CN107240026A - A kind of community discovery method suitable for noise network - Google Patents
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Abstract
The invention belongs to social networks technical field, a kind of community discovery method suitable for noise network is disclosed, including：The importance values of calculating network interior joint, establish core point set and border point set；Choose core and represent point construction prior information；Choose border and represent point construction prior information；Prior information is attached to extremal optimization process；Network is randomly divided into two roughly equal parts of nodes by topological structure, initial community structure is formed；Contribution margin of each node to community module density is calculated, the minimum node motion of contribution is carried out self-organizing optimization to another part, this self-organizing optimization process is repeated, until the block density value of network is not further added by.The intercommunal even side of two finally given is removed, until the block density value of whole network reaches maximum.The degree of accuracy that the present invention is divided with less cost-effective raising community, improves the robustness that community is divided under noisy environment.
Description
Technical field
The invention belongs to social networks technical field, more particularly to a kind of community discovery method suitable for noise network.
Background technology
Many networks in real world, such as telephone network, mail network and criminal network, due to being difficult to obtain accurate
Complete network structure information, can usually include the individual annexation of some wrong or missings, and this kind of network is referred to as to make an uproar
Sound network.The method of Most current community discovery is all that the society in network is found according to the annexation between nodes
Plot structure.Because these methods place one's entire reliance upon the topological structure of network, it is impossible to the network of noise is applicable, when making an uproar in network
During signal to noise ratio example increase, finding the ability of community content structure can decline rapidly；Under real network environment, the part that community is divided
Priori can be known.Such as, our possible known certain users belong to some community, or certain known two user
Belong to identical or different community.These prior informations are dissolved into during community is divided and carry out community discovery, can be effectively improved
The degree of accuracy that community is divided, improves the robustness that community is divided under noisy environment.However, current existing method or not giving
Go out prior information from what to come, or the random part of nodes that extracted from network forms prior information.Generally, priori is believed
Breath is to be labeled what is obtained to the node chosen from network by the expert in corresponding field.Take during such mark working expenditure
Power is, it is necessary to high cost, and the mode randomly selected is excessively blindly, obtained prior information may and without very strong finger
Lead effect, it is impossible to the quality divided with less cost-effective lifting community.
In summary, the problem of prior art is present be：Pay a price higher, obtained prior information may and not have
Very strong directive function；The network of noise can not be applicable by currently having community discovery method, find the energy of community content structure
Power can decline rapidly with the increase of noise ratio in network；When obtaining prior information, it is impossible to obtained with less cost of labor
High-quality prior information is taken, the degree of accuracy of community discovery is reduced.
The content of the invention
The problem of existing for prior art, the invention provides a kind of community discovery method suitable for noise network.
The present invention is achieved in that a kind of community discovery method suitable for noise network, described to be applied to noise net
The combination of community division method and Active Learning Method of the community discovery method of network based on extremal optimization block density；
It is close that prior information is attached to extremal optimization module by the community division method based on extremal optimization block density
In the method for degree, optimize local variable and global variable using paired constraint set, draw during optimization object function
Lead community discovery；
The Active Learning Method by from network actively choose can represent the core node of local community structure with
And the node at community boundary is configured to constraint set, high-quality prior information is generated.
Further, community of the community discovery method suitable for noise network based on extremal optimization block density is divided
Method comprises the following steps：
Step one, the importance values of calculating network interior joint, establish core point set and border point set；
Step 2, chooses core and represents point construction prior information；
Step 3, chooses border and represents point construction prior information；
Step 4, extremal optimization process is attached to by prior information；
Network, is randomly divided into two roughly equal parts of nodes by topological structure, forms initial community by step 5
Structure；
Step 6, calculates the contribution margin of each node to community module density, the minimum node motion of contribution to another
Part carries out self-organizing optimization, repeats this self-organizing optimization process, until the block density value of network is not further added by；
Step 7, removes the intercommunal even side of two finally given, then perform step 5 and step to each sub-network
Rapid six, until the block density value of whole network reaches maximum.
Further, the step one is specifically included：What the importance values of calculate node were utilized is based on degree and gathers coefficient
The comprehensive index for weighing node importance, be expressed as：
pi=f (ki)+g(ci)；
Wherein,For the degree of node i,For the coefficient that gathers of node i, EiFor between these nodes
The side number actually having；f(ki) it is to kiStandardization, its value for node i angle value and nodes minimum angle value
Difference and nodes maximum angle value and nodes minimum angle value difference ratio；g(ci) it is to ciStandardization
Processing, its value gathers the difference for gathering coefficient and the maximum collection of nodes of coefficient and node i for the maximum of nodes
The minimum of poly- coefficient and nodes gathers the ratio of the difference of coefficient.
According to given parametersDetermine that all importance values are more than given in core point set and boundary node set, network
ParameterNode constitute core point set CS, border point set BS is the node set being made up of non-core node.
Further, the step 2 is specifically included：If it is sky to represent point set RS, selected from core point set CS
The maximum node k of importance values, which is added to, to be represented in point set RS；Otherwise select and represent point set from core point set CS
The minimum node i of RS similitudes is represented a little as candidate, and the similitude between node i and set C is expressed as here：
S (i, C)=max (Sim (i, j) | j ∈ C)；
Wherein,N+iIt is to be made up of node i itself with its neighbor node
Set, Δ is yield value, here choose Δ=1；
Point construction prior information is represented for representing each pair in point set RS<i,j>, transfer to domain expert to mark it about
Beam type.
Further, the step 3 is specifically included：The selection side maximum with node i similarity from boundary node set BS
Boundary point b1, if there are multiple nodes for meeting condition, minimum the electing as of importance values is represented a little, prior information is constructed<i,
b1>, transfer to domain expert to mark its constrained type；
In the point set BS of the border selection boundary point b2 minimum with node i similarity, if there are multiple conditions that meet
Node, then represent maximum the electing as of importance values a little, construct prior information<i,b2>, transfer to domain expert to mark it and constrain class
Type.
Further, the step 4 is specifically included：The block density D global variables of network are with each node to block density
Contribution qiLocal variable is relevant, and the form of constraints is violated by punishing to mould using known paired constraint information
Block density D optimizes solution, and the general type for defining penalty is：
Wherein, α1、α2It is the coefficient of balance of punishment and reward,<i,j,w,type>∈ C represent node i and j related communities
Member relation,Represent to violate the non-negative cost constrained, CiIt is the community belonging to node i, works as Ci=CjWhen, δ (Ci,Cj)=
1, otherwise δ (Ci,Cj)=0；
The division for being unsatisfactory for constraints is punished by the way of punishment, i.e. the block density contribution margin of node i
It should reduce.Now, α in U (C) is made1=0, α2=1, therefore, the local variable q ' after optimizing with reference to prior informationiIt is expressed as：
Wherein,Represent community CiInterior node i and community CiInterior other nodes connect the number on side
Mesh,Represent community CiInterior node i and community CiThe number on the connection side of outer other nodes, | Ci| represent community CiInterior
Interstitial content；
The division for meeting constraints is rewarded by the way of reward, i.e., global variable D values should increase；Now,
Make α in U (C)1=1, α2=0, therefore, the global variable D ' after optimizing with reference to prior information is expressed as：
Wherein,Represent C1With
C2Between side number；Represent C12 times of internal edges number sum；Represent V1It is interior
Company's side sum of portion's node and external node, whereinOne division of given network G：G1(C1,E1), G2(C2,
E2) ..., Gm(Cm,Em), wherein CiAnd EiIt is Gi(i=1,2 ..., vertex set and Bian Ji m), | Ci| it is community CiInterior nodes
Number.
Further, in the step 5：Network G is randomly divided into two part G by topological structure1And G2, it is every partly to have
Roughly equal nodes, the node being connected in every part by side constitutes community, forms initial community structure.
Further, in the step 6：Calculate contribution margin q ' of each node to community module densityi, to community's mould
The minimum node motion of block density contribution carries out self-organizing optimization to another part；Every time each section is all recalculated after movement
The contribution margin of point；This self-organizing optimization process is repeated, until the block density value D ' of network is not further added by.
Further, in the step 7：The intercommunal even side of two finally given is removed, the son of some connections is obtained
Network；Step 5 and step 6 are performed to each sub-network, until the block density of whole network reaches maximum.
Another object of the present invention is to provide a kind of society of the community discovery method described in application suitable for noise network
Hand over network.
Advantages of the present invention and good effect are：
1st, semi-supervised community discovery is carried out due to prior information is dissolved into during community is divided, effective compensation noise band is come
Influence, improve noisy environment under community divide robustness.
2nd, prior information is obtained using active learning techniques, effectively lifting community can be obtained with less cost of labor and is drawn
The prior information of sub-prime amount.
3rd, the resolution ratio limitation based on modularity optimization method is overcome existing as community's valuation functions using block density
As.
The present invention is when noise ratio is respectively set to 2%, 4%, 6%, 8%, 10%, in Dolphins networks, only
10 pairs of constraint NMI values of addition can improve 1-7%, and 3-14% can be improved by adding 20 pairs of constraint NMI values；In Football networks
Also there is similar result, 2-7% can be improved by adding 10 pairs of constraint NMI values, 6-13% can be improved by adding 20 pairs of constraint NMI values.
Brief description of the drawings
Fig. 1 is the community discovery method flow chart provided in an embodiment of the present invention suitable for noise network.
Fig. 2 is the community discovery method implementation process schematic diagram provided in an embodiment of the present invention suitable for noise network.
Fig. 3 is performance evaluating figure of the present invention provided in an embodiment of the present invention on Dophins networks under different noise ratios.
Fig. 4 is performance evaluating of the present invention provided in an embodiment of the present invention on Football networks under different noise ratios
Figure.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.
Community discovery method provided in an embodiment of the present invention suitable for noise network is one and is based on extremal optimization module
The combination of the community division method of density and an Active Learning Method；Prior information is attached to extremal optimization module close
In the method for degree, optimize local variable and global variable using paired constraint set, draw during optimization object function
Lead community discovery；It can be represented at the core node and community boundary of local community structure by actively being chosen from network
Node is configured to constraint set, generates high-quality prior information.
As shown in figure 1, the community discovery method provided in an embodiment of the present invention suitable for noise network comprises the following steps：
S101：The importance values of calculating network interior joint, establish core point set and border point set；
S102：Choose core and represent point construction prior information；
S103：Choose border and represent point construction prior information；
S104：Prior information is attached to extremal optimization process；
S105：Network is randomly divided into two roughly equal parts of nodes by topological structure, initial community's knot is formed
Structure；
S106：Contribution margin of each node to community module density is calculated, the minimum node motion of contribution to another portion
Divide to carry out self-organizing optimization, this self-organizing optimization process is repeated, until the block density value of network is not further added by；
S107：The intercommunal even side of two finally given is removed, then step S105 and step are performed to each sub-network
Rapid S106, until the block density value of whole network reaches maximum.
Community discovery method provided in an embodiment of the present invention suitable for noise network specifically includes following steps：
Step 1：The importance values of calculating network interior joint, determine core point set and border point set.
Further, the importance of each node in network is assessed using a kind of node importance measurement index, according to given
Parameter, constitutes core point set, border point set is by non-core by the node that all importance values in network are more than given parameters
The node set that heart point is constituted.
Step 2：Choose core and represent point construction prior information.
Further, if representing point set is combined into sky, the node k additions that importance values are maximum are selected from core point set
To representing point set；Otherwise the minimum node i of point set similitude is selected and represents from core point set to represent as candidate
Point；
Further, point construction prior information is represented for representing each pair in point set, transfers to domain expert to mark it about
Beam type.
Step 3：Choose border and represent point construction prior information.
Further, the selection boundary point b1 maximum with node i similarity from the point set of border, multiple bar is met if existing
The node of part, then represent minimum the electing as of importance values a little, construct prior information<i,b1>, transfer to domain expert to mark it about
Beam type；
Further, the selection boundary point b2 minimum with node i similarity in the point set of border, multiple bar is met if existing
The node of part, then represent maximum the electing as of importance values a little, construct prior information<i,b2>, transfer to domain expert to mark it about
Beam type.
Step 4：Whether judgement, which has obtained prior information and reach, specifies number, and is specified number if having reached, continues executing with step
Rapid 5, otherwise, return to step 2.
Step 5：Prior information is attached to extremal optimization process.
Further, the block density (global variable) of network and each node are (local to become to the contribution of block density
Amount) it is relevant, it is close to module by the form for punishing (reward) violation (meeting) constraints using known paired constraint information
Degree optimizes solution；
Further, the division for being unsatisfactory for constraints is punished by the way of punishment, that is, reduces local variable
Value；
Further, the division for meeting constraints is rewarded by the way of reward, that is, increases the value of global variable.
Step 6：Initialization：Whole network is randomly divided into two parts, there are roughly equal nodes per part,
The node being connected in per part by side constitutes community, and material is thus formed initial community structure.
Step 7：Iteration：Excellent to carry out self-organizing to another part to the minimum node motion of community module density contribution
Change, all recalculate the contribution margin of each node after movement every time, this self-organizing optimization process is repeated, until the module of network
Density value is not further added by.
Step 8：Optimizing：The intercommunal even side of two finally given is removed, the sub-network of some connections is obtained, then it is right
Each sub-network performs step 6 and step 7, until the block density value of whole network reaches maximum.
The application principle of the present invention is further described below in conjunction with the accompanying drawings.
As shown in Fig. 2 the implementation steps of the present invention are as follows：
Step 1：The importance values of calculate node, establish core point set and border point set.
Further, what the importance values of calculate node were utilized is based on the comprehensive measurement node importance for spending and gathering coefficient
Index, be expressed as：
pi=f (ki)+g(ci)；
Wherein,For the degree of node i,For the coefficient that gathers of node i, EiFor between these nodes
The side number actually having.f(ki) it is to kiStandardization, its value for node i angle value and nodes minimum angle value
Difference and nodes maximum angle value and nodes minimum angle value difference ratio；g(ci) it is to ciStandardization
Processing, its value gathers the difference for gathering coefficient and the maximum collection of nodes of coefficient and node i for the maximum of nodes
The minimum of poly- coefficient and nodes gathers the ratio of the difference of coefficient.
Further, according to given parametersDetermine all importance values in core point set and boundary node set, network
More than given parametersNode constitute core point set CS, border point set BS is the node set being made up of non-core node.
Step 2：Selecting Representative Points from A constructs prior information from core point set.
Further, if it is sky to represent point set RS, the maximum node k of importance values is selected from core point set CS
It is added to and represents in point set RS；Otherwise the minimum node i of point set RS similitudes is selected and represented from core point set CS
Represented a little as candidate, the similitude between node i and set C is expressed as here：
S (i, C)=max (Sim (i, j) | j ∈ C)；
Wherein,N+iIt is to be made up of node i itself with its neighbor node
Set, Δ is yield value, here choose Δ=1；
Further, point construction prior information is represented for representing each pair in point set RS<i,j>, transfer to domain expert to mark
Note its constrained type.
Step 3：Selecting Representative Points from A constructs prior information from the point set of border.
Further, the selection boundary point b1 maximum with node i similarity from boundary node set BS, if existing multiple full
The node of sufficient condition, then represent minimum the electing as of importance values a little, construct prior information<i,b1>, transfer to domain expert to mark
Its constrained type；
Further, the selection boundary point b2 minimum with node i similarity in the point set BS of border, if there are multiple satisfactions
The node of condition, then represent maximum the electing as of importance values a little, construct prior information<i,b2>, transfer to domain expert to mark it
Constrained type.
Step 4：Prior information is attached to extremal optimization process.
Further, the block density D (global variable) of network and contribution q of each node to block densityiIt is (local
Variable) it is relevant, using known paired constraint information by punishing that (reward) violates the form of (meeting) constraints to module
Density D optimizes solution, and the general type of definition punishment (reward) function is：
Wherein, α1、α2It is the coefficient of balance of punishment and reward,<i,j,w,type>∈ C represent node i and j related communities
Member relation,Represent to violate the non-negative cost constrained, CiIt is the community belonging to node i, works as Ci=CjWhen, δ (Ci,Cj)=
1, otherwise δ (Ci,Cj)=0；
Further, the division for being unsatisfactory for constraints is punished by the way of punishment, i.e. the block density of node i
Contribution margin should reduce.Now, α in U (C) is made1=0, α2=1, therefore, the local variable q ' after optimizing with reference to prior informationiRepresent
For：
Wherein,Represent community CiInterior node i and community CiInterior other nodes connect the number on side,Represent community CiInterior node i and community CiThe number on the connection side of outer other nodes, | Ci| represent community CiInterior node
Number；
Further, the division for meeting constraints is rewarded by the way of reward, i.e., global variable D values should increase
Greatly.Now, α in U (C) is made1=1, α2=0, therefore, the global variable D ' after optimizing with reference to prior information is expressed as：
Wherein,Represent C1With
C2Between side number；Represent C12 times of internal edges number sum；Represent V1
Company's side sum of internal node and external node, whereinOne division of given network G：G1(C1,E1), G2
(C2,E2) ..., Gm(Cm,Em), wherein CiAnd EiIt is Gi(i=1,2 ..., vertex set and Bian Ji m), | Ci| it is community CiInternal segment
The number of point.
Step 5：Network G is randomly divided into two part G by topological structure1And G2, there is roughly equal node per part
Number, the node being connected in every part by side constitutes community, forms initial community structure.
Step 6：Calculate contribution margin q ' of each node to community module densityi, minimum to community module density contribution
Node motion carry out self-organizing optimization to another part；The contribution margin of each node is all recalculated after movement every time；Weight
This multiple self-organizing optimization process, until the block density value D ' of network is not further added by.
Step 7：The intercommunal even side of two finally given is removed, the sub-network of some connections is obtained；To every height
Network performs step 5 and step 6, until the block density of whole network reaches maximum.
The application effect of the present invention is explained in detail with reference to performance evaluating.
Performance evaluating figures of the Fig. 3 for the present invention on Dophins networks under different noise ratios.
Performance evaluating figures of the Fig. 4 for the present invention on Football networks under different noise ratios.
Dophins networks are to perching in the one wide of New Zealand Doubtful Sound straits by D.Lusseau et al.
Kiss dolphin colony and carry out what is built up to the observation of 7 years.The network includes 62 nodes and 159 sides, wherein every in network
A bottle-nosed dolphin in the individual node on behalf colony, frequently contacts while representing that two bottle-nosed dolphins of connection have.
Football networks are to the abstract structure of 2000 racing seasons American college league football match by Girvan and Newman
Network.The network includes 115 nodes and 613 sides, one football team of each node on behalf wherein in network, while representing two
Branch team carried out match during the racing season.Competed between team in same alliance relatively frequently, team between different alliances it
Between compete it is less.
It can be seen from Fig. 3 and Fig. 4 under each noise ratio of two networks, the increase of prior information can be carried significantly
The performance of high algorithm.In Dolphins networks, 1-7% can be improved by only adding 10 pairs of constraint NMI values, add 20 pairs of constraints
NMI values can improve 3-14%；Also there is similar result in Football networks, 2- can be improved by adding 10 pairs of constraint NMI values
7%, 6-13% can be improved by adding 20 pairs of constraint NMI values.
With the noise ratio increase in network, the performance for being completely dependent on the community discovery method of network topology structure can be rapid
Decline, and prior information is dissolved into during community discovery, the influence that can be come with effective compensation noise band keeps higher society
The Division degree of accuracy.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.
Claims (10)
1. a kind of community discovery method suitable for noise network, it is characterised in that send out the community suitable for noise network
The combination of existing community division method and Active Learning Method of the method based on extremal optimization block density；
Prior information is attached to extremal optimization block density by the community division method based on extremal optimization block density
In method, optimize local variable and global variable using paired constraint set, society is guided during optimization object function
Area is found；
The Active Learning Method can represent core node and the society of local community structure by actively being chosen from network
The node of area's boundary is configured to constraint set, generates high-quality prior information.
2. it is applied to the community discovery method of noise network as claimed in claim 1, it is characterised in that described to be applied to noise
Community division method of the community discovery method of network based on extremal optimization block density comprises the following steps：
Step one, the importance values of calculating network interior joint, establish core point set and border point set；
Step 2, chooses core and represents point construction prior information；
Step 3, chooses border and represents point construction prior information；
Step 4, extremal optimization process is attached to by prior information；
Network, is randomly divided into two roughly equal parts of nodes by topological structure, forms initial community structure by step 5；
Step 6, calculates contribution margin of each node to community module density, the minimum node motion of contribution to another part
To carry out self-organizing optimization, this self-organizing optimization process is repeated, until the block density value of network is not further added by；
Step 7, removes the intercommunal even side of two finally given, then performs step 5 and step 6 to each sub-network,
Until the block density value of whole network reaches maximum.
3. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that the step one is specific
Including：What the importance values of calculate node were utilized is based on the comprehensive index for weighing node importance for spending and gathering coefficient, table
It is shown as：
pi=f (ki)+g(ci)；
Wherein,For the degree of node i,For the coefficient that gathers of node i, EiFor reality between these nodes
The side number having；f(ki) it is to kiStandardization, its value for node i angle value and nodes minimum angle value difference
And the ratio of the difference of the maximum angle value of nodes and the minimum angle value of nodes；g(ci) it is to ciStandardization at
Reason, its value gathers coefficient and the difference for gathering coefficient of node i for the maximum of nodes and the maximum of nodes is gathered
The minimum of coefficient and nodes gathers the ratio of the difference of coefficient；
According to given parametersDetermine that all importance values are more than given parameters in core point set and boundary node set, networkNode constitute core point set CS, border point set BS is the node set being made up of non-core node.
4. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that the step 2 is specific
Including：If it is sky to represent point set RS, the node k for selecting importance values maximum from core point set CS is added to representative
In point set RS；Otherwise the minimum node i of point set RS similitudes is selected and represented from core point set CS as candidate's generation
Table point, here the similitude between node i and set C be expressed as：
S (i, C)=max (Sim (i, j) | j ∈ C)；
Wherein,N+iIt is the collection being made up of node i itself with its neighbor node
Close, Δ is yield value, Δ=1 is chosen here；
Point construction prior information is represented for representing each pair in point set RS<i,j>, transfer to domain expert to mark it and constrain class
Type.
5. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that the step 3 is specific
Including：The selection boundary point b1 maximum with node i similarity from boundary node set BS, if there are multiple sections for meeting condition
Point, then represent minimum the electing as of importance values a little, construct prior information<i,b1>, transfer to domain expert to mark it and constrain class
Type；
The selection boundary point b2 minimum with node i similarity in the point set BS of border, if there are multiple nodes for meeting condition,
Then maximum the electing as of importance values is represented a little, prior information is constructed<i,b2>, transfer to domain expert to mark its constrained type.
6. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that the step 4 is specific
Including：The block density D global variables of network and contribution q of each node to block densityiLocal variable is relevant, utilizes
The form that known paired constraint information violates constraints by punishing optimizes solution, definition punishment to block density D
The general type of function is：
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<mo><</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>m</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>></mo>
</mrow>
</munder>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>&delta;</mi>
<mo>(</mo>
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<mi>C</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>+</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>c</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>></mo>
</mrow>
</munder>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
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<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<msub>
<mi>&alpha;</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<mi>i</mi>
<mo>,</mo>
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<msub>
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<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
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<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>m</mi>
<mi>l</mi>
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<mo>></mo>
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</munder>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&delta;</mi>
<mrow>
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<msub>
<mi>C</mi>
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</mrow>
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<mi>w</mi>
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<mo>)</mo>
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</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>;</mo>
</mrow>
Wherein, α1、α2It is the coefficient of balance of punishment and reward, ＜ i, j, w, type ＞ ∈ C represent node i and j related communities member
Relation,Represent to violate the non-negative cost constrained, CiIt is the community belonging to node i, works as Ci=CjWhen, δ (Ci,Cj)=1, it is no
Then δ (Ci,Cj)=0；
The division for being unsatisfactory for constraints is punished by the way of punishment, i.e. the block density contribution margin of node i should subtract
It is small；Now, α in U (C) is made1=0, α2=1, therefore, the local variable q ' after optimizing with reference to prior informationiIt is expressed as：
<mrow>
<msubsup>
<mi>q</mi>
<mi>i</mi>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<msub>
<mi>q</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mrow>
<mo>(</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>m</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>></mo>
</mrow>
</munder>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>+</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>c</mi>
<mi>l</mi>
</mrow>
</msub>
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</mrow>
</munder>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
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<mi>&delta;</mi>
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<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
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<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, Represent community CiInterior node i and community CiInterior other nodes connect the number on side,Table
Show community CiInterior node i and community CiThe number on the connection side of outer other nodes, | Ci| represent community CiInterior nodes
Mesh；
The division for meeting constraints is rewarded by the way of reward, i.e., global variable D values should increase；Now, U is made
(C) α in1=1, α2=0, therefore, the global variable D ' after optimizing with reference to prior information is expressed as：
<mrow>
<msup>
<mi>D</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mi>D</mi>
<mo>+</mo>
<mrow>
<mo>(</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>v</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>m</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>></mo>
</mrow>
</munder>
<msub>
<mi>w</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>&delta;</mi>
<mo>(</mo>
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
<mo>+</mo>
<munder>
<mi>&Sigma;</mi>
<mrow>
<mo><</mo>
<msub>
<mi>v</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>v</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>c</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>></mo>
</mrow>
</munder>
<msub>
<mover>
<mi>w</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&delta;</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mi>j</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein,Represent C1And C2It
Between side number；Represent C12 times of internal edges number sum；Represent V1It is internal
Company's side sum of node and external node, whereinOne division of given network G：G1(C1,E1), G2(C2,
E2) ..., Gm(Cm,Em), wherein CiAnd EiIt is Gi(i=1,2 ..., vertex set and Bian Ji m), | Ci| it is community CiInterior nodes
Number.
7. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that in the step 5：
Network G is randomly divided into two part G by topological structure1And G2, there are roughly equal nodes per part, in every part
The node being connected by side constitutes community, forms initial community structure.
8. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that in the step 6：
Calculate contribution margin q ' of each node to community module densityi, the node motion to community module density contribution minimum to separately
A part carries out self-organizing optimization；The contribution margin of each node is all recalculated after movement every time；Repeat this self-organizing excellent
Change process, until the block density value D ' of network is not further added by.
9. it is applied to the community discovery method of noise network as claimed in claim 2, it is characterised in that in the step 7：
The intercommunal even side of two finally given is removed, the sub-network of some connections is obtained；To each sub-network perform step 5 and
Step 6, until the block density of whole network reaches maximum.
10. it is applied to the social network of the community discovery method of noise network described in a kind of application claim 1~9 any one
Network.
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