CN105574541A - Compactness sorting based network community discovery method - Google Patents
Compactness sorting based network community discovery method Download PDFInfo
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- CN105574541A CN105574541A CN201510926334.6A CN201510926334A CN105574541A CN 105574541 A CN105574541 A CN 105574541A CN 201510926334 A CN201510926334 A CN 201510926334A CN 105574541 A CN105574541 A CN 105574541A
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/22—Matching criteria, e.g. proximity measures
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/23—Clustering techniques
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
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- G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
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Abstract
The invention discloses a compactness sorting based network community discovery method. The method comprises the following operational steps: 1, calculating compactness centrality values of nodes in a network, sorting the values of the nodes, and selecting an initial central node set through a threshold; 2, based on a signal transmission thought, converting network topology structure information into spatial vector information, standardizing the spatial vector information, and calculating a similarity matrix of the nodes by adopting a cosine distance; 3, putting the nodes in the network into a nearest community by utilizing the similarity among the nodes; 4, after all the nodes are arranged, performing community division again on the nodes in a community with less than three nodes, and deleting a central node of the community from the central node set; and 5, updating the central node set, and until a new central node set is the same as an original center node set, indicating that the community structure reaches a stable state, thereby finishing the community division. The method has an important significance for discovering a hiding law in a complicated network and predicting a behavior of the complicated network.
Description
Technical field
The present invention relates to complex network community discovery field, particularly relate to a kind of network community discovery method based on tight ness rating sequence.
Background technology
A lot of complication systems in real world can abstractly be a complex network, as interpersonal relationship, WWW, invest in network and banking network etc.Complex network is owing to himself having in large scale, node and connecting the features such as complicated, directly study often tool to complex network entirety to acquire a certain degree of difficulty, but ubiquity community structure in complex network, namely the node of inside, community has closer contact.Community discovery is conducive to the structure and fuction probing into network, find wherein hiding rule and predict its behavior, such as, risk identification can be carried out, the economic assets in financial supply chain is carried out to project evaluation chain, Real-Time Pricing clearing etc. are carried out to block chain investment guarantee network.Community, as the important attribute of in complex network, has caused increasing concern and attention to the research of community in complex network.
In complex network, the node contacts be in identical corporations is tight, and the node contacts between different corporations is sparse.Find according to this feature, the community structure of complex network finds very similar to the cluster analysis of data, after defining the similarity of network node, just with comparalive ease Web Community's partition problem can be converted into clustering problem.A lot of existing community discovery algorithm all adopts the relevant cluster algorithm in data mining, carries out cluster result, wherein tight node is flocked together to the node in network with the similarity of definition, thus realizes community's division.Such as typical K-means method, the clustering algorithms such as K-median method, its thought is widely used among community discovery algorithm, and achieves good division effect.But such algorithm needs to provide community to divide some prior imformations such as number, community's scale, and these prior imformations are generally difficult to obtain in advance.
Summary of the invention
Although clustering problem and Web Community's partition problem exist inherent consistance, the two is also not exclusively equivalent in itself.Each data point in cluster analysis problem is isolated existence, and each node in network possesses the network topology structure character not available for cluster analysis problem, for this problem, present invention employs the similarity building method of topological structure character Network Based; Simultaneously in order to avoid the setting to prior imformation, the present invention also passes through the selection threshold value of computing center's node and merges little community, the adaptive implicit structure determining network.
Foregoing invention object is achieved through the following technical solutions:
Step 1: computational grid initial center set of node.The tight ness rating centrality value of each node of computational grid, sorts according to tight ness rating centrality value, and arranges threshold value according to network structure, select initial center set of node with this.
Step 2: the similarity of computational grid node.Consider each node in network not only by the impact of its neighbor node, also be subject to other node passes to it impact through topological property, adopt the thought of signal transmission that network topology information is converted into space vector information, then use COS distance to calculate corresponding similarity matrix after carrying out standardization to it.
Step 3: divide community.Utilize the similarity between node by the node division in network in nearest community, be referred in community belonging to Centroid the most similar with it by each node.
Step 4: little community merges.After all node division complete, if the node number in community is less than 3, then the Centroid of this community is deleted from the set of node of center, and its all node re-starts community's division.
Step 5: upgrade centromere point set.Each community is used as a little network and again carries out the calculating of tight ness rating centrality, utilize the tight ness rating of node to sort and find the Centroid of each little network, then upgrade all Centroids.If all new Centroids are all identical with former Centroid, then stop iteration; Otherwise, return step 3 and re-start community's division, until centromere point set no longer changes.
The concrete steps of described step 1 are:
1) the tight ness rating centrality of each node of computational grid, first calculates the mean distance of a node to all nodes of other in network:
Wherein, v
ifor required node, n is the node number in network, g (v
i, v
j) be node v
iwith node v
jbetween shortest path.Node v
itight ness rating centrality is D
avg(v
i) inverse.
2) descending sort is carried out to the tight ness rating centrality value of node, by the node after sequence successively alternatively Centroid.
3) threshold value is set.May due to what have that the larger node of two tight ness rating centrality values belongs to a community, therefore, in order to avoid this situation, when a node is added centromere point set, the common neighbours' number considering all nodes that this node and existing Centroid are concentrated is needed whether to be all less than predetermined threshold γ: if be less than γ, then illustrate that this node and existing Centroid belong to the possibility of a community less, Centroid can be joined as a new Centroid and concentrate; If common neighbours' number is greater than γ, then this node and existing Centroid belong to the possibility of a community comparatively greatly, then abandoned by this node, proceed the judgement of next node.
The average number of degrees of all nodes in the value of threshold gamma and network are closely related, we choose γ=< k >/2 in this article, and wherein < k > is the average degree of network.
4) initial center set of node is calculated.Next node is taken out from candidate centers set of node, if this node and Centroid concentrate common neighbours' number of all nodes to be all less than threshold gamma, then this node is joined Centroid to concentrate, if all nodes have judged complete all, then centromere point set has chosen end.
The concrete steps of described step 2 are: network topology information is converted into space vector information by the thought based on signal transmission.The process of signal transmission can represent with mathematical formulae, namely
V=(I
n+A)
w
Wherein, I
nrepresentation unit matrix, A represents the adjacency matrix of network, and w represents the number of times of signal transmission, through experimental results demonstrate that w=3 obtains good effect.After signal transmission w time, the semaphore comprising each node in the network of n node is a n-dimensional vector, what it represented is the influence degree of this node to network others node, such n node just has n n-dimensional vector, thus by the convert information of cyberspace topological structure in order to vector space information, then after standardization is carried out to it, use the similarity matrix between COS distance computing node.
The concrete steps of described step 3 are: utilize the similarity matrix obtained in step 2, search the similarity between node and all Centroids, by all node division in network in nearest community, be referred to by each node and spend similarly in community belonging to maximum Centroid.
The concrete steps of described step 4: in order to avoid producing empty community or too small community, after community has divided, little community is merged.It is generally acknowledged, if community's node number is less than 3, then this community is not enough to become an independently community, thus is integrated with other community, the all nodes comprised by this community repartition other community, and the Centroid of this community is deleted from the set of node of center.
The concrete steps of described step 5: upgrade centromere point set.Each community is used as a little network and again carries out the calculating of tight ness rating centrality, utilize the tight ness rating of node to sort and find the Centroid of each little network, then upgrade all Centroids.If new centromere point set is identical with former centromere point set, then illustrate that existing community structure reaches steady state (SS), stop iteration; Otherwise return step 3 and utilize new centromere point set to re-start community's division, until centromere point set no longer changes, community reaches rock-steady structure.
Classical community discovery algorithm generally needs to provide community to divide some prior imformations such as number, community's scale, and only considers when carrying out node Similarity Measure that in network, each node is subject to the impact of its neighbor node, ignores other non-neighbor node; Or consider the impact of non-neighbor node but computation process is too complicated and quite consuming time.The network community discovery method that the present invention is based on tight ness rating sequence, then by the calculating of threshold value and the adaptive implicit structure determining community of the merging of little community, avoids the setting to prior imformation; And based on the thought of signal transmission, construct the similarity matrix of topology information Network Based, not only consider that in network, each node is subject to the impact of its neighbor node, also consider that other node passes to its impact through topological property, and computation complexity is low, there is stronger adaptability and the efficiency of Geng Gao.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet of the network community discovery method that the present invention is based on tight ness rating sequence.
Embodiment
Below in conjunction with the drawings and specific embodiments, the network community discovery method that the present invention is based on tight ness rating sequence is further described:
As shown in the figure, the close centers of the present invention's first each node of computational grid, sorts to its value, and by Threshold selection initial center set of node; Network topology information is converted into space vector information by the thought then based on signal transmission, and adopts the similarity matrix between COS distance computing node after carrying out standardization to it; Again utilize the similarity between node by the node division in network in nearest community, and after all node division complete, the node be less than by nodes in the community of 3 re-starts community and divides, and the Centroid of community is deleted from the set of node of center; Last iteration upgrades centromere point set, until new centromere point set is identical with former centromere point set, community structure reaches steady state (SS), and community has divided.
Its specific implementation process is:
Step 1: computational grid initial center set of node, concrete steps are:
1) the tight ness rating centrality of each node of computational grid, first calculates the mean distance of a node to all nodes of other in network:
Wherein, v
ifor required node, n is the node number in network, g (v
i, v
j) be node v
iwith node v
jbetween shortest path.
Node v
itight ness rating centrality C
c(v
i) be D
avg(v
i) inverse:
2) descending sort is carried out to the tight ness rating centrality value of node, by the node after sequence successively alternatively Centroid.
3) threshold value is set.There is the node very possible close proximity each other of larger tight ness rating centrality value, belong to a community, therefore, in order to avoid this situation, when a node is added centromere point set, need to consider that this node and existing Centroid concentrate common neighbours' number of all nodes whether to be all less than predetermined threshold γ: if be less than γ, then illustrate that this node and existing Centroid belong to the possibility of a community less, Centroid can be joined as a new Centroid and concentrate; If common neighbours' number is greater than γ, then this node and existing Centroid belong to the possibility of a community comparatively greatly, then abandoned by this node, proceed the judgement of next node.
The average number of degrees of all nodes in the value of threshold gamma and network are closely related, we choose γ=< k >/2 in this article, wherein < k > is the average degree of network, and the average degree < k > of network is the degree averaged to nodes all in network:
Wherein, N is the number of all nodes, d
ifor node v
idegree.
4) initial center set of node is calculated.Next node is taken out from candidate centers set of node, if this node and Centroid concentrate common neighbours' number of all nodes to be all less than threshold gamma, then this node is joined Centroid to concentrate, if all nodes have judged complete all, then centromere point set has chosen end.
Step 2: network topology information is converted into space vector information by the thought based on signal transmission, the node in network is used as the node having and receive and transmit by it.First an optional node from network, composes a signal value to it, and then this node launches this signal value to oneself and oneself neighbor node, receives the nodes records of signal and preserves corresponding signal value.In like manner, other node also carries out the process of same reception and transmission signal, so hands on, and after w time is transmitted, the semaphore of node to other node transmission of network be arranged in same community is close.The process of signal transmission can represent with mathematical formulae, namely
V=(I
n+A)
w
Wherein, I
nrepresentation unit matrix, A represents the adjacency matrix of network, and w represents the number of times of signal transmission, through experimental results demonstrate that w=3 obtains good effect.After signal transmission w time, the semaphore comprising each node in the network of n node is a n-dimensional vector, what it represented is the influence degree of this node to network others node, such n node just has n n-dimensional vector, thus by the convert information of cyberspace topological structure in order to vector space information.
The i-th row supposing V is V
i=(v
i1, v
i2, v
in), i=1,2 ..., n, it represents that i-th node of network is as the impact of start node on network.Standardization V
ifor U
i=(u
i1, u
i2..., u
in), wherein
the internodal COS distance of vector calculation after utilizing standardization obtains corresponding similarity matrix.
Step 3: utilize the similarity matrix obtained in step 2, search the similarity between node and all Centroids, by all node division in network in nearest community, be referred to by each node and spend similarly in community belonging to maximum Centroid.
Step 4: in order to avoid producing empty community or too small community, after community has divided, little community is merged.It is generally acknowledged, if community's node number is less than 3, then this community is not enough to become an independently community, thus is integrated with other community, the all nodes comprised by this community repartition other community, and the Centroid of this community is deleted from the set of node of center.By the calculating of threshold value and the merging of little community, adaptively can obtain community's number of network, avoid the setting to prior imformation.
Step 5: upgrade centromere point set.Each community is used as a little network and again carries out the calculating of tight ness rating centrality, utilize the tight ness rating of node to sort and find the Centroid of each little network, then upgrade all Centroids.If new centromere point set is identical with former centromere point set, then illustrate that existing community structure reaches steady state (SS), stop iteration; Otherwise return step 3 and utilize new centromere point set to re-start community's division, until centromere point set no longer changes, community reaches rock-steady structure, and community has divided.
Should be understood that, the above-mentioned description for embodiment is comparatively concrete, and therefore can not think the restriction to scope of patent protection of the present invention, scope of patent protection of the present invention should be as the criterion with claims.
Claims (6)
1., based on a network community discovery method for tight ness rating sequence, it is characterized in that, the method is carried out according to following steps:
Step 1: computational grid initial center set of node.By the importance of the tight ness rating centrality decision node of each node of network, select initial center set of node with the importance of node.
Step 2: the similarity of computational grid node.Consider each node in network not only by the impact of its neighbor node, also be subject to other node passes to it impact through topological property, adopt the thought of signal transmission that network topology information is converted into space vector information, then use COS distance to calculate corresponding similarity matrix after carrying out standardization to it.
Step 3: divide community.Utilize the similarity between node by the node division in network in nearest community, be referred in community belonging to Centroid the most similar with it by each node.
Step 4: little community merges.After all node division complete, if the node number in community is less than 3, then the Centroid of this community is deleted from the set of node of center, and its all node re-starts community's division.
Step 5: upgrade centromere point set.Each community is used as a little network and again carries out the calculating of tight ness rating centrality, utilize the tight ness rating of node to sort and find the Centroid of each little network, then upgrade all Centroids.If all new Centroids are all identical with former Centroid, then stop iteration; Otherwise, return step 3 and re-start community's division, until centromere point set no longer changes.
2. the network community discovery method based on tight ness rating sequence according to claim 1, is characterized in that: the concrete steps of described step 1 are:
1) the tight ness rating centrality of each node of computational grid, first calculates the mean distance of a node to all nodes of other in network:
Wherein, v
ifor required node, n is the node number in network, g (v
i, v
j) be node v
iwith node v
jbetween shortest path.
Node v
itight ness rating centrality C
c(v
i) be D
avg(v
i) inverse:
2) descending sort is carried out to the tight ness rating centrality value of node, by the node after sequence successively alternatively Centroid.
3) threshold value is set.There is the node very possible close proximity each other of comparatively large closely angle value, belong to a community, therefore, in order to avoid this situation, when a node is added centromere point set, need to consider that this node and existing Centroid concentrate common neighbours' number of all nodes whether to be all less than predetermined threshold γ: if be less than γ, then illustrate that this node and existing Centroid belong to the possibility of a community less, Centroid can be joined as a new Centroid and concentrate; If common neighbours' number is greater than γ, then this node and existing Centroid belong to the possibility of a community comparatively greatly, then abandoned by this node, proceed the judgement of next node.
The average number of degrees of all nodes in the value of threshold gamma and network are closely related, we choose γ=< k >/2 in this article, wherein < k > is the average degree of network, and the average degree < k > of network is the degree averaged to nodes all in network:
Wherein, N is the number of all nodes, d
ifor node v
idegree.
4) initial center set of node is calculated.Next node is taken out from candidate centers set of node, if this node and Centroid concentrate common neighbours' number of all nodes to be all less than threshold gamma, then this node is joined Centroid to concentrate, if all nodes have judged complete all, then centromere point set has chosen end.
3. the network community discovery method based on tight ness rating sequence according to claim 1, it is characterized in that: the concrete steps of described step 2 are: network topology information is converted into space vector information by the thought based on signal transmission, the node in network is used as the node having and receive and transmit by it.First an optional node from network, composes a signal value to it, and then this node launches this signal value to oneself and oneself neighbor node, receives the nodes records of signal and preserves corresponding signal value.In like manner, other node also carries out the process of same reception and transmission signal, so hands on, and after w time is transmitted, the semaphore of node to other node transmission of network be arranged in same community is close.The process of signal transmission can represent with mathematical formulae, namely
V=(I
n+A)
w
Wherein, I
nrepresentation unit matrix, A represents the adjacency matrix of network, and w represents the number of times of signal transmission, through experimental results demonstrate that w=3 obtains good effect.After signal transmission w time, the semaphore comprising each node in the network of n node is a n-dimensional vector, what it represented is the influence degree of this node to network others node, such n node just has n n-dimensional vector, thus by the convert information of cyberspace topological structure in order to vector space information.
The i-th row supposing V is V
i=(v
i1, v
i2, v
in), i=1,2 ..., n, it represents that i-th node of network is as the impact of start node on network.Standardization V
ifor U
i=(u
i1, u
i2..., u
in), wherein
the internodal COS distance of vector calculation after utilizing standardization obtains corresponding similarity matrix.
4. the network community discovery method based on tight ness rating sequence according to claim 1, it is characterized in that: the concrete steps of described step 3 are: utilize the similarity matrix obtained in step 2, search the similarity between node and all Centroids, by all node division in network in nearest community, be referred to by each node and spend similarly in community belonging to maximum Centroid.
5. the network community discovery method based on tight ness rating sequence according to claim 1, is characterized in that: the concrete steps of described step 4: in order to avoid producing empty community or too small community, after community has divided, merge little community.It is generally acknowledged, if community's node number is less than 3, then this community is not enough to become an independently community, thus is integrated with other community, the all nodes comprised by this community repartition other community, and the Centroid of this community is deleted from the set of node of center.By the calculating of threshold value and the merging of little community, adaptively can obtain community's number of network, avoid the setting to prior imformation.
6. the network community discovery method based on tight ness rating sequence according to claim 1, is characterized in that: the concrete steps of described step 5: upgrade centromere point set.Each community is used as a little network and again carries out the calculating of tight ness rating centrality, utilize the tight ness rating of node to sort and find the Centroid of each little network, then upgrade all Centroids.If new centromere point set is identical with former centromere point set, then illustrate that existing community structure reaches steady state (SS), stop iteration; Otherwise return step 3 and utilize new centromere point set to re-start community's division, until centromere point set no longer changes, community reaches rock-steady structure.
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CN111444454A (en) * | 2020-03-24 | 2020-07-24 | 哈尔滨工程大学 | Dynamic community dividing method based on spectrum method |
CN111444454B (en) * | 2020-03-24 | 2023-05-05 | 哈尔滨工程大学 | Dynamic community division method based on spectrum method |
CN112579831A (en) * | 2020-11-18 | 2021-03-30 | 南京信息职业技术学院 | Network community discovery method and device based on SimRank global matrix smooth convergence and storage medium |
CN112579831B (en) * | 2020-11-18 | 2024-04-12 | 南京信息职业技术学院 | Network community discovery method, device and storage medium based on SimRank global matrix smooth convergence |
CN113221016A (en) * | 2021-07-08 | 2021-08-06 | 北京达佳互联信息技术有限公司 | Resource recommendation method and device, computer equipment and medium |
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