of Liang Ge communities is randomly choosed from non-dominant population as intersection behaviour
Father's individual of work, randomly chooses a node, and same operation is carried out to two father's individuals：Find out in father's individual it is all and
The node has the individual of identical community's label, and assigns their community's label to corresponding individual in another individual.Two
Individual father's individual intersection generates two son individuals, repeats the processSecondary, all newly-generated sub- group of individuals divide into cross-community
Population.
Mutation operation is carried out to cross-community division population, dividing each division in population to cross-community becomes
It is different, to each node in division, its community's label is assigned to its all neighbor node with mutation probability, generates new variation
Body.The individual of all new variations and the individual Composition Variation community division population not made a variation.
Step 5, Local Search community division space and more new communities division population.The outside non-dominant population of selection and variation
Community divides two initial populations of the population respectively as Local Search, finds out all non-dominant individuals point in each initial population
Not Xing Cheng Local Search non-dominant population.Local Search direction is calculated for each non-dominant division in two non-dominant populations
Vector, as shown in figure 1, search direction vector ωPNFor the approximation method of community division individual position in purpose-function space
Line vector, calculation formula are as follows：
Wherein, π=f2(X1)-f2(X2)+f1(X2)-f1(X1),f1And f2Two target letters of community's division are represented respectively
Number.The gradient direction that the approximate corresponding object function of the direction increases.
Local Search maximum iteration MI is set, for each non-dominant community's Definition of Division local neighborhood and neighborhood, office
Portion's neighborhood definition is the set for community's division composition that some mobile node is formed into its adjacent community, and neighborhood is that it is all
The union of local neighborhood.The more excellent society that network structure search is new is utilized in the local neighborhood of each community division and neighborhood
Division replaces original community to divide, and concrete operations form division relative to original to calculate some node motion to neighbours community
The increment of object function caused by division in the direction of search, select the maximum neighbours of increment to divide in local neighborhood and replace
Division originally, the process is repeated to each node, find community's division optimal in neighborhood.The weight on two non-dominant populations
Process MI times again, form two sub- populations of Local Search.
Step 6, two sub- populations of Local Search are combined, generate population B of future generationg, population algebraically g=g+1 is set, if
G ＜ Gmax, then return to step 4, otherwise carry out step 7；
Step 7, final community's division population B is found outgIn all non-dominant communities divisions, calculate each non-dominant society
The community's number and modularity Q of Division, modularity Q calculation formula are as follows：
Wherein, lCRepresent the quantity on the side inside community C；kCRepresent the total number of degrees of community's C interior joints；M represents that network is total
Side number.Module angle value is bigger, represents that community's intensity of division is bigger.Divided in population and selected from community according to community's number and modularity
Select and analyze multi-level community's partition structure.
Effectiveness of the invention can be further illustrated by following emulation experiment.It should be noted that in experiment
The parameter of application does not influence the generality of the present invention.
1) simulated conditions：
CPU IntelDual-Core 2.80GHz, RAM 3.00GB, operating system Windows 7, emulation
Software Matlab2010.
2) emulation content：
Manually generated network and real world network is chosen respectively to be tested.Manually generated Web vector graphic Girvan and
Newman in 2002《Proceedings of the National Academy of Sciences of the
United States of America》On " the Community structure in social and that deliver
The GN baseline networks proposed in biological networks ".Web vector graphic hybrid parameter μ adjusts the fog-level of network,
μ values are bigger, and community structure is more difficult to be found well.In order to weigh the performance of invention, two performance indications, standard are used
Mutual information (NMI) and modularity (Q).NMI values are closer to 1, and the community structure that illustration method is found is closer to real community
Structure, Q value is bigger, and the community structure for illustrating to find more meets the definition of community, i.e. community's internal node connects dense, community
Between connect it is sparse.
The present invention is represented in emulation experiment with MMCD.In order to verify the Local Search of the invention integrated to community discovery
The influence of energy, designs a variant MOA of the invention, and the variant eliminates the local search procedure in the present invention.First in GN
Tested on baseline network, parameter setting of the invention is as follows, Population Size 100, and Local Search iterations is 1, is become
Different probability is 0.01.In order to verify that the present invention can more effectively have found outstanding community structure, run not on GN baseline networks
The MMCD and MOA of group algebra of the same race, experimental result as shown in Fig. 2 the present invention it is average only need twice iteration just can obtain truly
Community's division, and variant MOA is not obtaining the division of real community yet after 80 iteration, and the performance of the present invention is more
Add stabilization.The emulation experiment demonstrates validity of the Local Search of the invention integrated for method performance boost.
The present invention is further subjected to simulation comparison with 8 other community discovery methods on GN networks.This eight sides
Method is as follows, Clauset et al. in 2004《Physical Review E》On " the Finding community that deliver
The CNM methods, Vincent et al. proposed in structure in very large networks " in 2008
《Journal of Statistical Mechanics》On " the Fast unfolding of communities in that deliver
The Louvian methods proposed in large networks ", Rosvall and Bergstrom in 2008《Proceedings
of the National Academy of Sciences of the United States of America》On deliver
" proposed in Maps of random walks on complex networks reveal community structure "
Infomap methods, Pizzuti was in " the GA-Net delivered in 2008:A genetic algorithm for community
The GA-Net methods proposed in detection in social networks ", Pizzuti is in 2012 in article " A
Carried in multiobjective genetic algorithm to find communities in complex networks "
The MOGA-Net methods, Gong et al. gone out are in 2011 in article " Memetic algorithm for community
The Meme-Net methods proposed in detection in networks ", of the invention two changing methods MOA and LSA, wherein
LSA is the method that Local Search part of the present invention is formed.
For the simulation experiment result as shown in figure 3, when hybrid parameter is less than 0.05, all methods can find real society
Plot structure, with the increase of hybrid parameter value, GA-Net, MOGA-Net and MOA hydraulic performance decline.When hybrid parameter is more than 0.25
During less than 0.4, only Infomap, Louvain and MMCD can be found that real community structure.Enter one with hybrid parameter
Step increase, all methods can not all find real community structure, but from NMI values and Q values as can be seen that the present invention is than other
All methods all have better performance.
Finally, the present invention is being verified known to one on the real world network of true community structure.The network is magazine net,
Include 40 kinds of magazines.These magazines derive from 4 different fields, i.e. physics, chemistry, and biology and ecology, each field has
10 magazines.If at least an article quotes the article of another magazine in a kind of magazine, then deposited between both magazines
On side.The result of the present invention is run on that network as shown in figure 4, wherein (a) represents final division colony in two target letters
Value figure on number, 3 representational community's divisions are chosen on the value figure and are visualized, visualization result is figure
(b), (c), (d).Visualize in figure, circular, square, rhombus and triangle represent physics respectively, chemistry, biological and ecological
Magazine.Different gray scale depth represents the community structure that the present invention marks off in each figure.It can be found that in Fig. 4 (b), this hair
It is bright successfully to find real community structure.In Fig. 4 (c), present invention discover that three communities, wherein by real physical magazine and
The Chemicals is divided into a community.In Fig. 4 (d), present invention discover that Liang Ge communities, wherein by real physical magazine and change
Learn magazine and be divided into a community, real biological magazine and ecological magazine are divided into a community.According to general knowledge, physics and
Chemical generally contact is close, and biology and ecological generally contact are close, therefore present invention discover that several community structures be all
Significant.
The specific embodiment of the present invention is described above.It is to be appreciated that the invention is not limited in above-mentioned
Particular implementation, those skilled in the art can make various deformations or amendments within the scope of the claims, this not shadow
Ring the substantive content of the present invention.
Claims (5)
1. a kind of multiple target community discovery method based on Local Search, it is characterised in that comprise the following steps：
S1, the adjacency matrix A for establishing network to be analyzed, it is that all nodes of network carry out serial number, numbers since 1, build
Square matrices A；
S2, two object functions IntraQ and InterQ for building community discovery,
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Wherein, X be network certain community division, C be community division in some community, lCRepresent the number on the side inside community C
Amount, m represent the total side number of network；
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Wherein, kCThe total number of degrees of community's C interior joints are represented, the number of degrees of node represent the side number with node adjacency；M represents that network is total
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S3, initialization Web Community division population；
S4, global search Web Community division space and more new communities division population；
S5, Local Search community division space and more new communities division population；
Two S6, combination sub- populations of Local Search, generate population B of future generationg, population algebraically g=g+1 is set, if g ＜ Gmax,
Wherein, GmaxFor Evolution of Population iterations, then return to step S4, otherwise carries out step S7；
S7, find out final community's division population BgIn all non-dominant communities divisions, calculate each non-dominant community's division
Community's number and modularity, multi-level community's partition structure is analyzed according to community's number and modularity.
2. the multiple target community discovery method according to claim 1 based on Local Search, it is characterised in that described step
Rapid S3, it is specially：
S31, division individual in community's is encoded using community's label coding method, that is, dividing individual has N number of position, and wherein N is network section
Point sum, each one node of position correspondence, the value of each opening position represent community's label of its corresponding node, have identical
All nodes of community's label belong to same community, setting Population Size SD, setting Evolution of Population iterations Gmax, initially
Change population algebraically g=0；
S32, generation SDIndividual identical community division, randomly selects a part of node, by its community's label in being divided in each community
Its all adjacent node is assigned, so as to be randomized each community's division, generates SDIndividual various community's division is as initial kind
Group B0。
3. the multiple target community discovery method according to claim 1 based on Local Search, it is characterised in that described step
Rapid S4, it is specially：
S41, colony B found out according to non-dominant relationgIn all non-dominant individuals, by crowding distance descending choose before SDIndividual non-branch
Non-dominant population is formed with individual, replicates the non-dominant outside non-dominant population of population generation, it is outstanding in the population for retaining
Individual；
S42, crossover operation is carried out to non-dominant population, the division of Liang Ge communities is randomly choosed from non-dominant population as intersection behaviour
Father's individual of work, randomly chooses a node, and same operation is carried out to two father's individuals：Find out in father's individual it is all and
The node has an individual of identical community's label, and assigns their community's label to corresponding individual in another individual, and two
Individual father's individual intersection generates two son individuals, repeats the processSecondary, all newly-generated sub- group of individuals divide into cross-community
Population；
S43, mutation operation is carried out to cross-community division population, dividing each division in population to cross-community becomes
It is different, to each node in division, its community's label is assigned to its all neighbor node with mutation probability, generates new variation
Body, the individual of all new variations and the individual Composition Variation community division population not made a variation.
4. the multiple target community discovery method according to claim 1 based on Local Search, it is characterised in that described step
Rapid S5, it is specially：
S51, the outside non-dominant population of selection and variation community divide population respectively as two initial populations of Local Search, look for
Go out the non-dominant population that all non-dominant individuals in each initial population form Local Search respectively；
S52, calculate Local Search direction vector for each non-dominant community's division in two non-dominant populations, the direction of search to
Measure ωPNIt is as follows for the approximate normal line vector of community division individual position in purpose-function space, calculation formula：
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Wherein, π=f2(X1)-f2(X2)+f1(X2)-f1(X1),f1And f2Two object functions of community's division, X are represented respectively1With
X2It is the division of the X communities that two adjacent in purpose-function space, direction approximation corresponds to the gradient direction that object function increases；
S53, setting Local Search maximum iteration MI, for each non-dominant community's Definition of Division local neighborhood and neighborhood,
The more excellent community's division for utilizing network structure search new in the local neighborhood and neighborhood of each community's division replaces originally
Community divides, and the process is repeated on two non-dominant populations MI times, forms two sub- populations of Local Search.
5. the multiple target community discovery method according to claim 1 based on Local Search, it is characterized in that, described step
S7, it is specially：Find out final community's division population BgIn all non-dominant communities divisions, calculate each non-dominant community and draw
The community's number and modularity Q, calculation formula divided is as follows：
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<mo>(</mo>
<mfrac>
<msub>
<mi>k</mi>
<mi>C</mi>
</msub>
<mrow>
<mn>2</mn>
<mi>m</mi>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
</mrow>
Wherein, lCRepresent the quantity on the side inside community C；kCRepresent the total number of degrees of community's C interior joints；M represents the total side of network
Number.
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