CN110070177A - Community structure detection method in a kind of nonoverlapping network and overlapping network - Google Patents
Community structure detection method in a kind of nonoverlapping network and overlapping network Download PDFInfo
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Abstract
The invention discloses community structure detection methods in a kind of nonoverlapping network and overlapping network, under the guidance of obfuscation module degree function, directionality search is carried out in the corresponding feasible degree of membership distributed combination space of constraint condition, converge to the degree of membership distribution for being optimal obfuscation module degree function, it is distributed by optimal degree of membership, real community division is obtained, so that it is determined that community structure.This method can get really fuzzy community division, and it is distributed according to degree of membership and determines community structure, final degree of membership distribution obtained can embody the diversified topological property difference of overlapping nodes, overcome in degree of membership calculating process due to the single bring inexactness of parameter.
Description
Technical field
The present invention relates to a kind of community structure detection method, corporations in specifically a kind of nonoverlapping network and overlapping network
Structure detection method.
Background technique
Community structure is that complex network is one of key property, excavates the community structure in complex network to announcement network function
Can have great importance.Network community detection can excavate the community structure for having realistic meaning in complex network, but in reality
In border, the form of network is varied, and inner link form is also mostly different, and which results in internal community structures also to show
Diversity.Therefore, for these various informative networks, in order to accurately and effectively analyze community structure therein, it is born
Many corporations' detection algorithms.
It is compared to corporations' detection, corporations' detection algorithm of non-overlap is suggested at first, and at present in the mark of python
It can be invoked directly there are many corporations' detection algorithm in quasi- library.Such as the modularity based on multiresolution version
MultiLevel algorithm, the WalkTrap algorithm based on random walk, is based on side at the FastGreedy algorithm based on greedy algorithm
The GN algorithm of betweenness, the Kclique algorithm based on node and subgraph relationship, the InfoMap algorithm based on dynamics random walk,
The label propagation algorithm (LP) propagated based on label node and the Eigenvector based on modular matrix dominant characteristics vector are calculated
Method.However, community division mode becomes more complicated with the increase of complex network scale, these classical corporations, which are detected, is calculated
Method is no longer satisfied demand.
In corporations' detection, there are two kinds of overlappings: discrete overlapping and fuzzy overlapping.Each node in discrete overlapping
There is identical degree of membership for the corporations belonging to it, and fuzzy overlapping has more accurate requirement to division, i.e., node is to affiliated
The degree of membership of corporations is not quite similar.Typical discrete corporations' detection algorithm includes: factions' filtering, link clustering, local expansion, mould
Lumpiness optimization, multiple-objection optimization and label propagation etc..
2011, Gregory was put forward for the first time the concept of " fuzzy overlapping divides " for corporations' detection of social networks.Mesh
Before, there are many fuzzy corporations' detection algorithms to be suggested both at home and abroad, including extension tag is propagated, Non-negative Matrix Factorization and fuzzy
Modularity optimization etc..The label propagation algorithm Typical Representative algorithm of extension includes COPRA algorithm, SLPA algorithm and LPPB algorithm
Deng, wherein COPRA is the first fuzzy corporations' detection algorithm propagated based on label that Gregory was proposed in 2010.Based on non-
Negative matrix decomposition is the algorithms most in use in machine learning, is used in corporations' detection solution in recent years, Typical Representative algorithm includes
Zhao etc. 2010 symmetrical NMF algorithm s-NMF, Psorakis proposed etc. the 2011 Bayes's NMF algorithms etc. proposed.It is fuzzy
The typical representative algorithm of cluster includes that Wang in 2013 etc. proposes the fuzzy clustering algorithm based on FCM.
In corporations' detection, discrete overlapping is only concerned whether node belongs to some corporation, to community division without more accurate
Requirement.However currently, most of corporations' detection algorithm is only limitted to discrete corporations' detection, this kind of algorithm is by node to each
The degree of membership of corporations regards identical as, however many true community structure interior joint degrees of membership are incomparable inconsistent.
Nowadays both at home and abroad in existing multi-Fuzzy corporations detection algorithm, including extension tag is propagated, nonnegative matrix point
Solution and the optimization of obfuscation module degree etc. lack effective setting degree of membership threshold based on fuzzy corporations' detection algorithm that extension tag is propagated
The method of value.It is high based on Algorithms of Non-Negative Matrix Factorization computation complexity, it is not suitable for large scale network.Using FCM as the mould of representative
The modularity for pasting clustering algorithm detection gained community structure is lower.Ability is not in terms of global optimizing for obfuscation module degree optimization algorithm
Fall into enough and easily local optimum.
Summary of the invention
For the prior art, there are the above problems, and this application provides corporations in a kind of nonoverlapping network and overlapping network to tie
Structure detection method, under the guidance of obfuscation module degree function, in the corresponding feasible degree of membership distributed combination space of constraint condition
Directionality search is carried out, the degree of membership distribution for being optimal obfuscation module degree function is converged to, is distributed by optimal degree of membership,
Real community division is obtained, so that it is determined that community structure.
To achieve the above object, a kind of technical solution of the application are as follows: community structure in nonoverlapping network and overlapping network
Detection method, the specific steps are as follows:
One, community structure detection mode in nonoverlapping network are as follows:
Step1 encodes population at individual and constructs initial population；
Step2 obtains the corresponding fuzzy community division of population at individual using subordinated-degree matrix coding；
Whether Step3 obtains optimal fuzzy community division: if it is, exporting optimal fuzzy community division in current population
As testing result, Step4 is otherwise gone to；
Step4 executes mutation operation, crossover operation, selection operation evolution generation progeny population to parent population, evolves
Journey retains good community division gene in parent individuality；
Step5 carries out fitness value evaluation to filial generation population at individual and carries out obfuscation module degree meter to fuzzy community division
It calculates；
Whether Step6 judges whether objective function number m is greater than 1, i.e., be multiple-objection optimization；If single object optimization, then
Elitist selection is directly carried out according to the obfuscation module degree function Q of progeny population individual, retains high-quality individual and enters next-generation parent
Population goes to Step3；If multiple-objection optimization, then other target function values of progeny population individual are calculated first, and to merging
Parent progeny population set later carries out Pareto non-dominated ranking and population density estimation, then according to individual accuracy and
Distributivity result carries out environmental selection, and the Pareto optimum individual for retaining same size enters next-generation parent population, goes to
Step3；
Two, community structure detection mode in overlapping network are as follows:
S1. initialization of population:
Network parameter: number of nodes n is arranged in S1.1, and corporations' quantity is k, and the degree distribution list of node is m, even side matrix
For adj；Population scale is NP, and the scale factor of clean-up is cleanup, and current population algebra is t, and the total algebra of population is
gen；
S1.2 constructs initial population using random number, and initial population is normalized；
S2. according to broad sense overlay module degree function QgThe fitness value of each individual in population is calculated, it is optimal as history
Pmax_value is solved, population pop is as optimal population pmax_pop；
S3. correction operation is carried out to population, calculates individual adaptation degree at this time, and more new historical optimal solution pmax_value
With optimal population pmax_pop；
S4. when current population algebra t is less than population total algebra gen:
S5. when current population algebra t is more than or equal to population total algebra gen, output descriptor overlay module degree function is overlapped mould
Lumpiness function, the historical record of network module degree.
Further, community structure detects in nonoverlapping network, and the node degree of membership combination for corresponding to constraint conditions is excellent
Shown in the following formula of change problem mathematical model:
Mathematical model: y=F (x)=(f1(x),f2(x)...fm(x))
U∈Rn×c
Constraint condition:
Y=F (x) represents the mapping function by decision space to m dimension object space in formula, draws comprising m fuzzy corporations
Sub-prime amount evaluation function；It is single-object problem as m=1, objective function is obfuscation module degree function Q；Turn as m > 1
Multi-objective optimization question is turned to, objective function is to measure community division in multinomial evaluation criterion comprising the function set including Q
Performance superiority and inferiority；U={ uik}∈Rn×cFor node degree of membership distribution matrix, uikRepresent node i being subordinate to for k-th corporation
It spends, wherein [1, n] i ∈, k ∈ [1, c], and meets constraint condition；It is distributed the mapping of U for degree of membership, represents U pairs
The fuzzy community division answered.
It is further: current population is handled in step S4, is comprised the concrete steps that:
S41. mutation operation is carried out to contemporary group's generation；
S42. according to broad sense overlay module degree function QgCalculate each individual adaptation degree in variation population mutation_pop
It is worth and updates optimal population pmax_pop and history optimal solution pmax_value；
S43. clean-up operation is carried out to variation population, legitimacy maintenance and normalized then is carried out to individual；
S44. according to broad sense overlay module degree function QgCalculate each individual in variation population mutation_pop at this time
Fitness value simultaneously updates optimal population pmax_pop and history optimal solution pmax_value；
S45. it enables cross-species cross_pop quantity be equal to population pop quantity, parameter i is made to rise to population scale from 1
NP calculates individual cross_pop according to ideal adaptation angle valueiIn the crossover probability factor CR in t generationi, carry out crossover operation；
S46. according to broad sense overlay module degree function QgCalculate cross-species cross_pop in each ideal adaptation angle value simultaneously
Update optimal population pmax_pop and history optimal solution pmax_value；
S47. clean-up operation is carried out to cross-species, legitimacy maintenance and normalized then is carried out to individual；
S48. according to broad sense overlay module degree function QgCalculate each ideal adaptation in cross-species cross_pop at this time
Angle value simultaneously updates optimal population pmax_pop and history optimal solution pmax_value；
S49. Population Regeneration pop value makes population pop quantity be equal to optimal population pmax_pop quantity, updates ideal adaptation
Angle value is pmax_value；
S410. current population optimum individual bestx is recorded, calculate and records the corresponding broad sense overlay module degree letter of bestx
Number Qg, overlay module degree function Qov, network module degree Q；
S411. step S41-S410 is repeated, until completing t for the processing of population.
Further, mutation operation specific implementation step is, the individual in population is divided into excellent individual and outstanding non-
Body: the fitness value of individual and gen are compared for the average fitness value of population, ideal adaptation angle value is greater than average fitness
Individual be excellent individual, otherwise be non-excellent individual；
For excellent individual, mutation operation is carried out using following formula:
mutation_popi=Fi×popi+KKi×(popr2,i-popr3,i)
r1,r2,r3It is three arrays, indicates randomly selected individual index sequence, these three arrays are different two-by-two, and all
It is the out-of-order arrangement of [1, NP]；r1,iIt is array r1In i-th individual index, r2,iIt is array r2In i-th individual index, r3,iIt is
Array r3In i-th individual index, popr2,i-popr3,iTwo different random individuals in population are corresponded to for each differential vector
Difference vector；After differential vector is weighted with current variation individual vector popiIt sums after weighting and just generates a target individual
Vector mutation_popi, that is, variation population at individual；FiAnd KKiIt is that i-th of individual respectively corresponds variation in gen generation
The weight of individual vector sum differential vector, controls the scaling amplitude of variation individual vector sum difference vector, and numerical value is that basis is worked as
What the fitness value calculation of evolution algebraical sum individual obtained；
For non-excellent individual, mutation operation is carried out using following formula:
mutation_popi=Wi×popr1,i+KKi×(popmax_index-popi)
The target individual vector mutation_pop of non-excellent individualiBy random individual vector popr1,iAfter weighting with one
It sums and obtains after differential vector weighting；Max_index is gen for the maximum individual label of fitness value in population,
popmax_indexIt is the optimal solution in current population, for enhancing individual popiExploring ability, differential vector at this time is
popmax_index-popi；WiThe weight of corresponding random individual vector, numerical value are the fitness according to current evolutionary generation and individual
What value was calculated；
Further, legitimacy maintenance and normalization operation are carried out to the individual nodes after variation, legitimacy maintenance is to protect
The degree of membership value of each node is demonstrate,proved between [0,1], operation formula is as follows:
When the individual j in population i is when the degree of membership of corporations k is less than 0, current degree of membership is set as 0.0001；Work as kind
Current degree of membership is set as 0.9999 when the degree of membership of corporations k is greater than 1 by the individual j in group i.
Further, to parameter Fi、KKi、Wi、CRiIt carries out being adaptively adjusted value, each individual is during evolution
It can be dynamically controlled, adjustment formula is as follows:
Wherein, fmax,tFor maximum adaptation angle value, fmin,tFor minimum fitness value, fi,tFor current fitness value.
Further, cross-species individual generates as follows:
Wherein i=1 ..., NP, j=1 ..., n；Random ∈ [0,1] is a random number；K is current corporations, com_k
∈ [1, c] is a randomly selected corporations from c corporations, is subordinate to for guaranteeing to intersect at least one corporation in individual
Degree distribution is from variation individual；Crossover probability factor CRi∈ [0,1] determines corporations' quantity of variation individual in generation
Intersect ratio shared in individual corporations quantity.
Further, clean-up is operated specifically: one node i of random selection and a corporations k calculate separately neighbour
For domain node to the average membership f1 of corporations k and the average membership f2 of non-neighboring domain node, formula is as follows:
Wherein, Neighbor (i) indicates the neighbor node set of node i, unode,cIndicate node node in corporations c
It is subordinate to angle value, | Neighbor | it is the quantity of neighbor node, n is nodes sum,
Compare the size of f1 and f2, if f1 is greater than f2, illustrates that the neighbours of node i have more been assigned to and node i is same
One corporation, it is correct that division result, which has a possibility that larger, then, increase by one to degree of membership of the node i to corporations k
Fixed value；If f1 is less than f2, reduce by a fixed value to degree of membership of the node i to corporations k.
The present invention due to using the technology described above, can obtain following technical effect: mutation operation in the application,
Crossover operation not only has a stronger robustness, but also can be intelligent in large-scale complex search space and efficiently restrains
To globally optimal solution；This method can get really fuzzy community division, and is distributed according to degree of membership and determines community structure, be obtained
The final degree of membership distribution obtained can embody the diversified topological property difference of overlapping nodes, overcome in degree of membership calculating process
Due to the single bring inexactness of parameter.
Detailed description of the invention
Fig. 1 is the application flow chart；
Fig. 2 is mutation operation flow chart；
Fig. 3 is crossover operation flow chart；
Fig. 4 is the process schematic of crossover operation；
Fig. 5 is community structure overhaul flow chart in nonoverlapping network.
Specific embodiment
The present invention is described in further detail in the following with reference to the drawings and specific embodiments: doing as example to the application
Further description explanation.
The present embodiment provides community structure detection methods in a kind of nonoverlapping network and overlapping network, comprising:
Embodiment 1
As shown in figure 5, the present embodiment provides community structure detection modes in a kind of nonoverlapping network are as follows: ask corporations' detection
Topic is abstracted as the fuzzy membership distributed combination optimization problem of with constraint conditions, utilizes differential evolution algorithm (Differential
Evolution, DE) it is distributed in corresponding continuous space in node degree of membership and carries out global search, in the guidance of obfuscation module degree
The degree of membership distribution that global optimum is converged under lower and fuzzy overlapping constraint condition, thus obtains really obscuring community division,
And it is distributed according to degree of membership and determines community structure.
There is n node with one, it is right for fuzzy corporations' test problems of c corporations and m quality evaluation function
It answers shown in the following formula of node degree of membership combinatorial optimization problem mathematical model of with constraint conditions.
Mathematical model: y=F (x)=(f1(x),f2(x)...fm(x))
U∈Rn×c
Constraint condition:
Y=F (x) represents the mapping function by decision space to m dimension object space in formula, draws comprising m fuzzy corporations
Sub-prime amount evaluation function.It is single-object problem as m=1, objective function is obfuscation module degree function Q；Turn as m > 1
Multi-objective optimization question is turned to, objective function is to measure community division in multinomial evaluation criterion comprising the function set including Q
Performance superiority and inferiority.U={ uik}∈Rn×cFor node degree of membership distribution matrix, uikRepresent node i being subordinate to for k-th corporation
It spends, wherein [1, n] i ∈, k ∈ [1, c], and meets constraint condition.It is distributed the mapping of U for degree of membership, represents U pairs
The fuzzy community division answered.
Population at individual needs to meet the corresponding multinomial constraint condition of fuzzy corporations' detection in initialization and evolutionary process, specifically
It include: the legitimacy for meeting the corresponding General Constraint Condition of feasible community division 1) to guarantee individual.2) it is special to meet fuzzy overlapping
Corresponding two Special Constraint Conditions of property: degree of membership u of the arbitrary node i to any corporations kikThe value in [0,1] range；Arbitrarily
Node i is " 1 " to the degree of membership summation value perseverance of all corporations.
It is distributed in feasible search space in the node degree of membership that above-mentioned constraint condition limits and carries out global search, converging to makes
The degree of membership distribution U* that objective function is optimal simultaneously in set F, corresponding optimal fuzzy community division is x*=argmaxF
(x)。
Specific implementation method are as follows:
Step1 encodes population at individual and constructs initial population；
Step2 obtains the corresponding fuzzy community division of population at individual using subordinated-degree matrix coding；
Whether Step3 obtains optimal fuzzy community division: if it is, exporting optimal fuzzy community division in current population
As testing result, Step4 is otherwise gone to；
Step4 executes mutation operation, crossover operation, selection operation evolution generation progeny population to parent population, evolves
Journey retains good community division gene in parent individuality；
Step5 carries out fitness value evaluation to filial generation population at individual and carries out obfuscation module degree meter to fuzzy community division
It calculates；
Whether Step6 judges whether objective function number m is greater than 1, i.e., be multiple-objection optimization；If single object optimization, then
Elitist selection is directly carried out according to the obfuscation module degree function Q of progeny population individual, retains high-quality individual and enters next-generation parent
Population goes to Step3；If multiple-objection optimization, then other target function values of progeny population individual are calculated first, and to merging
Parent progeny population set later carries out Pareto non-dominated ranking and population density estimation, then according to individual accuracy and
Distributivity result carries out environmental selection, and the Pareto optimum individual for retaining same size enters next-generation parent population, goes to
Step3；
Embodiment 2
As shown in Figure 1, the present embodiment provides community structure detection modes in a kind of overlapping network are as follows:
S1. initialization of population:
The degree of membership random assignment for being each node when this method starts in each corporations, value range are [0,1],
Thus each individual in population pop primary is formed.Assuming that initial evolutionary generation t=0, is randomly generated the NP for meeting constraint condition
Individual constitutes initial population.Initial population indicates are as follows:
popk(0)={ x1,x2,···,xn, k=1 ..., NP
In formula, popk(0) k-th of individual in the 0th generation population is indicated.
However, the individual generated at random, which is likely to result in node degree of membership, is unsatisfactory for constraint condition.It is needed at this time to every
Corporations' degree of membership distribution of a node is normalized, and guarantees that each node is 1 to the sum of degree of membership of each corporations.Namely
It says, for arbitrary node i, its degree of membership summation in c whole corporations is 1.It is formulated are as follows:
S2. according to broad sense overlay module degree function QgThe fitness value for calculating each individual in initial population pop, as going through
History optimal solution pmax_value, population pop are as optimal population pmax_pop；
S3. correction operation is carried out to initial population pop, calculates individual adaptation degree at this time, and more new historical optimal solution
Pmax_value and optimal population pmax_pop；
S4. when current population algebra t is less than population total algebra gen:
S41. mutation operation is carried out to contemporary group's generation；
S42. according to broad sense overlay module degree function QgCalculate each individual adaptation degree in variation population mutation_pop
It is worth and updates optimal population pmax_pop and history optimal solution pmax_value；
S43. clean-up operation is carried out to variation population, legitimacy maintenance and normalized then is carried out to individual；
S44. according to broad sense overlay module degree function QgCalculate each individual in variation population mutation_pop at this time
Fitness value simultaneously updates optimal population pmax_pop and history optimal solution pmax_value；
S45. it enables cross-species cross_pop quantity be equal to population pop quantity, parameter i is made to rise to population scale from 1
NP calculates individual cross_pop according to ideal adaptation angle valueiIn the crossover probability factor CR in t generationi, carry out crossover operation；
S46. according to broad sense overlay module degree function QgCalculate cross-species cross_pop in each ideal adaptation angle value simultaneously
Update optimal population pmax_pop and history optimal solution pmax_value；
S47. clean-up operation is carried out to cross-species, legitimacy maintenance and normalized then is carried out to individual；
S48. according to broad sense overlay module degree function QgCalculate each ideal adaptation in cross-species cross_pop at this time
Angle value simultaneously updates optimal population pmax_pop and history optimal solution pmax_value；
S49. Population Regeneration pop value makes population pop quantity be equal to optimal population pmax_pop quantity, updates ideal adaptation
Angle value is pmax_value；
S410. current population optimum individual bestx is recorded, calculate and records the corresponding broad sense overlay module degree letter of bestx
Number Qg, overlay module degree function Qov, network module degree Q；
S411. step S41-S410 is repeated, until completing t for the processing of population.
S5. when current population algebra t is more than or equal to population total algebra gen, output descriptor overlay module degree function is overlapped mould
Lumpiness function, the historical record of network module degree.
Embodiment 3
The present embodiment is further qualified Examples 1 and 2:
Mutation operation: the individual in population is divided into excellent individual and non-excellent individual: by the fitness value of individual and the
Gen is compared for the average fitness value of population, and the individual that ideal adaptation angle value is greater than average fitness is excellent individual, otherwise is
Non- excellent individual；
For excellent individual, mutation operation is carried out using following formula:
mutation_popi=Fi×popi+KKi×(popr2,i-popr3,i)
r1,r2,r3It is three arrays, indicates randomly selected individual index sequence, these three arrays are different two-by-two, and all
It is the out-of-order arrangement of [1, NP]；r1,iIt is array r1In i-th individual index, r2,iIt is array r2In i-th individual index, r3,iIt is
Array r3In i-th individual index, popr2,i-popr3,iTwo different random individuals in population are corresponded to for each differential vector
Difference vector；After differential vector is weighted with current variation individual vector popiIt sums after weighting and just generates a target individual
Vector mutation_popi, that is, variation population at individual；FiAnd KKiIt is that i-th of individual respectively corresponds variation in gen generation
The weight of individual vector sum differential vector, controls the scaling amplitude of variation individual vector sum difference vector, and numerical value is that basis is worked as
What the fitness value calculation of evolution algebraical sum individual obtained；
For non-excellent individual, mutation operation is carried out using following formula:
mutation_popi=Wi×popr1,i+KKi×(popmax_index-popi)
The target individual vector mutation_pop of non-excellent individualiBy random individual vector popr1,iAfter weighting with one
It sums and obtains after differential vector weighting；Max_index is gen for the maximum individual label of fitness value in population,
popmax_indexIt is the optimal solution in current population, for enhancing individual popiExploring ability, differential vector at this time is
popmax_index-popi；WiThe weight of corresponding random individual vector, numerical value are the fitness according to current evolutionary generation and individual
What value was calculated；
The above variation method can act on each individual in every generation population, therefore the variation of each individual can obtain
To targeted adjustment.On the one hand, the exploring ability of excellent individual can be reinforced, find global optimum in its neighborhood to increase
A possibility that；On the other hand, the producing capacity of non-excellent individual can be reinforced, to accelerate its search speed to global optimization
Degree.Under the guidance of directivity information, the blindness in search process be can be effectively reduced, and offspring individual and optimal solution
Quality also can be improved, and while guaranteeing good population diversity in this method, reduce difference individual in population
Property, help speed up convergence speed of the algorithm.
Due to changing corporations' degree of membership of each node in mutation process, it may cause node degree of membership and be unsatisfactory for about
Therefore beam condition carries out legitimacy maintenance and normalization operation to the individual nodes after variation, legitimacy maintenance is to guarantee each
For the degree of membership value of node between [0,1], operation formula is as follows:
When the individual j in population i is when the degree of membership of corporations k is less than 0, current degree of membership is set as 0.0001；Work as kind
Current degree of membership is set as 0.9999 when the degree of membership of corporations k is greater than 1 by the individual j in group i.
Dynamic parameter adjustment: in Mutation Strategy, there are three control parameter W, KK and F, they respectively correspond mutation process
In random element, social ingredient and cognitive component.In addition, a crucial control parameter has also been introduced in crossover operation
CR, it is the decimal between one [0,1], indicates that each individual executes succession row with great percentage from variation individual
For.
For the degree of variation of each individual of dynamic self-adapting during evolution, a kind of dynamic self-adapting is proposed
Parameter strategy.All parameters are adjusted according to the fitness value characteristic and evolution the number of iterations of each individual.Due to ginseng
Number W, KK and F control random partial in mutation process, society part and cognition part respectively, and CR determine variation result after
It holds, therefore its numerical value should be adjusted according to following two principles:
1. carrying out parameter adaptive adjustment according to the fitness value of individual.To non-excellent individual, it should reinforce variation and hand over
The degree of fork, to introduce more directivity informations during evolution.Therefore, the random element in mutation process, society
Succession in ingredient and crossover process should all enhance, the W and KK in corresponding following formula, and the CR value in intersecting compared with
Greatly.On the contrary, for excellent individual, it should reinforce the cognition part in mutation process, parameter adjustment should defer to opposite original
Then, correspond to biggish F value and lesser W value in formula.
2. according to evolution the number of iterations dynamic self-adapting.In early stage of evolving, it should reinforce the exploration energy of individual
Power, to ensure sufficiently to be searched in each individual neighborhood.On the contrary, in the later stage of evolution stage, it should reinforce the exploitation of individual
Ability reinforces the exchange between individual, accelerates the convergence of entire group.According to this principle, in evolutionary process, F, W, the value of CR
It is gradually reduced, and KK value is gradually increased.
Based on mentioned above principle, parameter can obtain being adaptively adjusted value, and each individual during evolution can be by
Dynamic controls, and adjustment formula is as follows:
Wherein, fmax,tFor maximum adaptation angle value, fmin,tFor minimum fitness value, fi,tFor current fitness value.
Crossover operation: it is the process of a heredity and succession, is become according to a certain percentage on the basis of initial population
All nodes are distributed the degree of membership of some corporation in xenogenesis group, i.e., remain the community information in variation individual.The behaviour
Work can generate a new population, and the individual in new population not only individual partial information but also inherited change in heredity initial population
Individual partial information in xenogenesis group.This method is by initial population individual popiCorresponding variation population at individual
mutation_popiCrossover operation is carried out, cross-species individual cross_pop is generatedi.For the evolution for guaranteeing initial population, it is necessary to
Guarantee that the node degree of membership of at least one corporation in each cross-species individual is contributed by variation population at individual, and other societies
The node degree of membership of group is then by crossover probability factor CRiIt determines.
Cross-species individual generates as follows:
Wherein i=1 ..., NP, j=1 ..., n；Random ∈ [0,1] is a random number；K is current corporations, com_k
∈ [1, c] is a randomly selected corporations from c corporations, is subordinate to for guaranteeing to intersect at least one corporation in individual
Degree distribution is from variation individual；Crossover probability factor CRi∈ [0,1] determines corporations' quantity of variation individual in generation
Intersect ratio shared in individual corporations quantity.
It is com_k with current corporations, that is, for the condition for meeting k=com_k, Fig. 4 illustrates the process of crossover operation, figure
The meaning that middle variable indicates is as follows: pop [i] is i-th of individual of initial population, and mutation_pop [i] is variation population
I-th of individual, cross_pop [i] are i-th of individuals of cross-species.Node_1 to node_n indicates n section in individual
Point, com_1 to com_c indicate the c corporations that node belongs to, and com_k is current corporations.
For initial population individual pop [i], dark gray section is the node degree of membership information in corporations com_k, light grey
Part indicates the node degree of membership information of other corporations.In variation population at individual mutation_pop [i], dark gray section table
Show the node degree of membership information in corporations com_k, bright gray parts indicate the node degree of membership information of other corporations.Cross-species
Individual obtains the node degree of membership of corporations com_k from variation individual, i.e. figure mutation_pop [i] Oxford gray part, from
The node degree of membership of other corporations, i.e. bright gray parts in figure pop [i] are obtained in initial population individual, complete the intersection of individual
Operation, obtains cross-species individual cross_pop [i].Same operation is executed to obtain new population to each individual
cross_pop。
Clean-up operation: this method is substantially randomness searching algorithm, during evolution constantly in adjustment individual
Each dimension component, until converge to global optimum, so community division result is likely that there are error during evolution.These
Error can reduce the search capability of community division, and algorithm is made to fall into local optimum, the final quality for influencing community division.To understand
Certainly this problem takes clean-up operation to each individual with certain probability, that is, according to known network topological structure
Information is artificially modified the individual in evolutionary process, to accelerate its convergence rate.
Randomly choose a node i and a corporations k, calculate separately neighborhood node to the average membership f1 of corporations k and
The average membership f2 of non-neighboring domain node, formula are as follows:
Wherein, Neighbor (i) indicates the neighbor node set of node i, uNode, cIndicate node node in corporations c
It is subordinate to angle value, | Neighbor | it is the quantity of neighbor node, n is nodes sum,
Compare the size of f1 and f2, if f1 is greater than f2, illustrates that the neighbours of node i have more been assigned to and node i is same
One corporation, it is correct that division result, which has a possibility that larger, then, increase by one to degree of membership of the node i to corporations k
Fixed value；If f1 is less than f2, reduce by a fixed value to degree of membership of the node i to corporations k.
Correction operation: although the individual after initializing meets constraint condition, but still have unreasonable place, with
It is illustrated in case where lower chart:
Node 1 actually has bigger degree of membership in corporations A and corporations B, but the node 1 after initialization has in corporations C
Bigger degree of membership；Node 2, which is pertaining only to corporations A, but has degree of membership etc. in each corporations after initialization.In view of the above feelings
Condition proposes correction operation (biased operation) and reduces these problems: to individual newly-generated in population, randomly selecting a section
The node, is assigned to all neighbor nodes of the node, this is because neighborhood by point and a corporations in the degree of membership of the corporations
The probability that node is under the jurisdiction of same corporations is bigger.By carrying out biased operation (correction operation), solution space is by certain
Limitation, makes the convergence rate of this method get a promotion.
It no matter is non-corporations' detection or corporations' detection, this method can obtain preferable network module degree, by this method
It applies in link prediction, can be improved the accuracy of link prediction.
The preferable specific embodiment of the above, only the invention, but the protection scope of the invention is not
It is confined to this, anyone skilled in the art is in the technical scope that the invention discloses, according to the present invention
The technical solution of creation and its inventive concept are subject to equivalent substitution or change, should all cover the invention protection scope it
It is interior.
Claims (8)
1. community structure detection method in a kind of nonoverlapping network and overlapping network, which is characterized in that specific step is as follows:
Community structure detection mode in nonoverlapping network are as follows:
Step1 encodes population at individual and constructs initial population；
Step2 obtains the corresponding fuzzy community division of population at individual using subordinated-degree matrix coding；
Whether Step3 obtains optimal fuzzy community division: if it is, exporting optimal fuzzy community division conduct in current population
Otherwise testing result goes to Step4；
Step4 executes mutation operation, crossover operation, selection operation evolution generation progeny population to parent population, and evolutionary process is protected
Stay good community division gene in parent individuality；
Step5 carries out fitness value evaluation to filial generation population at individual and carries out the calculating of obfuscation module degree to fuzzy community division；
Whether Step6 judges whether objective function number m is greater than 1, i.e., be multiple-objection optimization；If single object optimization, then directly
Elitist selection is carried out according to the obfuscation module degree function Q of progeny population individual, retains high-quality individual and enters next-generation parent population,
Go to Step3；If multiple-objection optimization, then first calculate progeny population individual other target function values, and to merging after
Parent progeny population set carry out Pareto non-dominated ranking and population density estimation, then according to individual accuracy and distribution
Property result carry out environmental selection, the Pareto optimum individual for retaining same size enters next-generation parent population, goes to Step3；
Community structure detection mode in overlapping network are as follows:
S1. initialization of population:
Network parameter: number of nodes n is arranged in S1.1, and corporations' quantity is k, and the degree distribution list of node is m, and even side matrix is
adj；Population scale is NP, and the scale factor of clean-up is cleanup, and current population algebra is t, and the total algebra of population is gen；
S1.2 constructs initial population using random number, and initial population is normalized；
S2. according to broad sense overlay module degree function QgThe fitness value for calculating each individual in population, as history optimal solution
Pmax_value, population pop are as optimal population pmax_pop；
S3. correction operation is carried out to population, calculates individual adaptation degree at this time, and more new historical optimal solution pmax_value and most
Excellent population pmax_pop；
S4. when current population algebra t is less than population total algebra gen:
S5. when current population algebra t is more than or equal to population total algebra gen, output descriptor overlay module degree function, overlay module degree
Function, the historical record of network module degree.
2. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 1, which is characterized in that
Community structure detects in nonoverlapping network, and the node degree of membership combinatorial optimization problem mathematical model for corresponding to constraint conditions is as follows
Shown in formula:
Mathematical model: y=F (x)=(f1(x),f2(x)...fm(x))
U∈Rn×c
Constraint condition:
Y=F (x) represents the mapping function by decision space to m dimension object space in formula, includes m fuzzy community division matter
Measure evaluation function；It is single-object problem as m=1, objective function is obfuscation module degree function Q；It is converted into as m > 1
Multi-objective optimization question, objective function are to measure property of the community division in multinomial evaluation criterion comprising the function set including Q
It can superiority and inferiority；U={ uik}∈Rn×cFor node degree of membership distribution matrix, uikNode i is represented for the degree of membership of k-th of corporation,
Middle i ∈ [1, n], k ∈ [1, c], and meet constraint condition；It is distributed the mapping of U for degree of membership, represents the corresponding mould of U
Paste community division.
3. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 1, which is characterized in that
Current population is handled in step S4, is comprised the concrete steps that:
S41. mutation operation is carried out to contemporary group's generation；
S42. according to broad sense overlay module degree function QgCalculate each ideal adaptation angle value and more in variation population mutation_pop
New optimal population pmax_pop and history optimal solution pmax_value；
S43. clean-up operation is carried out to variation population, legitimacy maintenance and normalized then is carried out to individual；
S44. according to broad sense overlay module degree function QgCalculate each individual adaptation degree in variation population mutation_pop at this time
It is worth and updates optimal population pmax_pop and history optimal solution pmax_value；
S45. it enables cross-species cross_pop quantity be equal to population pop quantity, parameter i is made to rise to population scale NP, root from 1
Individual cross_pop is calculated according to ideal adaptation angle valueiIn the crossover probability factor CR in t generationi, carry out crossover operation；
S46. according to broad sense overlay module degree function QgIt calculates each ideal adaptation angle value in cross-species cross_pop and updates
Optimal population pmax_pop and history optimal solution pmax_value；
S47. clean-up operation is carried out to cross-species, legitimacy maintenance and normalized then is carried out to individual；
S48. according to broad sense overlay module degree function QgCalculate each ideal adaptation angle value in cross-species cross_pop at this time
And update optimal population pmax_pop and history optimal solution pmax_value；
S49. Population Regeneration pop value makes population pop quantity be equal to optimal population pmax_pop quantity, updates ideal adaptation angle value
For pmax_value；
S410. current population optimum individual bestx is recorded, calculate and records the corresponding broad sense overlay module degree function Q of bestxg,
Overlay module degree function Qov, network module degree Q；
S411. step S41-S410 is repeated, until completing t for the processing of population.
4. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 3, which is characterized in that
Mutation operation specific implementation step is that the individual in population is divided into excellent individual and non-excellent individual: by the fitness of individual
Value is compared with gen for the average fitness value of population, and the individual that ideal adaptation angle value is greater than average fitness is excellent individual,
It otherwise is non-excellent individual；
For excellent individual, mutation operation is carried out using following formula:
r1,r2,r3It is three arrays, indicates randomly selected individual index sequence, these three arrays are different two-by-two, and be all [1,
NP] out-of-order arrangement；r1,iIt is array r1In i-th individual index, r2,iIt is array r2In i-th individual index, r3,iIt is array
r3In i-th individual index,For each differential vector correspond in population the difference of two different random individuals to
Amount；After differential vector is weighted with current variation individual vector popiIt sums after weighting and just generates a target individual vector
mutation_popi, that is, variation population at individual；FiAnd KKiIt is that i-th of individual respectively corresponds variation individual in gen generation
The weight of vector sum differential vector, controls the scaling amplitude of variation individual vector sum difference vector, and numerical value is according to when advance
What the fitness value calculation of change algebraical sum individual obtained；
For non-excellent individual, mutation operation is carried out using following formula:
The target individual vector mutation_pop of non-excellent individualiBy random individual vectorAfter weighting with a difference
Summation obtains after vector weighting；Max_index is gen for the maximum individual label of fitness value in population, popmax_indexIt is
Optimal solution in current population, for enhancing individual popiExploring ability, differential vector at this time is popmax_index-popi；
WiThe weight of corresponding random individual vector, numerical value are obtained according to the fitness value calculation of current evolutionary generation and individual.
5. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 4, which is characterized in that
Legitimacy maintenance and normalization operation are carried out to the individual nodes after variation, legitimacy maintenance is the degree of membership for guaranteeing each node
For value between [0,1], operation formula is as follows:
When the individual j in population i is when the degree of membership of corporations k is less than 0, current degree of membership is set as 0.0001；When in population i
Individual j corporations k degree of membership be greater than 1 when, current degree of membership is set as 0.9999.
6. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 4, which is characterized in that
To parameter Fi、KKi、Wi、CRiIt carries out being adaptively adjusted value, each individual can be dynamically controlled during evolution, be adjusted
Whole formula is as follows:
Wherein, fmax,tFor maximum adaptation angle value, fmin,tFor minimum fitness value, fi,tFor current fitness value.
7. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 6, which is characterized in that
Cross-species individual generates as follows:
Wherein i=1 ..., NP, j=1 ..., n；Random ∈ [0,1] is a random number；K is current corporations, com_k ∈ [1,
C] it is a randomly selected corporations from c corporations, for guaranteeing the degree of membership point for intersecting at least one corporation in individual
Cloth is from variation individual；Crossover probability factor CRi∈ [0,1] determines intersection of corporations' quantity in generation of variation individual
Shared ratio in individual corporations' quantity.
8. community structure detection method in a kind of nonoverlapping network and overlapping network according to claim 1, which is characterized in that
Clean-up operation specifically: one node i of random selection and a corporations k calculate separately neighborhood node and be averaged to corporations k
The average membership f2 of degree of membership f1 and non-neighboring domain node, formula are as follows:
Wherein, Neighbor (i) indicates the neighbor node set of node i, unode,cIndicate node node being subordinate in corporations c
Angle value, | Neighbor | it is the quantity of neighbor node, n is nodes sum,
Compare the size of f1 and f2, if f1 is greater than f2, illustrates that the neighbours of node i have more been assigned to and node i is same
Corporations, it is correct that division result, which has a possibility that larger, then, increase a fixation to degree of membership of the node i to corporations k
Value；If f1 is less than f2, reduce by a fixed value to degree of membership of the node i to corporations k.
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