CN104657442A - Multi-target community discovering method based on local searching - Google Patents

Abstract

The invention discloses a multi-target community discovering method based on local searching. The method can be used for network function analysis and structure visualization, a local searching direction with faster increase speed is designed, the local neighborhood and the neighborhood are defined on the basis of network features, and the time complexity of the local searching is reduced by adopting a calculation target function increment value method. The local searching method and the traditional evolution searching method are organically combined, and a multilayer community structure can be more effectively analyzed.

Description

Based on the multiple goal community discovery method of Local Search

Technical field

The invention belongs to complex network technical field, specifically, relate to multi-level community structure discovery method in a kind of complex network, can be used for network function analysis and structures visualization.

Background technology

Community discovery method in complex network is most important for the structure etc. of the function and visual network of understanding network.As a rule, a community is a subset of the set of all individuality compositions in network, and the individuality in this subset connects closely based on certain attribute, and is connected sparse with the individuality outside subset.

Through finding the literature search of prior art, most of community discovery method can be divided into heuristic and optimization method.Heuristic obtains community's division based on observing intuitively by performing some heuristic rules usually, but these class methods lack the accurate description to network overall situation community structure feature usually.Community discovery problem is planned to combinatorial optimization problem by optimization method, finds community structure by optimizing the objective function describing certain character of community.Traditional method optimizes single objective function, can only obtain the community structure of reacting single community characteristics.In order to portray community structure from multiple angle, the people such as Pizzuti published an article on " IEEE Transactions on EvolutionaryComputation " in 2012 " A multiobjective genetic algorithm to find communitiesin complex networks ", proposed to carry out the multiple community structure of disposable discovery by optimizing multiple objective function.In order to while optimized network on two objective functions, the people such as Community Score (community scores) and Community Fitness (community health degree), Pizzuti expansion devises a kind of multi-objective genetic algorithm MOGA-Net.The method is from initial community structure population, interlace operation, mutation operation etc. are carried out to original population and forms new community population, in original population and new population, select outstanding individuality according to two objective functions, form new sub-population and carry out follow-on evolution.Through too much taking turns evolution, the community structure representated by the individuality in population will more and more meet the community structure of two objective function definition.The essence of the method, based on genetic principle, has stronger ability of searching optimum, can in community's defined basis quick position to the good region of quality.But the method lacks effective local search ability, be easy to, before searching optimum community structure, jump to another region from a good region of quality.Therefore, the method is unfavorable for the community structure effectively finding near-optimization.The present invention is directed to this problem, in multi-target evolution community discovery method, integrate fast local search process, community structure multi-level in effective discovery complex network.

Summary of the invention

Weak in order to solve multiple goal community discovery method local search ability, effectively cannot find the shortcoming of optimum community structure, the invention provides multi-level community structure discovery method in a kind of complex network, and multi-target evolution community discovery algorithm and local search approach are organically integrated formation one multi-level community structure discovery method more effectively accurately.

For solving the problems of the technologies described above, embodiments of the invention provide a kind of multiple goal community discovery method based on Local Search, comprise the steps:

S1, set up the adjacency matrix A of network to be analyzed, for all nodes of network carry out serial number, number from 1.Build square matrices A; Elements A in matrix _ijbe 1 representative correspondence node between have limit to be connected, be 0 representative correspondence node between there is not limit;

Two objective function IntraQ and InterQ of S2, structure community discovery,

$\mathrm{IntraQ}={\mathrm{\Σ}}_{C\∈X}\frac{l_C}{m},$

Wherein, X is that certain community of network divides, and C is certain community during community divides, l _crepresent the quantity on the limit of C inside, community, m represents the limit number that network is total;

$\mathrm{InterQ}=1-{\mathrm{\Σ}}_{C\∈X}{\left(\frac{k_C}{2m}\right)}^2,$

Wherein, k _crepresent the number of degrees that C interior joint in community is total, the number of degrees of node represent the limit number with node adjacency;

S3, initialization Web Community divide population:

Described step S3, is specially:

S31, label coding method coding community of employing community divide individual, namely divide individuality and have N number of position, wherein N is network node sum, the corresponding node in each position, the value of each position represents community's label of its corresponding node, all nodes with identical community label belong to same community, setting Population Size S _d, setting Evolution of Population iterations G _max, initialization population algebraically g=0;

S32, generation S _dindividual identical community divides, and in each community divides, random selecting part node, gives its all adjacent node by its community's label, thus each community of randomization divides, and generates S _dindividual various community divides as initial population B ₀.

S4, global search Web Community defined basis and more new communities divide population;

Described step S4, is specially:

S41, two target function values definition non-dominant relations according to individuality, body is arranged another and is individually represented that this individuality is better than on objective function that another is individual, finds out colony B according to non-dominant relation one by one _gin all non-dominant individual, non-dominant individuality represents that a part best in colony is individual.Definition crowding distance weighs the density that community divides individual present position in colony, and the more representative and diversity of the more sparse individuality in present position, is more suitable for generating better individuality, chooses front S by crowding distance descending _dindividual non-dominant individuality composition non-dominant population, copies non-dominant population and generates outside non-dominant population, for retaining the excellent individual in this population;

S42, interlace operation is carried out to non-dominant population, the father that Stochastic choice Liang Ge community divides as interlace operation from non-dominant population is individual, Stochastic choice node, same operation is carried out to two fathers individuality: find out the individuality that all in father's individuality and this node has identical community label, and their community's label is given individuality corresponding in another individuality, two father's individuality intersection generation two are individual, repeat this process secondary, all newly-generated sub-group of individuals become cross-community to divide population;

S43, to cross-community divide population carry out mutation operation, each division that cross-community divides in population is made a variation, to each node in division, its all neighbor node is given by its community's label with mutation probability, generate new variation individual, the individuality of all new variations and the individual Composition Variation community division population do not made a variation.

S5, Local Search community defined basis and more new communities divide population;

Described step S5, is specially:

S51, select outside non-dominant population and variation community to divide population respectively as two initial population of Local Search, find out all non-dominant individualities in each initial population and form the non-dominant population of Local Search respectively;

S52, be that each non-dominant in two non-dominant populations divides and calculates Local Search direction vector, search direction vector ω ^pNfor community divides the approximate normal line vector of individual position in purpose-function space, computing formula is as follows:

${\mathrm{\ω}}^{\mathrm{PN}}\left(X\right)=(\frac{f_2\left(X^1\right)-f_2\left(X^2\right)}{\mathrm{\π}},\frac{f_1\left(X^2\right)-f_1\left(X^1\right)}{\mathrm{\π}})$

Wherein, π=f ₂(X ¹)-f ₂(X ²)+f ₁(X ²)-f ₁(X ¹), f ₁and f ₂represent two objective functions that community divides respectively, X ¹and X ²be that X two adjacent communities in purpose-function space divide, this direction is similar to the gradient direction that corresponding objective function increases;

S53, setting Local Search maximum iteration time MI, for each non-dominant community Definition of Division local neighborhood and neighborhood, local neighborhood is defined as the set that the community formed in certain node mobile to its adjacent community divides composition, neighborhood is the union of its all local neighborhood, utilize network structure to search for new more outstanding community in the local neighborhood divided in each community and neighborhood to divide and replace original community to divide, the increment of the objective function in the direction of search that concrete operations divide bring relative to former division for certain node motion of calculating is formed to neighbours community, in local neighborhood, select the maximum neighbours of increment to divide replace original division, this process is repeated to each node, community optimum in neighborhood is found to divide, two non-dominant populations repeat this process MI time, form two sub-populations of Local Search.

S6, combination two sub-populations of Local Search, generate population B of future generation _g, population algebraically g=g+1 is set, if g < is G _max, then return step S4, otherwise carry out step S7;

S7, find out final community and divide population B _gin all non-dominant communities divide, calculate community's number and modularity that each non-dominant community divides, according to community's number and the multi-level community's partition structure of modularity analysis.

Described step S7, is specially: find out final community and divide population B _gin all non-dominant communities divide, the computing formula calculating community's number that each non-dominant community divides and modularity Q, modularity Q is as follows:

$Q={\mathrm{\&Sigma;}}_{C\&Element;X}[\frac{l_C}{m}-{\left(\frac{k_C}{2m}\right)}^2]$

Wherein, l _crepresent the quantity on the limit of C inside, community; k _crepresent the number of degrees that C interior joint in community is total; M represents the limit number that network is total.Module angle value is larger, represents that the community's intensity divided is larger, selects according to community's number and modularity and analyzes multi-level community's partition structure from community's division population.

The present invention has following beneficial effect:

In traditional multi-target evolution community algorithm, incorporate local search approach, enhance the local search ability of community space, make population converge to significant multi-level community structure faster; The local search approach adopted is that each individuality arranges the suitable direction of search and defines local domain and field, and adopt the local searching strategy of structure Network Based, compared with the local search approach in existing evolution community algorithm, population can converge to faster stablizes outstanding community structure.

Accompanying drawing explanation

The direction of search schematic diagram of the Local Search that Fig. 1 designs for the present invention.

Fig. 2 is the performance comparison figure of the present invention when integrating Local Search and unconformability Local Search.

Fig. 3 is the performance comparison figure between the present invention and multiple existing method.

Fig. 4 is the schematic diagram that the present invention analyzes a real network.

Embodiment

For making the technical problem to be solved in the present invention, technical scheme and advantage clearly, be described in detail below in conjunction with the accompanying drawings and the specific embodiments.

Embodiments provide a kind of multiple goal community discovery method based on Local Search, comprise the steps:

Step 1, sets up the adjacency matrix of network to be analyzed.For all nodes of network carry out serial number, number from 1.Build square matrices A, its elements A _ijbeing there is undirected limit between 1 expression node i and node j, is there is not limit between 0 expression node.

Step 2, builds two objective function IntraQ and InterQ of community discovery, divides the target function value of population for calculating community.Objective function IntraQ is:

$\mathrm{IntraQ}={\mathrm{\&Sigma;}}_{C\&Element;X}\frac{l_C}{m},$

Wherein, X is that certain community of network divides, and C is certain community during community divides, l _crepresent the quantity on the limit of C inside, community, m represents the limit number that network is total.This objective function calculates all communities internal edges in community's division and accounts for the ratio on all limits of network.This value is larger, represents that the connection of community's internal edges is tightr.

Objective function InterQ is:

$\mathrm{InterQ}=1-{\mathrm{\&Sigma;}}_{C\&Element;X}{\left(\frac{k_C}{2m}\right)}^2,$

Wherein, k _crepresent the number of degrees that C interior joint in community is total, the number of degrees of node represent the limit number with node adjacency; This objective function calculating 1 deducts community's internal node number of degrees in community's division and accounts for the quadratic sum of the total number of degrees ratio of network.This value is larger, connects more sparse between expression community.

Step 3, initialization Web Community divides population.Label coding method coding community of community is adopted to divide individual, namely divide individuality and have N number of position, wherein N is network node sum, the corresponding node in each position, the value of each position represents community's label of its corresponding node, and all nodes with identical community label belong to same community.Setting Population Size S _d, setting Evolution of Population iterations G _max, initialization population algebraically g=0.

Generate S _dindividual identical community divides, and in each community divides, random selecting part node, gives its all adjacent node by its community's label, thus each community of randomization divides, and generates S _dindividual various community divides as initial population B ₀.

Step 4, global search Web Community defined basis and more new communities divide population.According to two target function values definition non-dominant relations of individuality, body is arranged another and is individually represented that this individuality is better than on objective function that another is individual one by one.Colony B is found out according to non-dominant relation _gin all non-dominant individual, non-dominant individuality represents that a part best in colony is individual.Definition crowding distance weighs the density that community divides individual present position in colony, and the more representative and diversity of the more sparse individuality in present position, is more suitable for generating better individuality, chooses front S by crowding distance descending _dindividual non-dominant individuality composition non-dominant population.Copy non-dominant population and generate outside non-dominant population, for retaining the excellent individual in this population.

Interlace operation is carried out to non-dominant population, the father that Stochastic choice Liang Ge community divides as interlace operation from non-dominant population is individual, Stochastic choice node, same operation is carried out to two fathers individuality: find out the individuality that all in father's individuality and this node has identical community label, and their community's label is given individuality corresponding in another individuality.Two father's individuality intersection generation two are individual, repeat this process secondary, all newly-generated sub-group of individuals become cross-community to divide population.

Population is divided to cross-community and carries out mutation operation, each division that cross-community divides in population is made a variation, to each node in division, give its all neighbor node with mutation probability by its community's label, generate new variation individual.The individuality of all new variations and the individual Composition Variation community do not made a variation divide population.

Step 5, Local Search community defined basis and more new communities divide population.Select outside non-dominant population and variation community to divide two initial population of population respectively as Local Search, find out all non-dominant individualities in each initial population and form the non-dominant population of Local Search respectively.Be each non-dominant division calculating Local Search direction vector in two non-dominant populations, as shown in Figure 1, search direction vector ω ^pNfor community divides the approximate normal line vector of individual position in purpose-function space, computing formula is as follows:

${\mathrm{\&omega;}}^{\mathrm{PN}}\left(X\right)=(\frac{f_2\left(X^1\right)-f_2\left(X^2\right)}{\mathrm{\&pi;}},\frac{f_1\left(X^2\right)-f_1\left(X^1\right)}{\mathrm{\&pi;}})$

Wherein, π=f ₂(X ¹)-f ₂(X ²)+f ₁(X ²)-f ₁(X ¹), f ₁and f ₂represent two objective functions that community divides respectively.This direction is similar to the gradient direction that corresponding objective function increases.

Setting Local Search maximum iteration time MI, for each non-dominant community Definition of Division local neighborhood and neighborhood, local neighborhood is defined as the set that the community formed in certain node mobile to its adjacent community divides composition, and neighborhood is the union of its all local neighborhood.Utilize network structure to search for new more outstanding community in the local neighborhood divided in each community and neighborhood to divide and replace original community to divide, the increment of the objective function in the direction of search that concrete operations divide bring relative to former division for certain node motion of calculating is formed to neighbours community, in local neighborhood, select the maximum neighbours of increment to divide replace original division, this process is repeated to each node, finds community optimum in neighborhood to divide.Two non-dominant populations repeat this process MI time, forms two sub-populations of Local Search.

Step 6, combines two sub-populations of Local Search, generates population B of future generation _g, population algebraically g=g+1 is set, if g < is G _max, then return step 4, otherwise carry out step 7;

Step 7, finds out final community and divides population B _gin all non-dominant communities divide, the computing formula calculating community's number that each non-dominant community divides and modularity Q, modularity Q is as follows:

$Q={\mathrm{\&Sigma;}}_{C\&Element;X}[\frac{l_C}{m}-{\left(\frac{k_C}{2m}\right)}^2]$

Wherein, l _crepresent the quantity on the limit of C inside, community; k _crepresent the number of degrees that C interior joint in community is total; M represents the limit number that network is total.Module angle value is larger, represents that the community's intensity divided is larger.Select from community's division population according to community's number and modularity and analyze multi-level community's partition structure.

Validity of the present invention can be further illustrated by emulation experiment below.It should be noted that, the parameter applied in experiment does not affect generality of the present invention.

1) simulated conditions:

CPU Intel dual-Core 2.80GHz, RAM 3.00GB, operating system Windows 7, software Matlab 2010.

2) content is emulated:

Choose artificial generating network respectively and real world network is tested.The GN baseline network proposed in " Community structure in social and biologicalnetworks " that artificial generating network uses Girvan and Newman to deliver on " Proceedings of the National Academy of Sciences of the UnitedStates of America " in 2002.This Web vector graphic hybrid parameter μ adjusts the fog-level of network, and μ value is larger, and community structure is more difficult well to be found.In order to weigh the performance of invention, use two performance index, standard mutual information (NMI) and modularity (Q).NMI value is more close to 1, and the community structure that illustration method finds is close to real community structure, and the value of Q is larger, and illustrate that the community structure found more meets the definition of community, namely community's internal node connects dense, connects sparse between community.

The present invention represents with MMCD in emulation experiment.In order to verify that Local Search that the present invention integrates is on the impact of community discovery performance, design a variant MOA of the present invention, this variant eliminates the local search procedure in the present invention.First test on GN baseline network, optimum configurations of the present invention is as follows, and Population Size is 100, and Local Search iterations is 1, and mutation probability is 0.01.In order to verify the community structure that the more effective discovery of the present invention's energy is outstanding, GN baseline network runs MMCD and MOA of different population algebraically, experimental result as shown in Figure 2, the present invention on average only needs twice iteration just can obtain the division of real community, and variant MOA is not obtaining the division of real community yet after 80 iteration, and performance of the present invention is more stable.The Local Search that the present invention of this Simulation experiments validate integrates is for the validity of method performance boost.

Further other community discovery method of the present invention and 8 is carried out simulation comparison on GN network.These eight methods are as follows, the CNM method proposed in " Finding communitystructure in very large networks " that the people such as Clauset delivered on " Physical Review E " in 2004, the Louvian method proposed in " Fast unfolding of communities inlarge networks " that the people such as Vincent delivered on " Journal of Statistical Mechanics " in 2008, the Infomap method proposed in " Maps of random walks on complex networks reveal communitystructure " that Rosvall and Bergstrom delivered on " Proceedings of the National Academy of Sciences of the United States ofAmerica " in 2008, the GA-Net method proposed in " GA-Net:A geneticalgorithm for community detection in social networks " that Pizzuti delivered in 2008, the MOGA-Net method that Pizzuti proposed in article " A multiobjective genetic algorithm to find communitiesin complex networks " in 2012, the Meme-Net method that the people such as Gong proposed in article " Memeticalgorithm for community detection in networks " in 2011, two changing method MOA and LSA of the present invention, wherein LSA is the method that Local Search part of the present invention is formed.

As shown in Figure 3, when hybrid parameter is less than 0.05, all methods can find real community structure to the simulation experiment result, along with the increase of hybrid parameter value, and the hydraulic performance decline of GA-Net, MOGA-Net and MOA.When hybrid parameter be greater than 0.25 be less than 0.4 time, only have Infomap, Louvain and MMCD can find real community structure.Along with the further increase of hybrid parameter, all methods all cannot find real community structure, but as can be seen from NMI value and Q value, the present invention's method more all than other all has better performance.

Finally, the real world network of a known true community structure verifies the present invention.This network is magazine net, comprises 40 kinds of magazines.These magazines derive from 4 different fields, i.e. physics, and chemistry, biological and ecological, there are 10 magazines in each field.If have at least one section of article to quote an article for another kind of magazine in magazine, then there is limit between these two kinds of magazines.Run result of the present invention on that network as shown in Figure 4, wherein (a) represents the final division value figure of colony on two objective functions, this value figure chooses 3 representational communities divisions to carry out visual, visualization result is figure (b), (c), (d).In visual figure, circular, square, rhombus and triangle represent physics respectively, chemistry, biological and ecological magazine.The gray scale degree of depth different in each figure represents the community structure that the present invention marks off.Can find in Fig. 4 (b), the present invention successfully finds real community structure.In Fig. 4 (c), the present invention finds three communities, wherein real physical magazine and The Chemicals is divided into a community.In Fig. 4 (d), the present invention finds Liang Ge community, wherein real physical magazine and The Chemicals is divided into a community, and real biological magazine and ecological magazine are divided into a community.According to general knowledge, physics and chemistry contacts closely usually, and biology and ecology contact closely usually, and several community structures that therefore the present invention finds are all significant.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (5)

1., based on a multiple goal community discovery method for Local Search, it is characterized in that, comprise the steps:

S1, set up the adjacency matrix A of network to be analyzed, for all nodes of network carry out serial number, number from 1, build square matrices A;

Two objective function IntraQ and InterQ of S2, structure community discovery,

$\mathrm{IntraQ}={\mathrm{\&Sigma;}}_{C\&Element;X}\frac{l_C}{m},$

Wherein, X is that certain community of network divides, and C is certain community during community divides, l _crepresent the quantity on the limit of C inside, community, m represents the limit number that network is total;

$\mathrm{InterQ}=1-{\mathrm{\&Sigma;}}_{C\&Element;X}{\left(\frac{k_C}{2m}\right)}^2,$

Wherein, k _crepresent the number of degrees that C interior joint in community is total, the number of degrees of node represent the limit number with node adjacency;

S3, initialization Web Community divide population;

S4, global search Web Community defined basis and more new communities divide population;

S5, Local Search community defined basis and more new communities divide population;

S6, combination two sub-populations of Local Search, generate population B of future generation _g, population algebraically g=g+1 is set, if g < is G _max, then return step S4, otherwise carry out step S7;

S7, find out final community and divide population B _gin all non-dominant communities divide, calculate community's number and modularity that each non-dominant community divides, according to community's number and the multi-level community's partition structure of modularity analysis.

2. the multiple goal community discovery method based on Local Search according to claim 1, it is characterized in that, described step S3, is specially:

S31, label coding method coding community of employing community divide individual, namely divide individuality and have N number of position, wherein N is network node sum, the corresponding node in each position, the value of each position represents community's label of its corresponding node, all nodes with identical community label belong to same community, setting Population Size S _d, setting Evolution of Population iterations G _max, initialization population algebraically g=0;

S32, generation S _dindividual identical community divides, and in each community divides, random selecting part node, gives its all adjacent node by its community's label, thus each community of randomization divides, and generates S _dindividual various community divides as initial population B ₀.

3. the multiple goal community discovery method based on Local Search according to claim 1, it is characterized in that, described step S4, is specially:

S41, find out colony B according to non-dominant relation _gin all non-dominant individual, choose front S by crowding distance descending _dindividual non-dominant individuality composition non-dominant population, copies non-dominant population and generates outside non-dominant population, for retaining the excellent individual in this population;

S42, interlace operation is carried out to non-dominant population, the father that Stochastic choice Liang Ge community divides as interlace operation from non-dominant population is individual, Stochastic choice node, same operation is carried out to two fathers individuality: find out the individuality that all in father's individuality and this node has identical community label, and their community's label is given individuality corresponding in another individuality, two father's individuality intersection generation two are individual, repeat this process secondary, all newly-generated sub-group of individuals become cross-community to divide population;

S43, to cross-community divide population carry out mutation operation, each division that cross-community divides in population is made a variation, to each node in division, its all neighbor node is given by its community's label with mutation probability, generate new variation individual, the individuality of all new variations and the individual Composition Variation community division population do not made a variation.

4. the multiple goal community discovery method based on Local Search according to claim 1, it is characterized in that, described step S5, is specially:

S51, select outside non-dominant population and variation community to divide population respectively as two initial population of Local Search, find out all non-dominant individualities in each initial population and form the non-dominant population of Local Search respectively;

S52, be that each non-dominant in two non-dominant populations divides and calculates Local Search direction vector, search direction vector ω ^pNfor community divides the approximate normal line vector of individual position in purpose-function space, computing formula is as follows:

${\mathrm{\&omega;}}^{\mathrm{PN}}\left(X\right)=(\frac{f_2\left(X^1\right)-f_2\left(X^2\right)}{\mathrm{\&pi;}},\frac{f_1\left(X^2\right)-f_1\left(X^1\right)}{\mathrm{\&pi;}})$

Wherein, π=f ₂(X ¹)-f ₂(X ²)+f ₁(X ²)-f ₁(X ¹), f ₁and f ₂represent two objective functions that community divides respectively, X ¹and X ²be that X two adjacent communities in purpose-function space divide, this direction is similar to the gradient direction that corresponding objective function increases;

S53, setting Local Search maximum iteration time MI, for each non-dominant community Definition of Division local neighborhood and neighborhood, utilize network structure to search for new more outstanding community in the local neighborhood divided in each community and neighborhood to divide and replace original community to divide, two non-dominant populations repeat this process MI time, forms two sub-populations of Local Search.

5. the multiple goal community discovery method based on Local Search according to claim 1, it is characterized in that, described step S7, is specially: find out final community and divide population B _gin all non-dominant communities divide, calculate community's number and modularity Q that each non-dominant community divides, computing formula is as follows:

${Q=\mathrm{\&Sigma;}}_{C\&Element;X}[\frac{l_C}{m}-{\left(\frac{k_C}{2m}\right)}^2]$

Wherein, l _crepresent the quantity on the limit of C inside, community; k _crepresent the number of degrees that C interior joint in community is total; M represents the limit number that network is total.