CN103605793A - Heterogeneous social network community detection method based on genetic algorithm - Google Patents

Abstract

The invention discloses a heterogeneous social network community detection method based on a genetic algorithm and the heterogeneous social network community detection method is used for mainly solving the problem that the accuracy rate of the detected community structure is obviously reduced when the social network data and relationship are large in scale in the prior art. The implementation scheme of the method comprises the following steps: constructing an adjacency matrix for describing a heterogeneous social network according to the number of nodes in the network and information of relation among the nodes; generating random symbolic coding individual according to the adjacency matrix; evaluating the advantages and disadvantages of the individuals by taking the improved modularity density as a fitness function; optimizing the individual according to the fitness function value of the individual by adopting a genetic algorithm; reducing the optimized individual with the highest fitness function value into a corresponding heterogeneous network, and decoding to obtain a partitioned community structure. The experimental result proves that the community structure of the heterogeneous social network can be effectively detected, the detection accuracy rate is high, and the method can be used for community detection of a large-scale heterogeneous social network.

Description

Isomery community network community detection method based on genetic algorithm

Technical field

The invention belongs to community network computing technique field, particularly a kind of isomery community network community detection method, can be used for the structural research to complex social system and large scale community network.

Background technology

Social system, refers to the system consisting of economic relation, political relation and cultural relations between social man and social man and social man, such as family, political party, community are all the social systems of different levels.Social system is a kind of typical complication system, can be abstracted into and process for complex network, and being about to entity in system abstract is node, by the contact of inter-entity abstract be company limit between node, obtain a community network being formed by node and Lian Bian.Complex network abstract by social system and that obtain is called community network.

Community's test problems is an important research direction of complex network, starts be in recent years subject to the extensive concern in the fields such as computer science, biology, sociology and economics and embodied certain using value.Community in complex network refers to that some are more similar each other, and has the node cluster of larger difference with other the most of node in network.The community structure of complex network show community inner connect between tight ，Er community, connect sparse.Community's testing goal of complex network is to survey and disclose the intrinsic community structure of complex network, and community structure contributes to understand and infer the 26S Proteasome Structure and Function of whole network.Community structure can be used for protein function identification, metabolic pathway prediction, web community mining, connects in the practical problemss such as prediction.

The community network generally studied is all comprised of same node, but the formation of community network is more complicated in real life, and node species may surpass a kind of.The community network that comprises more than one nodes is called isomery community network.Such as evaluating in tag system at a film, the entity of film, label, user's three types has formed whole system, a user marks and has added a label a film, is just related like this between these three kinds of entities, between corresponding node, has the limit of company; And between different user, between different films, between different labels, be do not have associated, so with not connecting limit between category node.

Community's test problems of isomery community network can be described as: the isomery community network that comprises k class entity represents by scheming G, schemes G (V, E) and is comprised of node set V and Lian Bian set E.Wherein, node set V can regard as by k category node subset V ₁, V ₂..., V _kform, between non-same category node, have to connect and with not connecting between category node.In such a isomery community network, according to the link division community between non-same category node, the community structure that makes to mark off has the non-same category node that the non-same category node in community connects between tight ，Er community and connects sparse feature.

At present, the community network community detection method proposing in existing document, the single traditional society's network of research node type mostly, mainly contain figure dividing method, spectral method and fast algorithm, the common ground of these methods is to build similarity matrix, and by solving proper vector, realizes the division of community structure.These methods are not all considered the situation of multiple node in network, and in actual applications, node diversity in community network is very common and be not allow to ignore, and therefore traditional community network community detection method cannot be applied to community's test problems of isomery community network.In addition, also have now a kind of community detection method of isomery community network, i.e. many relations clustering method, the method is that similarity is calculated in the contact based on multiple inter-entity, and according to similarity by entity division cluster.Though this method can mark off the community structure of isomery community network, yet because community network type is many, data are a large amount of, relation is complicated, there is scaling concern, along with community network data be related to the increase of scale, survey community structure accuracy and obviously reduce.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of isomery community network community detection method based on genetic algorithm is proposed, so that isomery community network data are classified or cluster, and then realize the detection of community function and prediction, be met the isomery community network community structure compared with high-accuracy.

Technical scheme of the present invention is achieved in that

For achieving the above object, performing step of the present invention is as follows:

1) the node classification in heterogeneous network is counted to the number n of k and every category node ₁, n ₂..., n _kadd up, obtain the total number n=n of nodes ₁+ n ₂+ ... + n _k; By contact details between the number of every category node and node, build the k dimension adjacency matrix A that describes isomery community network, the size of A is n ₁* n ₂* n _k;

2) make the big or small pn=50 of initial population, according to the total number n of node, produce at random the individuality of pn symbolization coding, with these individual initial population p that forms ₀; Crossover probability pc=0.8 is set, variation Probability p m=0.2, first initial algebra g ₀=1, maximum algebraically mg=50, current algebraically g=g ₀, make g godfather for population p _gequal initial population p ₀, i.e. p _g=p ₀;

3) calculate g godfather for population p _gin each individual fitness function value D:

$D=\underset{c=1}{\overset{m}{\mathrm{\Σ}}}\frac{L\left(V^c\right)-L\left({\stackrel{\‾}{V}}^c\right)}{\left|V^c\right|}-\frac{L\left(V\right)}{n},$

In formula, m is the genic value kind number in individuality, V ¹, V ²..., V ^mbe the node set of m community being obtained by individuality, V is all node set, i.e. V=V in network ¹∪ V ²∪ ... ∪ V ^m,

node set V ^cdifference set in V,

1≤c≤m, | V ^c| be the V of community ^cin node number, L (V ^c) be c the company's edge strip number in community,

be from c community, to be connected to c the company's edge strip number in community, L (V) always connects edge strip number in network;

4) according to g godfather for population p _gin each individual fitness function value D, to g godfather for population p _gcarry out elite's reservation operations and algorithm of tournament selection operation, the g godfather after being upgraded is for population p _g';

5) produce at random the first random number rand ₁, and to the first random number rand ₁pc compares with crossover probability, if rand ₁<pc, carries out the 6th) step; Otherwise, obtain with upgrade after g godfather for population p _g' g that equates is for progeny population chp _g, i.e. chp _g=p _g', carry out the 7th) step;

6) to the g godfather after upgrading for population p _g' carry out single channel interlace operation, obtain g for progeny population chp _g;

7) to g for progeny population chp _gin each individual R carry out mutation operation, the g after being upgraded is for progeny population chp _g';

8) make current algebraically g=g+1, current algebraically g and maximum algebraically mg are compared, if g≤mg, the parent population p in g generation _gwith upgrade after g-1 for progeny population chp _g-1' equate i.e. p _g=chp _g-1', return to step 3); Otherwise, perform step 9);

9) get g-1 after renewal for progeny population chp _g-1' the middle the highest individuality of fitness function value, this individuality is reduced into corresponding heterogeneous network, the community structure that decoding obtains marking off.

The present invention has the following advantages compared with prior art:

1. the present invention is directed to the feature of isomery community network, designed the fitness function of weighing isomery community network community structure quality, not only solved conventional module density function and can not weigh the problem of heterogeneous network community structure quality, and guaranteed that the community structure of using the present invention to obtain has higher accuracy.

2. the mutation operation of the present invention's design has local search ability, makes evolutionary process easily jump out local optimum, has not only improved efficiency of evolution, and can efficiently obtain optimum solution.

3. with respect to existing heterogeneous network community detection method, the present invention can obtain the community structure that accuracy is higher to the test of user-commodity network.

Experimental result shows, the community detection method based on genetic algorithm that the present invention proposes can effectively detect the community structure of heterogeneous network.

Accompanying drawing explanation

Fig. 1 is the general flow chart of realizing of the present invention;

Fig. 2 is the mutation operation sub-process figure in the present invention;

Fig. 3 is user-commodity network topological diagram that emulation of the present invention is used;

Fig. 4 is the adjacency matrix schematic diagram of describing user-commodity network;

Fig. 5 is to the detected community structure schematic diagram of user-commodity network with the present invention.

Embodiment

For the present invention being known to user-commodity network topological diagram that Fig. 3 provides is take in description, this example, be example, but do not form any limitation of the invention, the present invention goes for all isomery community networks.

With reference to Fig. 1, implementation step of the present invention is as follows:

Node classification in step 1. pair heterogeneous network is counted the number n of k and every category node ₁, n ₂..., n _kadd up, obtain the total number n=n of nodes ₁+ n ₂+ ... + n _k.

As described in Figure 3, it is user-commodity heterogeneous network to the heterogeneous network of this example.In this network, have 2 kinds of nodes, node classification is counted k=2, the 1st category node representative of consumer wherein, and the 2nd category node represents commodity, the square in figure represents the 1st category node, has 50, i.e. n ₁=50, circle represents the 2nd category node, has 50, i.e. n ₂=50, the total number of node in network is 100, i.e. n=100;

Step 2. builds the k dimension adjacency matrix A that describes isomery community network by contact details between the number of every category node and node.

2a) according to the every category node number n in network ₁, n ₂..., n _k, the size of setting adjacency matrix A is n ₁* n ₂* n _k;

In the heterogeneous network of this example, the 1st category node number n ₁be 50, the 2 category node number n ₂be 50, setting 2 dimension adjacency matrix A sizes is 50 * 50;

2b) according to the contact details between nodes, determine the value of each element in adjacency matrix A:

If the 1st category node v in network _i1, the 2nd category node v _i2..., k category node v _ikbetween mutually have connection, between this k node, have limit to be connected, the elements A (i in corresponding adjacency matrix ₁, i ₂..., i _k)=1,

If the 1st category node v _i1, the 2nd category node v _i2..., k category node v _ikbetween be not mutually to have connection, between this k node, do not have limit to be connected, the elements A (i in corresponding adjacency matrix ₁, i ₂..., i _k)=0, wherein 1≤i ₁≤ n ₁, 1≤i ₂≤ n ₂..., 1≤i _k≤ n _k;

In this example, if the i in user-commodity heterogeneous network ₁individual user is to i ₂individual commodity have a purchaser record, A (i ₁, i ₂)=1; If the i in user-commodity heterogeneous network ₁individual user is to i ₂individual commodity do not have purchaser record, A (i ₁, i ₂)=0, wherein 1≤i ₁≤ 50,1≤i ₂≤ 50, as shown in Figure 4.In Fig. 4, horizontal ordinate represents the 1st category node label, and ordinate represents the 2nd category node label, and in figure, stain represents that the element value that transverse and longitudinal coordinate is corresponding is 1.

Step 3. makes the big or small pn=50 of initial population, produces at random the individuality of pn symbolization coding according to the total number n of node, with these individual initial population p that forms ₀.

The individuality that above-mentioned symbolic coding obtains, refers to each individual R=(r ₁, r ₂..., r _i..., r _n) in each gene r _iget at random the integer between 1 to n, wherein, 1≤i≤n, i genic value r _irepresent i node v _icommunity's label at place.

In the heterogeneous network of this example, symbolization coding produces 50 individualities, wherein each individual R=(r ₁, r ₂..., r _i..., r ₁₀₀) in each gene r _iget at random the integer between 1 to 100, wherein, 1≤i≤100.

Step 4. arranges crossover probability pc=0.8, variation Probability p m=0.2, first initial algebra g ₀=1, maximum algebraically mg=50, current algebraically g=g ₀, make g godfather for population p _gequal initial population p ₀, i.e. p _g=p ₀;

Step 5. is calculated g godfather for population p _gin each individual fitness function value D:

5a) according to g godfather for population p _gin individuality, obtain m genic value kind in individuality, obtain m the node set in community simultaneously and be: V ¹, V ²..., V ^c, V ^m, 1≤c≤m; The all node set that obtained in network by the union of m node set are V, i.e. V=V ¹∪ V ²∪ ... ∪ V ^m, wherein ∪ is union operational symbol, according to c node set V ^cwith all node set V, obtain c node set V ^cdifference set in all node set V is ${\stackrel{\&OverBar;}{V}}^c,$ ? ${\stackrel{\&OverBar;}{V}}^c=V-V^c;$

5b) according to adjacency matrix A, calculate c the company's edge strip in community and count L (V ^c):

$L\left(V^c\right)=\underset{{\mathrm{<figure-callout\; id="1"\; label="v\; i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,{\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{ik}}{\&Element;V}^c}{\mathrm{\&Sigma;}}A({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,i_k);$

5c) according to adjacency matrix A, calculate company's edge strip number that Cong Ge c community is connected to other communities except c community in network

$L\left({\stackrel{\&OverBar;}{V}}^c\right)=\underset{{\mathrm{<figure-callout\; id="1"\; label="v\; i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,{\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{ik}}}{\mathrm{\&Sigma;}}A({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,i_k),$

Wherein, k node v _i1, v _i2..., v _ikin have a node at least at c node set V ^cin, at least separately there is a node at c node set V ^cdifference set in all node set V in;

5d) according to adjacency matrix A, the edge strip that always connects calculating in network is counted L (V):

$L\left(V\right)=\underset{{\mathrm{<figure-callout\; id="1"\; label="v\; i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,{\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{ik}}\&Element;V}{\mathrm{\&Sigma;}}A({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,i_k);$

5e) according to the company's edge strip in above-mentioned c the community calculating, count L (V ^c), from c community, be connected to company's edge strip number of other communities except c community network

count L (V) with the edge strip that always connects in network, calculate g godfather for population p _gin each individual corresponding fitness function value D:

$D=\underset{c=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{L\left(V^c\right)-L\left({\stackrel{\&OverBar;}{V}}^c\right)}{\left|V^c\right|}-\frac{L\left(V\right)}{n},$

Wherein, | V ^c| be c node set V ^cin node number.

Step 6. according to g godfather for population p _gin each individual fitness function value D, to g godfather for population p _gcarry out elite's reservation operations and algorithm of tournament selection operation, the g godfather after being upgraded is for population p _g'.

In the prior art, the selection operation of genetic algorithm has elite's reservation operations, roulette to select operation, algorithm of tournament selection operation, random ergodic select operation and block and select operation etc., because elite's reservation operations wherein can make classic individuality in parent population preserve, and algorithm of tournament selection operation can make the parent population obtaining after operation have more much higher sample, so the present invention has adopted elite's reservation operations and algorithm of tournament selection operation.

Concrete is described below:

6a) establishing new population pnew is empty set, carries out elite's reservation operations 1 time, is about to parent population p _gthe individuality of middle fitness function value maximum is put into new population pnew;

6b) carry out pn-1 algorithm of tournament selection operation, at parent population p _gin choose at random two individualities, relatively these two individual fitness function values sizes, put into new population pnew by the larger individuality of fitness function value;

6c) the g godfather after order renewal is for population p _g' equal new population pnew, i.e. p _g'=pnew.

The random first random number rand that produces of step 7. ₁, and to the first random number rand ₁pc compares with crossover probability, if rand ₁<pc, performs step 8; Otherwise, obtain with upgrade after g godfather for population p _g' g that equates is for progeny population chp _g, i.e. chp _g=p _g', perform step 9.

G godfather after step 8. pair renewal is for population p _g' carry out single channel interlace operation, obtain g for progeny population chp _g.

In prior art, the interlace operation of genetic algorithm has single-point interlace operation, multiple spot interlace operation, uniform crossover operator, discrete interlace operation and single channel interlace operation etc., due to single channel wherein, intersecting is a kind of interlace operation that is more suitable for symbolic coding individuality, so the present invention has adopted single channel interlace operation.

The concrete operations that single channel is intersected are as follows:

8a) establish iterations q=1, establish g for progeny population chp _gfor empty set;

8b) random g godfather after renewal is for population p _g' two individual R of middle selection ₁and R ₂, and by R ₁individual as source, by R ₂individual as object, for example, suppose the total number n=5 of nodes, random g godfather after renewal is for population p _g' two individual R of middle selection ₁=(3,2,4,4,2) and R ₂=(4,1,3,4,1), by R ₁individual as source, by R ₂individual as object;

8c) be chosen at random the integer i between 1 to n, establish genes of interest value e and equal the individual R in source ₁in i genic value r ¹ _i, i.e. e=r ¹ _i, establishing nodal scheme set U is empty set, the individual R of reference source ₁in each genic value r ¹ _jwith genes of interest value e, if r ¹ _j=e, puts into nodal scheme set U by nodal scheme j, obtains nodal scheme set V to be changed ^e=U, wherein 1≤j≤n, chooses the integer i being chosen between 1 to 5 at random, obtains i=3; If genes of interest value e equals the individual R in source ₁in the 3rd genic value r ¹ ₃, i.e. e=r ¹ ₃, e=4, establishing nodal scheme set U is empty set, the individual R of reference source ₁in each genic value r ¹ _jwith genes of interest value e, the individual R in source ₁the node that middle genic value equals genes of interest value e is the 3rd and the 4th, nodal scheme 3 and 4 is put into set U, obtains nodal scheme set V to be changed ⁴=U;

8d) for nodal scheme set V to be changed ^ein each nodal scheme j, by the individual R of object ₂j genic value r of middle correspondence ² _jchange into genes of interest value e, i.e. r ² _j=e, the new individual R after being intersected ₂', by new individual R ₂' put into g for progeny population chp _gin, for nodal scheme set V to be changed ⁴in each nodal scheme 3 and 4, by R ₂the 3rd of middle correspondence and the 4th genic value are all changed into genes of interest value e, i.e. R ₂in r ² ₃=e, r ² ₄=e, the new individual R after being intersected ₂'=(4, Isosorbide-5-Nitrae, 4,1), by new individual R ₂' put into g for progeny population chp _gin;

8e) make q=q+1, compare iterations q and parent Population Size np, if q≤np returns to step 8b); Otherwise, finish to carry out.

Step 9. couple g is for progeny population chp _gin each individual R carry out mutation operation, the g after being upgraded is for progeny population chp _g'.

With reference to Fig. 2, the specific descriptions of this step are as follows:

9a) establish iterations q=1;

9b) produce at random the second random number rand ₂m compares with variation Probability p, if rand ₂<pm, forwards step 9c to); Otherwise, forward step 9f to);

9c) establishing genic value set L is empty set, by adjacency matrix A, is obtained and q node v _qeach the node v that has connection _j, by each node v _jj genic value r of correspondence in individual R _jput into genic value set L, 1≤j≤n wherein, establishing maximum localized mode lumpiness max is minus infinity, i.e. max=-∞;

9d) for each the genic value r in genic value set L _j, suppose q genic value r in individual R _qequal genic value r _j, calculate r under this supposed situation _jthe localized mode lumpiness f of individual community _rj, and compare r _jthe localized mode lumpiness function f of individual community _rjwith maximum localized mode lumpiness max, if f _rj>max, makes max=f _rj, order obtains the label l of community of maximum localized mode lumpiness _q=r _j;

Wherein, r _jthe localized mode lumpiness f of individual community _rjcomputing formula is as follows:

$f_{r_j}=\underset{{\mathrm{<figure-callout\; id="1"\; label="v\; i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,{\mathrm{<figure-callout\; id="2"\; label="v\; i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{it}},\&CenterDot;\&CenterDot;\&CenterDot;v_{\mathrm{ik}}{V}^{r_j}}{\mathrm{\&Sigma;}}(A({\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="20131065189311000031.png"\; state="\{\{state\}\}">i</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">i</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,i_t,\&CenterDot;\&CenterDot;\&CenterDot;,i_k)-\frac{d_{i1}{\mathrm{<figure-callout\; id="2"\; label="d\; i"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">d</figure-callout>}}_i\&CenterDot;\&CenterDot;\&CenterDot;d_{\mathrm{it}}\&CenterDot;\&CenterDot;\&CenterDot;d_{\mathrm{ik}}}{{\left(2\right|V\left|\right)}^{k-1}}),$

In formula, V ^rjbe r _jnode set in individual community, 1≤c≤n wherein, d _itfor node v _itdegree, be connected to node v _itcompany's limit number, 1≤i wherein _t≤ n _t, 1≤t≤k, | V| always connects limit number in network;

If each genic value r 9e) in genic value set L _jcorresponding localized mode lumpiness f _rjall calculate completely, make q genic value r in individual R _qequal to obtain the label l of community of maximum localized mode lumpiness _q, i.e. r _q=l _q, execution step 9f); Otherwise, return to step 9d);

9f) make q=q+1, and compare iterations q and the total number n of node, if q≤n returns to step 9b); Otherwise, finish to carry out.

Step 10. makes current algebraically g=g+1, current algebraically g and maximum algebraically mg is compared, if g≤mg makes the g parent population p in generation _gwith upgrade after g-1 for progeny population chp _g-1' equate i.e. p _g=chp _g-1', return to step 5; Otherwise, perform step 11.

Step 11. is got g-1 after renewal for progeny population chp _g-1' the middle the highest individuality of fitness function value, this individuality is reduced into corresponding heterogeneous network, the community structure that decoding obtains marking off.

Effect of the present invention can be verified by following emulation experiment:

1. test running environment and evaluation criterion

The environment of experiment operation: processor is Intel (R) Core (TM) 2Duo CPU E6550 2.33GHz, inside saves as 1.99GB, and hard disk is 120G, and operating system is Microsoft windows7, and programmed environment is MATLAB7.13.

The community structure quality that this experimental selection normalized mutual information NMI comes evaluation experimental method to detect as the evaluation criterion of community structure:

$\mathrm{NMI}=\frac{H\left(C_0\right)+H\left(C_e\right)-H({\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="HDA0000431226200000032.png"\; state="\{\{state\}\}">C</figure-callout>}}_0,C_e)}{\sqrt{H\left(C_0\right)H\left(C_e\right)}},$

In above formula, C ₀represent real community structure, C _erepresent that experiment detects the community structure obtaining, H (C) represents the shannon entropy of community structure C.If community structure and Fiel's plot structure that experiment is found are on all four, the value of NMI is maximal value 1; If community structure and Fiel's plot structure that experiment is found are completely independently, the value of NMI is minimum value 0.

2. experiment content and interpretation of result

Emulation one, carries out community structure detection by the inventive method to the user-commodity network shown in Fig. 3, and as shown in Figure 5, in Fig. 5, the representative of the node of different gray scales is in different communities for testing result.

As can be seen from Figure 5, in user-commodity isomery community network, 3 communities have been detected.From the contrast of Fig. 5 and Fig. 3, can find out, the community structure that obtains of experiment can make to connect closely non-similar node division in same community, and makes to connect sparse non-similar node division in different communities.

Utilize above-mentioned evaluation criterion to calculate the present invention and normalized mutual information value NMI corresponding to community structure detected ₁, obtain NMI ₁=1, i.e. the community structure that the present invention detects has very high accuracy.Therefore the present invention is a kind of effective community detection method.

Emulation two, user-commodity network that the Multicomm method that adopts the people such as Xutao Li to propose represents Fig. 3 carries out community's detection, and utilizes above-mentioned evaluation criterion calculating Multicomm method normalized mutual information value NMI corresponding to community structure to be detected ₂, obtain NMI ₂=0.9315.

The normalized mutual information NMI that Multicomm method is obtained ₂=0.9315 normalized mutual information NMI obtaining with the present invention ₁=1 compares, and found that the community structure that the present invention detects has higher accuracy, and experiment effect of the present invention is better than Multicomm method.

Claims (6)

1. the isomery community network community detection method based on genetic algorithm, comprises the steps:

1) the node classification in heterogeneous network is counted to the number n of k and every category node ₁, n ₂..., n _kadd up, obtain the total number n=n of nodes ₁+ n ₂+ ... + n _k; By contact details between the number of every category node and node, build the k dimension adjacency matrix A that describes isomery community network, the size of A is n ₁* n ₂* n _k;

2) make the big or small pn=50 of initial population, according to the total number n of node, produce at random the individuality of pn symbolization coding, with these individual initial population p that forms ₀; Crossover probability pc=0.8 is set, variation Probability p m=0.2, first initial algebra g ₀=1, maximum algebraically mg=50, current algebraically g=g ₀, make g godfather for population p _gequal initial population p ₀, i.e. p _g=p ₀;

3) calculate g godfather for population p _gin each individual fitness function value D:

$D=\underset{c=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{L\left(V^c\right)-L\left({\stackrel{\&OverBar;}{V}}^c\right)}{\left|V^c\right|}-\frac{L\left(V\right)}{n},$

In formula, m is the genic value kind number in individuality, V ¹, V ²..., V ^mbe the node set of m community being obtained by individuality, V is all node set, i.e. V=V in network ¹∪ V ²∪ ... ∪ V ^m,

node set V ^cdifference set in V,

1≤c≤m, | V ^c| be the V of community ^cin node number, L (V ^c) be c the company's edge strip number in community,

shi Congge c community is connected to company's edge strip number of other communities except c community in network, and L (V) always connects edge strip number in network;

4) according to g godfather for population p _gin each individual fitness function value D, to g godfather for population p _gcarry out elite's reservation operations and algorithm of tournament selection operation, the g godfather after being upgraded is for population p _g';

5) produce at random the first random number rand ₁, and to the first random number rand ₁pc compares with crossover probability, if rand ₁<pc, carries out the 6th) step; Otherwise, obtain with upgrade after g godfather for population p _g' g that equates is for progeny population chp _g, i.e. chp _g=p _g', carry out the 7th) step;

6) to the g godfather after upgrading for population p _g' carry out single channel interlace operation, obtain g for progeny population chp _g;

7) to g for progeny population chp _gin each individual R carry out mutation operation, the g after being upgraded is for progeny population chp _g';

8) make current algebraically g=g+1, current algebraically g and maximum algebraically mg are compared, if g≤mg, the parent population p in g generation _gwith upgrade after g-1 for progeny population chp _g-1' equate i.e. p _g=chp _g-1', return to step 3); Otherwise, perform step 9);

9) get g-1 after renewal for progeny population chp _g-1' the middle the highest individuality of fitness function value, this individuality is reduced into corresponding heterogeneous network, the community structure that decoding obtains marking off.

2. the isomery community network community detection method based on genetic algorithm as claimed in claim 1, wherein the number between the every category node of the use described in step 1) and contact details build the k dimension adjacency matrix A that describes isomery community network, according to following rule, carry out:

If the 1st category node v _i1, the 2nd category node v _i2..., k category node v _ikbetween mutually have connection, between this k node, have limit to be connected, the elements A (i in corresponding adjacency matrix ₁, i ₂..., i _k)=1, wherein 1≤i ₁≤ n ₁, 1≤i ₂≤ n ₂..., 1≤i _k≤ n _k;

If the 1st category node v _i1, the 2nd category node v _i2..., k category node v _ikbetween be not mutually to have connection, between this k node, do not have limit to be connected, the elements A (i in corresponding adjacency matrix ₁, i ₂..., i _k)=0.

3. the isomery community network community detection method based on genetic algorithm as claimed in claim 1, wherein step 2) described according to the total number n of node, produce at random the individuality that pn symbolization encoded, refer to each individual R=(r ₁, r ₂..., r _i..., r _n) in each gene r _iget at random the integer between 1 to n, wherein, 1≤i≤n, i genic value r _irepresent i node v _icommunity's label at place.

4. the isomery community network community detection method based on genetic algorithm as claimed in claim 1, wherein described in step 4) to g godfather for population p _gcarry out elite's reservation operations and algorithm of tournament selection operation, carry out in accordance with the following steps:

4a) establishing new population pnew is empty set, carries out elite's reservation operations 1 time, is about to parent population p _gthe individuality of middle fitness function value maximum is put into new population pnew;

4b) carry out pn-1 algorithm of tournament selection operation, at parent population p _gin choose at random two individualities, relatively these two individual fitness function values sizes, put into new population pnew by the larger individuality of fitness function value;

4c) the g godfather after order renewal is for population p _g' equal new population pnew, i.e. p _g'=pnew.

5. the isomery community network community detection method based on genetic algorithm as claimed in claim 1, wherein described in step 6) to the g godfather after upgrading for population p _g' carry out single channel interlace operation, carry out in accordance with the following steps:

5a) establish iterations q=1, establish g for progeny population chp _gfor empty set;

5b) random g godfather after renewal is for population p _g' two individual R of middle selection ₁and R ₂, and by R ₁individual as source, by R ₂individual as object;

5c) be chosen at random the integer i between 1 to n, establish genes of interest value e and equal the individual R in source ₁in i genic value r ¹ _i, i.e. e=r ¹ _i, establishing nodal scheme set U is empty set, the individual R of reference source ₁in each genic value r ¹ _jwith genes of interest value e, if r ¹ _j=e, puts into nodal scheme set U by nodal scheme j, obtains nodal scheme set V to be changed ^e=U, wherein 1≤j≤n;

5d) for nodal scheme set V to be changed ^ein each nodal scheme j, by the individual R of object ₂j genic value r of middle correspondence ² _jchange into genes of interest value e, i.e. r ² _j=e, the new individual R after being intersected ₂', by new individual R ₂' put into g for progeny population chp _gin;

5e) make q=q+1, compare iterations q and parent Population Size np, if q≤np returns to step 5b); Otherwise, finish to carry out.

6. the isomery community network community detection method based on genetic algorithm as claimed in claim 1, wherein step 7) described to g for progeny population chp _gin each individual R carry out mutation operation, carry out in accordance with the following steps:

6a) establish iterations q=1;

6b) produce at random the second random number rand ₂m compares with variation Probability p, if rand ₂<pm, forwards step 6c to); Otherwise, forward step 6f to);

6c) establishing genic value set L is empty set, by adjacency matrix A, is obtained and q node v _qeach the node v that has connection _j, by each node v _jj genic value r of correspondence in individual R _jput into genic value set L, wherein 1≤j≤n, is made as minus infinity by maximum localized mode lumpiness max, i.e. max=-∞;

6d) to each the genic value r in genic value set L _j, suppose q genic value r in individual R _qequal genic value r _j, calculate r under this supposed situation _jthe localized mode lumpiness f of individual community _rj, and compare r _jthe localized mode lumpiness letter f of individual community _rjwith maximum localized mode lumpiness max, if f _rj>max, makes max=f _rj, order obtains the label l of community of maximum localized mode lumpiness _q=r _j;

Wherein, r _jthe localized mode lumpiness f of individual community _rjcomputing formula is as follows:

$f_{r_j}=\underset{v_{i1},v_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{it}},\&CenterDot;\&CenterDot;\&CenterDot;v_{\mathrm{ik}}{V}^{r_j}}{\mathrm{\&Sigma;}}(A(i_1,i_2,\&CenterDot;\&CenterDot;\&CenterDot;,i_t,\&CenterDot;\&CenterDot;\&CenterDot;,i_k)-\frac{d_{i1}{d}_{i2}\&CenterDot;\&CenterDot;\&CenterDot;d_{\mathrm{it}}\&CenterDot;\&CenterDot;\&CenterDot;d_{\mathrm{ik}}}{{\left(2\right|V\left|\right)}^{k-1}}),$

In formula, V ^rjbe r _jthe node set of individual community, 1≤c≤n wherein, d _itfor node v _itdegree, be connected to node v _itcompany's limit number, 1≤i wherein _t≤ n _t, 1≤t≤k, | V| always connects limit number in network;

If each genic value r 6e) in genic value set L _jcorresponding localized mode lumpiness f _rjall calculate completely, make q genic value r in individual R _qequal to obtain the label l of community of maximum localized mode lumpiness _q, i.e. r _q=l _q, execution step 6f); Otherwise, return to step 6d);

6f) make q=q+1, and compare iterations q and the total number n of node, if q≤n returns to step 6b); Otherwise, finish to carry out.

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