CN109902728A - A kind of fast community discovery method and system based on Average Mutual - Google Patents
A kind of fast community discovery method and system based on Average Mutual Download PDFInfo
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Abstract
The invention discloses a kind of, and the fast community based on Average Mutual finds method and system, the method includes the steps: the affiliated community of node is initialized according to community's partition request；It obtains all community's groups that there is connection in Exist Network Structure and is merged into capable traversal；It calculates Average Mutual value and modularity incremental value when the community Liang Ge merges, the revised Average Mutual value of weighting and is recorded；If the maximum community's combination of revised Average Mutual value that selection calculates when the community's combination traversal that there is connection in Exist Network Structure finishes merges；It calculates and records the Average Mutual value in this community's partition process；Above step is repeated until selecting community division result corresponding to the maximum value of the Average Mutual of record when all nodes belong to same community in current network as final community division result and exporting.Community division result provided by the invention is closer to true division result and community divides speed faster.
Description
Technical field
The present invention relates to communities to divide quality evaluation field, and in particular to a kind of fast community hair based on Average Mutual
Existing method and system.
Background technique
With the fast development of internet, technology of Internet of things, the connection between things is even closer, complicated connection
Various, changeable, in large scale network is formd, such network is referred to as complex network.So-called community, which refers to, has association
Individual composed by set, complex network is made of several communities.Community, which divides, is related to computer, physics, biology, sociology
And complex system science etc. is multidisciplinary, becomes one of the research hotspot of multiple subjects in recent years.In community divides, community
Dividing system would generally construct and judge a variety of community structures, and develop from a kind of community structure to another community structure.It is excellent
The key for changing community's dividing system is to find a kind of community's division quality evaluating method, passes through the evaluation method and optimizes community's division
System, to improve the accuracy of community's dividing system.But the thinking for dividing quality evaluating method to community at present is mainly gone back
It is to concentrate on modularity evaluation method, and modularity evaluation method has Resolution limit.Although Ye You society
Division quality evaluating method is the relevant knowledge based on information theory, but the evaluation method in terms of using based on information theory
When, need to know some priori conditions.
Summary of the invention
In view of the deficiencies of the prior art, it is an object of the present invention to provide a kind of, and the fast community based on Average Mutual is sent out
Existing method, the method divide the angle of quality evaluation, from community for existing classical community dividing system with average
Based on mutual information, optimal community is found out during hierarchical clustering using the algorithm and merges selection, effectively improves society
The speed and accuracy of Division.The invention also discloses a kind of simultaneously, and the fast community based on Average Mutual finds system.
The specific technical solution of the present invention are as follows:
A kind of fast community discovery method based on Average Mutual, comprising the following steps:
S1, server receive community's partition request；
S2, the initialization affiliated community of node, distribute unique community for each node；
S3, all community's combinations that there is connection in Exist Network Structure are obtained；
S4, it is traversed since the combination of starting community is selected in community's combination；
Average Mutual value I when S5, the merging of the calculating community Liang GepWith modularity increment value Δ Q, calculate after weighting amendment
Average Mutual value CIpAnd it is recorded；
If the community's combination traversal that there is connection in S6, Exist Network Structure finishes, step S7 is carried out, is otherwise selected
Next community's group merges return step S5；
The revised Average Mutual value CI calculated in S7, selection step S6pMaximum community's combination merges；
S8, it calculates and records the Average Mutual value in this community's partition process；
If all nodes belong to same community in S9, current network, step S10 is carried out, otherwise return step S3；
S10, select community division result corresponding to the maximum value of the Average Mutual recorded in step S8 as final society
Division result simultaneously exports.
Further, the concrete operations of the affiliated community of node are initialized described in step S2 are as follows: each node is arranged
For a community, that is, community's number is equal to node number after initializing.
Further, the detailed process of the step S3 are as follows: find out all community's combinations for meeting community and merging condition, i.e.,
Only there is the community Liang Ge of connection to be possible to carry out community's merging in current network, if not connected before the community Liang Ge,
It can not carry out community's merging.
Further, in step S5, the Average Mutual value IPCalculation formula are as follows:
Wherein, XiIndicate i-th of community in community structure X, YjIndicate j-th of community in community structure Y, I (Xi；
Yj) indicate community XiWith community YjAverage Mutual value, ωijIndicate XiCommunity and YjThe relevance of community；
The calculation formula of the modularity increment value Δ Q are as follows:
Δ Q=(eji+eij-2ai*aj(the e of)=2ij-2ai*aj),
Wherein ai=∑jeijIndicate the ratio when accounting for all being connected with community's i interior joint；aj=∑iejiExpression and society
The connected ratio when accounting for all of area's j interior joint；eijA node is indicated in community i, another node is in community j
The quantity on side；ejiA node is indicated in community j, the quantity on side of another node in community i is equal to eij。
The revised Average Mutual value CIpCalculation formula are as follows:
CIp=β Ip+ (1- β) Δ Q,
Wherein, C is identifier, indicates that the Average Mutual value is revised value；β is parameter preset, indicates community
When merging consider nodal information number, β is bigger, then it represents that consider that the nodal information of community is more, consider community connection letter
It ceases fewer；The preset value value range of β is 0~1, is needed in actual use according to specific community's nodal information and link information
Consider that weight is set.
Further, in step S7, Average Mutual value CI after selection amendmentpWhen maximum community's combination merges,
Since Average Mutual value considers nodal information and link information in complex network after amendment, can select at this time most
Excellent community's combination merges.
Further, the detailed process of step S9 are as follows: judge whether the node in current network belongs to same community, if
Then show that all the points have all merged into a community in community, that is, complete hierarchical clustering process.
A kind of system for realizing a kind of fast community discovery method based on Average Mutual, the system
Including client and server, wherein server is comprised the following modules:
Request receiving module: for receiving community's partition request of client transmission；
Community's merging module: for carrying out community's merging to the community Liang Ge, community's amalgamation result is obtained；
It calculates Average Mutual value module: for calculating the Average Mutual value calculated when the community Liang Ge merges, being put down
Equal association relationship result；
Computing module degree incremental value module: it is used for computing module degree incremental value, obtains modularity incremental value result；
It calculates Average Mutual value module after correcting: for Average Mutual value after calculating amendment, obtaining revised flat
Equal association relationship result；
Output module: community division result corresponding to the maximum value of the Average Mutual for that will record is as final community
Division result is simultaneously sent to client.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1, the present invention in community's dividing system by introducing the fast community partitioning algorithm based on Average Mutual, the calculation
Method is the coagulation type community detection algorithm based on hierarchical clustering, can be by two in network in community's partition process each time
Community merges, i.e., the community structure X and community structure Y after community's division before community divides has direct correlation.In community
Judged in partition process using the revised Average Mutual value of module angle value, Average Mutual value is maximum after selection amendment
The community Liang Ge merge.Above step is repeated until node all in network belongs to the same community, selection is simultaneously defeated
Average Mutual value I outpCommunity division result corresponding to maximum value is the community division result of AMI-FD algorithm.
2, the present invention has found method using the fast community based on Average Mutual, and the algorithm is relative to other community discoveries
For method, community division result is closer to true division result and community divides speed faster.
Detailed description of the invention
Fig. 1 is that the fast community based on Average Mutual of the embodiment of the present invention finds the flow chart of method.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment:
The embodiment of the present invention joined on the basis of the coagulation type community discovery method based on hierarchical clustering based on average
Community's merging method of mutual information.The affiliated community of node is initialized first, distributes unique community for each node；It obtains current
All community's groups that there is connection merge in network structure is traversed since the combination of starting community is selected in community's combination: being calculated
Average Mutual value I when the community Liang Ge mergesp, modularity increment value Δ Q and the revised Average Mutual value CI of weightingpAnd
It is recorded；The maximum community's combination of Average Mutual value merges after selection amendment, calculates and records the division of this community
Average Mutual value in the process；Above step is repeated until all nodes belong to same community in current network, selection is average
Community division result corresponding to mutual information maximum value is as final community division result and exports.
The embodiment of the present invention is additionally provided with a kind of fast community discovery system based on Average Mutual, the system packet
Client and server is included, wherein server comprises the following modules: request receiving module: for receiving the community of client transmission
Partition request；Community's merging module: for carrying out community's merging to the community Liang Ge, community's amalgamation result is obtained；It calculates average mutual
Value of information module: for calculating Average Mutual value, mutual information result is obtained；Computing module angle value module: average for calculating
Association relationship obtains module angle value result；Calculate Average Mutual value module after correcting: for Average Mutual after calculating amendment
Value, obtains mutual information result；Output module: for final community division result to be sent to client.
Below to it is provided in an embodiment of the present invention it is a kind of based on Average Mutual fast community discovery method and system do
It is described in detail.
Firstly, we provide as follows to relational language involved in method and system provided in an embodiment of the present invention
Definition, and combine the basic principle of the definition explanation invention:
Defining 1: community structure X indicates the community structure before community's division, XiIndicate i-th of community in community structure X.
Community structure Y indicates the community structure after community divides, YjIndicate j-th of community in community structure Y.nxiIndicate community
XiIn node total number, nyjIndicate community YjIn node total number, n indicate network in node total number.
Define 2:(Average Mutual) Average Mutual be a stochastic variable include another stochastic variable information content
Measurement.For two stochastic variables X and Y, their joint probability density function is P (x, y), marginal probability density function point
It is not P (x) and P (y).Average Mutual I (X；Y it) is distributed for Joint Distribution P (x, y) and product opposite between P (x) P (y)
Entropy, calculation formula are as follows:
I(X；Y)=ΣxΣyP(x,y)log2[P(x,y)/(P(x)*P(y))] (1)
Define 3:(modularity) module angle value Q be in network connect two it is same type of while (i.e. inside community while
Ratio eii) expectation that the ratio on the two node sides is arbitrarily connected under identical structure is subtracted, if the ratio of corporations' internal edges
No more than the expectation that corporations' internal edges connect at random, then Q=0, is 1 when maximum.In general, the maximum corresponding corporations of Q value
Structure is exactly the community structure in network, and calculation formula is as follows:
Q=∑i(eii-ai 2) (2)
Wherein ai=∑jeij, indicate the ratio when accounting for all being connected with community's i interior joint.eijIndicate a node
In community ii, side of another node in community j.eiiIndicate in community ii it is all while with whole network it is all while
A ratio.aiIndicate the degree (contain a little in community i some degree on side outside community i) of the node in the community i
Account for the degree ratio of whole network.The calculation formula of modularity increment is as follows:
Δ Q=(eji+eij-2ai*aj(the e of)=2ij-2ai*aj) (3)
Defining the revised Average Mutual of 4:() revised Average Mutual refers to modularity method is added to correct
Average Mutual value, revised Average Mutual value are denoted as CIp.If Liang Ge is not connected between community, they are can not
Carry out community's merging.So calculating revised Average Mutual value CI just for the community Liang Ge for having connectionp, CIpCalculating
Formula is as follows:
CIp=β Ip+(1-β)·ΔQ (4)
The flow chart of fast community discovery method provided in this embodiment based on Average Mutual is as shown in Figure 1, specific
The following steps are included:
Step 101: user inputs the network data divided to community in the form of putting with side.
The network data format of input is that every a line inputs two numbers, and centre is opened with space-separated, and two numbers are respectively
Indicate that two nodes, such as " 12 " indicate there is a link among node 1 and node 2.
Step 102: the initialization affiliated community of node, to carry out community's merging.
Step 103: obtaining all community's combinations that there is connection in Exist Network Structure.
Step 104: choosing community's combination from the combination of all communities and begin stepping through.
Step 105: Average Mutual after calculating the Average Mutual value when community Liang Ge merges, module angle value and correcting
Value, Average Mutual value after record amendment；Definition 2 is shown in the definition of Average Mutual, and definition 3 is shown in the definition of modularity, after amendment
Definition 4 is shown in the definition of Average Mutual.
The Average Mutual value I that community divides in this stepPCalculation formula are as follows:Wherein, Xi
Indicate i-th of community in community structure X, YjIndicate j-th of community in community structure Y, I (Xi；Yj) indicate community XiWith society
Area YjAverage Mutual value, ωijIndicate XiCommunity and YjThe relevance of community.The calculation formula of modularity (Δ Q) value are as follows: Δ Q
=(eji+eij-2ai*aj(the e of)=2ij-2ai*aj), wherein ai=∑jeijIndicate be connected with community's i interior joint when accounting for all
Ratio.Revised Average Mutual value CIpCalculation formula are as follows: CIp=β Ip+ (1- β) Δ Q, wherein β is default ginseng
Number, it indicate community merge when consider nodal information number, β is bigger, then it represents that consider that the nodal information of community is more, consider
The link information of community is fewer.The preset value value range of β is 0~1, is needed in actual use according to specific community's nodal information
And the considerations of link information weight is set.
Step 106: judging whether all community's combinations traverse and finish, if then carrying out step 108, if otherwise carrying out step
107。
Step 107: selecting next community to combine, and carry out step 105.
Step 108: community corresponding to Average Mutual maximum value is closed after the amendment that selection step 105 calculates
And.
Step 109: calculating and record the Average Mutual value in this community's partition process.
Step 110: judge whether all nodes belong to same community in network, if then carrying out step 111, if otherwise into
Row step 103.
Step 111: community division result corresponding to the Average Mutual maximum value calculated in selection step 109.
Step 113: exporting last community division result.
This step finally determines community division result, and the fast community discovery method based on Average Mutual is as follows:
AMI-FD Algorithm:
Input: indicate that (V indicates the node total number in network to primitive network, and E indicates the company in network in the form of G (V, E)
Connect sum)
Output: the community division result of network
In conclusion the embodiment of the present invention be to be a kind of based on Average Mutual fast community discovery method and system mention
A kind of improvement community dividing system supplied, the optimization community dividing system are directed to the coagulation type community discovery method of hierarchical clustering
Community's merging this stage of judge improves, and joined community's merging method based on Average Mutual.Initialization section first
Community belonging to point distributes unique community for each node；Obtain all community's combinations that there is connection in Exist Network Structure
And traversed since the combination of starting community is selected in community's combination: calculating the Average Mutual value I when community Liang Ge mergesp、
The modularity increment value Δ Q and revised Average Mutual value CI of weightingpAnd it is recorded；Average Mutual value after selection amendment
Maximum community's combination merges, and calculates and records the Average Mutual value in this community's partition process；Repeat the above step
Until all nodes belong to same community in current network, community division result corresponding to Average Mutual maximum value is selected to make suddenly
For final community division result and export.The raising community divide accuracy and speed so that improve community's dividing system at
For a kind of new community's dividing system.
The above, only the invention patent preferred embodiment, but the scope of protection of the patent of the present invention is not limited to
This, anyone skilled in the art is in the range disclosed in the invention patent, according to the present invention the skill of patent
Art scheme and its patent of invention design are subject to equivalent substitution or change, belong to the scope of protection of the patent of the present invention.
Claims (7)
1. a kind of fast community based on Average Mutual finds method, which comprises the following steps:
S1, server receive community's partition request；
S2, the initialization affiliated community of node, distribute unique community for each node；
S3, all community's combinations that there is connection in Exist Network Structure are obtained；
S4, it is traversed since the combination of starting community is selected in community's combination；
Average Mutual value I when S5, the merging of the calculating community Liang GepWith modularity increment value Δ Q, it is revised flat to calculate weighting
Equal association relationship CIpAnd it is recorded；
If the community's combination traversal that there is connection in S6, Exist Network Structure finishes, step S7 is carried out, is otherwise selected next
A community's group merges return step S5；
The revised Average Mutual value CI calculated in S7, selection step S6pMaximum community's combination merges；
S8, it calculates and records the Average Mutual value in this community's partition process；
If all nodes belong to same community in S9, current network, step S10 is carried out, otherwise return step S3；
S10, community division result corresponding to the maximum value of the Average Mutual recorded in step S8 is selected to draw as final community
Point result simultaneously exports.
2. a kind of fast community based on Average Mutual according to claim 1 finds method, which is characterized in that step
The concrete operations of the affiliated community of node are initialized described in S2 are as follows: each node is both configured to a community, that is, after initializing
Community's number is equal to node number.
3. a kind of fast community based on Average Mutual according to claim 1 finds method, which is characterized in that described
The detailed process of step S3 are as follows: find out all community's combinations for meeting community and merging condition, i.e., only have connection in current network
The community Liang Ge be possible to carry out community's merging, if the community Liang Ge before do not connect, community's merging can not be carried out.
4. a kind of fast community based on Average Mutual according to claim 1 finds method, which is characterized in that step
In S5, the Average Mutual value IPCalculation formula are as follows:
Wherein, XiIndicate i-th of community in community structure X, YjIndicate j-th of community in community structure Y, I (Xi；Yj) indicate
Community XiWith community YjAverage Mutual value, ωijIndicate XiCommunity and YjThe relevance of community；
The calculation formula of the modularity increment value Δ Q are as follows:
Δ Q=(eji+eij-2ai*aj(the e of)=2ij-2ai*aj),
Wherein ai=∑jeijIndicate the ratio when accounting for all being connected with community's i interior joint；aj=∑iejiIt indicates and community j
The connected ratio when accounting for all of interior joint；eijIndicate a node in community i, side of another node in community j
Quantity；ejiA node is indicated in community j, the quantity on side of another node in community i is equal to eij；
The revised Average Mutual value CIpCalculation formula are as follows:
CIp=β Ip+ (1- β) Δ Q,
Wherein, C is identifier, indicates that the Average Mutual value is revised value；β is parameter preset, indicates that community merges
When consider nodal information number, β is bigger, then it represents that considers that the nodal information of community is more, considers that the link information of community is got over
It is few；The considerations of preset value value range of β is 0~1, is needed in actual use according to specific community's nodal information and link information
Weight is set.
5. a kind of fast community based on Average Mutual according to claim 1 finds method, which is characterized in that step
In S7, Average Mutual value CI after selection amendmentpWhen maximum community's combination merges, due to Average Mutual value after amendment
The nodal information and link information in complex network are considered, therefore optimal community's combination can be selected at this time and merged.
6. a kind of fast community based on Average Mutual according to claim 1 finds that method and system, feature exist
In the detailed process of step S9 are as follows: judge whether the node in current network belongs to same community, if then showing institute in community
A community has a little all been merged into, that is, has completed hierarchical clustering process.
7. a kind of find method for realizing a kind of any fast community based on Average Mutual of claim 1-6
System, which is characterized in that the system comprises client and servers, and wherein server comprises the following modules:
Request receiving module: for receiving community's partition request of client transmission；
Community's merging module: for carrying out community's merging to the community Liang Ge, community's amalgamation result is obtained；
It calculates Average Mutual value module: for calculating the Average Mutual value calculated when the community Liang Ge merges, obtaining averagely mutually
Value of information result；
Computing module degree incremental value module: it is used for computing module degree incremental value, obtains modularity incremental value result；
Average Mutual value module after calculating amendment: it for Average Mutual value after calculating amendment, obtains revised averagely mutual
Value of information result；
Output module: community division result corresponding to the maximum value of the Average Mutual for that will record is divided as final community
As a result and it is sent to client.
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| CN111464343A (en) * | 2020-03-22 | 2020-07-28 | 华南理工大学 | Maximum-strain greedy expansion community discovery method and system based on average mutual information |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111464343A (en) * | 2020-03-22 | 2020-07-28 | 华南理工大学 | Maximum-strain greedy expansion community discovery method and system based on average mutual information |
| CN111464343B (en) * | 2020-03-22 | 2021-10-26 | 华南理工大学 | Maximum-strain greedy expansion community discovery method and system based on average mutual information |
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