CN109921921A - The detection method and device of aging stability corporations in a kind of time-varying network - Google Patents
The detection method and device of aging stability corporations in a kind of time-varying network Download PDFInfo
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Abstract
The invention belongs to Complex Networks Analysis technical field, the detection method and device of aging stability corporations in specially a kind of time-varying network.The method of the present invention includes: the case where connection between acquisition node changes over time, and constructs time-varying network；The dynamic change degree for connecting side in network is quantitatively portrayed using stability bandwidth；Community structure is initialized, the dynamic analog lumpiness of time-varying network is calculated in conjunction with stability bandwidth；Optimize dynamic analog lumpiness, the corresponding community structure of maximum value is the aging stability corporations of time-varying network.The present invention quantitatively portrays network dynamic variation using stability bandwidth, and network dynamic Variation Features are combined with corporations detection methods, give the method for stablizing corporations in identification time-varying network, improve the accuracy and reliability of corporations' detection, it is with a wide range of applications in different fields such as social networks, bio-networks, transportation networks, while the function of community structure, dynamic process provide new visual angle in complication system in real life to understand.
Description
Technical field
The invention belongs to Complex Networks Analysis technical fields, and in particular to the aging stability corporations inspection in a kind of time-varying network
Survey method and apparatus.
Background technique
Network is the effective tool for portraying complex relationship between magnanimity element in complication system, many systems in real life
System can be analyzed using network modelling, such as social networks, protein-protein interaction network, transportation network etc..
Research based on Network Science has discovered that many important properties of real system, including worldlet attribute, rich
People club and community structure etc..Corporations in network refer to the cluster of node, and the node of identical corporations is completely embedded, different
The node connection of corporations is sparse.The process that node division is corporations is referred to as corporations' detection based on network structure.Community structure
In real system, such as sociology, biology, computer science, economics, traffic system and electric system
Deng.The topological structure of network is emerged from nodal community, contacting for network function by corporations, and community structure is in network
Communication process has an impact.Detection and research community structure facilitates structure feature and Behavioral change we have appreciated that network.Together
When, corporations' detection has application scenarios abundant in real life, such as the commercial product recommending in online shopping website, in social software
Advertisement launch, protein and the prediction of gene function etc. in biological study.
Due to the generally existing and significance of community structure, corporations' detection algorithm has become the weight of Network Science in recent years
One of study a question.Figure such as cuts and clusters at corporations' detection that traditional algorithms are used directly for network, such as hierarchical clustering and spectrum
Cluster, wherein the most famous in hierarchical clustering algorithm is point based on even side betweenness center that Newman and Girvan is proposed
Split algorithm.Newman and Girvan proposes that the quality of modularity (modularity) Lai Hengliang community division, module angle value are bigger
Show that community structure is more obvious.Given network structure, maximizing modularity is to detect the effective means of community structure in network.By
It is a np hard problem in this, a series of heuritic approaches are suggested searching approximate solution, as Blondel et al. is proposed
Louvain algorithm is suitable for weighted network.The method optimized based on modularity is most widely used corporations' detection algorithm, but
It is that there are precision limitations for this method, the lesser corporations of size for Relative Network can not be found.In addition to directly analyzing opening up for network
Flutter structure, the dynamic process detection corporations being also based in network, including spin model, random walk with it is synchronous.
Existing corporations' detection algorithm is widely applied in static network, but most real system is not at any time not
Disconnected variation.For example, the connection meeting when stimulation of the brain by outer signals, between the active degree and Different brain region of brain area
Correspondingly change；During festivals or holidays, the magnitude of traffic flow between city can from it is on ordinary days different.For the angle of network topology, it is
The dynamic change of system is embodied in increasing and decreasing for node, even the appearing and subsiding on side, and even three sides of variation of side right weight
Face.It is unlikely to excessively high again to retain the complexity of information and model of the network structure on time dimension, it is a variety of about time-varying
The modeling pattern of network is suggested.
The increase of the dynamic change and modeling pattern complexity of structure brings a series of for corporations' detection in time-varying network
Challenge.Research about community structure in time-varying network can be we have appreciated that, control and the prediction evolution of network structure, network
The appearance and formation of structure feature, the communication process in network provide more deeply and comprehensive visual angle.In recent years, time-varying network
In corporations' detection cause the extensive concern of scholar.It indicates that structure changes with time using network sequence, and uses static network
The corporations of each network are the thinkings of a simple, intuitive in the method detection sequence of network, and such methods are referred to as Sequence Detection,
According to whether considering that the flatness of community structure variation can be divided into independent detection and the two class methods of cluster that develop.Such methods
Critical issue is to exclude the interference that the factors such as noise change community structure, and determines that the corresponding of adjacent time corporations is closed
System.And the detection algorithm based on multitiered network is referred to as whole detection method, but current interlayer connects side and is confined to adjacent networks
Between same node, there are also to be studied for the connection between non-adjacent network difference node.No matter the variation of community structure is tracked also
It is to find corporations constant in time-varying network, abundant not enough to the research of network structure timeliness variation, existing research is most
Be confined to network overall structure in a short time this feature of consecutive variations the considerations of, lack to network in longer time range
Interior timeliness variation characteristic connects the timeliness variation on side and the discussion of the discontinuous variation of network structure in network.
Summary of the invention
It is an object of that present invention to provide the detection methods and device of aging stability corporations in a kind of time-varying network, existing to solve
The problem of thering is corporations' detection method to be confined to static network, ignoring real system dynamic change characteristic, to improve corporations' inspection
The accuracy of survey deepens the understanding changed to real system timeliness.
The detection method of aging stability corporations, specific steps in time-varying network provided by the invention are as follows:
(1) the case where connection between a period of time interior nodes changes over time is obtained, time-varying network is constructed, uses adjoining
The network structure at the set expression of matrix each moment；
(2) time-varying network obtained based on step (1) calculates the fluctuation rate matrix on even side, and quantitatively the dynamic on the company of portraying side becomes
Change degree；
(3) community structure is initialized, the dynamic analog lumpiness of time-varying network is calculated in conjunction with stability bandwidth, for quantitatively portraying time-varying
Aging stability corporations in network；
(4) optimize the dynamic analog lumpiness of the step (3)；The corresponding community division of dynamic analog lumpiness maximum value is time-varying
Aging stability corporations in network.
In step (1) of the present invention, the time-varying network GdIndicate the case where company side between N number of node changes over time,
Specifically, Gd=(G (t), t=1 ... T), wherein G (t)=(V, E (t)) indicates the corresponding network structure of moment t, total T time
Point, V are the set that N number of node is constituted, and each moment is all the same, and E (t) is the set that t moment connects side composition, are become at any time
Change；The network structure at each moment is indicated with adjacency matrix, i.e. A (t)=[aij(t)]N×NIf in moment t node i and section
There is no even side, then a between point jij(t)=0, otherwise aij(t) it is equal to the weight on even side, network G (t) is to have no right Undirected networks,
So A (t) is symmetrical matrix.
In step (2) of the present invention, the dynamic change degree on the quantitatively company of the portraying side is to be indicated using stability bandwidth at one section
The degree of fluctuation for connecting side right weight in time, for quantitatively portraying the dynamic change of network；Connect side e between node i and jijFluctuation
Rate VijIt calculates as follows:
Wherein, std () indicates standard deviation operator, Δij(t) company of expression side eijGrowth rate of the weight in moment t；When
Become network GdIn it is all even sides stability bandwidths form stability bandwidth matrix V=[Vij]N×N。
In step (3) of the present invention, the combination stability bandwidth calculates the dynamic analog lumpiness of time-varying network, will pass through dynamic module
Degree quantitatively portrays the aging stability corporations in time-varying network；Aging stability corporations specific manifestation are as follows: node is subordinate to about corporations
Relationship does not change over, thus in different moments network corresponding aging stability community structure be it is identical, with vector C=
[C1,C2,…,CN] indicate corporations belonging to each node；Connection ratio between different moments, same corporations' interior nodes is not
It is close with the connection between corporations' node；Connect the variation of the dynamic change degree than same corporations Nei Lianbian on side between different corporations
More acutely；
The calculation method of dynamic analog lumpiness is as follows:
Wherein, siIt (t) is the sum of the company's side right weight being connected in moment t network with node i, ω (t) is all even sides
The sum of weight, CiCorporations belonging to node i are indicated, if node i and j belong to the same corporations, δ (Ci,Cj)=1, otherwise for
0, mtFor company's number of edges mesh in t moment network；Dynamic analog lumpiness is to combine stability bandwidth, by Girvan-Newman modularity from quiet
Expansion of the state network to time-varying network indicates the level of intimate of connection with the average weight of corporations Nei Lianbian, with being averaged for even side
Stability bandwidth indicates the dynamic change degree on even side.
In step (4) of the present invention, aging stability corporations are found using the method for optimization dynamic analog lumpiness；When in change network
Community division structure when, dynamic analog lumpiness changes；The corresponding community structure of maximum dynamic analog lumpiness is exactly time-varying network
Aging stability corporations.
The detection device of aging stability corporations includes: time-varying network building module, wave in time-varying network provided by the invention
Dynamic rate computing module, dynamic analog lumpiness optimization module, aging stability corporations output module, in which:
The time-varying network constructs module, and for obtaining the connection between different moments node, building includes N number of section
Point, the time-varying network at T time point, and network topological structure at various moments is indicated in the form of adjacency matrix set；
The stability bandwidth computing module, for the company's of calculating side right weight stability bandwidth whithin a period of time, and with stability bandwidth square
Battle array stores the stability bandwidth for connecting side between all nodes pair；
The dynamic analog lumpiness optimization module finds the maximum of dynamic analog lumpiness for optimizing the dynamic analog lumpiness of network
Value；
Aging stability corporations output module, for providing the corresponding community division of maximum dynamic analog lumpiness, i.e. time-varying
The aging stability community structure of network.
Technical solution provided by the invention has the advantages that
During the Aging Characteristic of corporations is introduced directly into corporations' detection for the first time by the present invention, pass through definition even side stability bandwidth
Quantitative portrays the approach that network connection changes over time, and defines dynamic analog lumpiness based on stability bandwidth, when giving discovery
Imitate the method and apparatus for stablizing corporations and quantitative measurement aging stability corporations quality.It is examined with the corporations for being confined to static network in the past
Survey technology is compared, and The present invention gives corporations' detection methods in time-varying network, it is contemplated that real system changed over time
Key property improves the accuracy and reliability of corporations' detection, to understand that the time-varying characteristics of network provide new visual angle.This
It invents the aging stability corporations detection method proposed and device is widely used scene and important use value in life,
It such as finds interactive relation stable in social networks, provides the crucial hinge in transportation network, analyze the function in bio-networks
It divides, excavates the user interest etc. in recommender system.
Detailed description of the invention
Fig. 1 is that the process blocks of aging stability corporations detection method in a kind of time-varying network provided in an embodiment of the present invention are shown
It is intended to.
Fig. 2 is aging stability community division result schematic diagram in ballot network provided in an embodiment of the present invention.
Fig. 3 be it is provided in an embodiment of the present invention ballot network in aging stability corporations multiple moment adjacency matrix figure.
Fig. 4 is that the composed structure of aging stability corporations detection device in a kind of time-varying network provided in an embodiment of the present invention is shown
It is intended to.
Specific embodiment
For the purposes, technical schemes and advantages of the application are more clearly understood, below in conjunction with attached drawing, with the U.S.
The voting records data instance of 114 Congress, is described in detail present invention embodiment.
Fig. 1 is the process blocks schematic diagram of present invention aging stability corporations detection method in time-varying network, comprising:
The case where connection between step 100, acquisition a period of time interior nodes changes over time, constructs time-varying network, makes
With the network structure at the set expression of adjacency matrix each moment.
With voting records data instance of the Congress, 114, the U.S. during 2015~2016 years, Congressman's ballot time-varying is constructed
Network.Congress, the 114th, the U.S. is made of 100 Congressmen, can vote for for each bill Congressman, negative vote or abandoning
Power.From website https: //www.senate.gov/legislative/LIS/roll_call_lists/vote_menu _
The ballot situation of Congressman in ballot every time can be obtained in 114_2.htm.
Using Congressman as node, the ballot similitude between Congressman is even to construct ballot time-varying net for chronomere in side, month
Network.The ratio measurement ballot similitude for voting total using two identical number of votes of Congressman's attitude in one month and this month,
The ratio is as the weight for connecting side between corresponding node, right if the voting results of two Congressmen are different always in one month
Answer the company of being not present side between node.When number of voting in one month is very few, analysis result does not have representativeness, and corresponding
Network is sparse, then removes ballot month of the sum less than 5 times, finally obtains 100 nodes 20 time points
The ballot time-varying network of connection.
In the present embodiment, step 100 obtains connection the case where changing over time between a period of time interior nodes, when building
Become network, using the network structure at the set expression of adjacency matrix each moment, the adjacency matrix for time-varying network of voting is 20
Matrix sequence A=that 100 × 100 symmetrical matrixes are sequentially arranged (A (t), t=1,2 ... 20), wherein A (t)=[aij
(t)]100×100, and 0≤aij≤1。
Step 101 quantitatively portrays the dynamic change degree for connecting side in network using stability bandwidth.
Firstly, for every company side e in networkij, the growth rate Δ of the company's of calculating side right weight since t=2ij, calculating side
Method is as follows:
Even side eijStability bandwidth calculate as follows:
The stability bandwidth on all even sides may be constructed stability bandwidth matrix V=[V in ballot networkij]100×100。
Step 102, initialization community structure, the dynamic analog lumpiness of time-varying network is calculated in conjunction with stability bandwidth；
With the variation of time in real life, the topological structure of network is in changing state, but such
In change procedure, community structure relevant to nodal community, network function and dynamic process may be remained unchanged, such as tranquillization state
Corporations etc. in brain network, this community structure are referred to as aging stability corporations, have the feature that person in servitude of the node about corporations
Category relationship does not change over, thus in different moments network corresponding aging stability community structure be it is identical, used here as
Vector C=
[C1,C2,…,C100] indicate corporations belonging to each node；Between different moments, same corporations' interior nodes
It connects closer than the connection between different corporations' nodes；Connect the dynamic change degree on side between different corporations than connecting in same corporations
The variation on side is more violent.
The characteristics of quantitatively portraying above-mentioned aging stability corporations using dynamic analog lumpiness, calculation method is as follows:
Wherein, VijIt is the element in stability bandwidth matrix V, siIt (t) is the company's side right being connected in moment t network with node i
The sum of weight, ω (t) are the sum of the weight on all even sides, CiIndicate node i belonging to corporations, if node i and j belong to it is same
Corporations, then δ (Ci,CjOtherwise)=1 is 0, mtFor company's number of edges mesh in t moment network.Dynamic analog lumpiness is to combine stability bandwidth, will
Expansion of the Girvan-Newman stability bandwidth from static network to time-varying network, indicates to connect with the average weight of corporations Nei Lianbian
Level of intimate, represent the dynamic change degree of Lian Bian with the average stability bandwidth on even side.
Step 103, the dynamic analog lumpiness for optimizing network
Aging stability corporations in network can be obtained by the method for maximizing dynamic analog lumpiness.Louvain algorithm is
Classical modularity optimization algorithm, basic thought are to regard corporations as node in static network, are up to modularity increment
Node is adjusted the corporations to where neighbor node by criterion, and hierarchical optimization is not until the modularity of network is further added by.Here will
Louvain algorithm is extended in time-varying network optimization dynamic analog lumpiness, with static network the difference is that, belonging to concept transfer
It will affect corresponding network of all time points when corporations, the increment of entire time-varying network dynamic analog lumpiness is equal to the increasing of each layer network
The sum of amount, calculation method are as follows:
Step 104, the corresponding community division of dynamic analog lumpiness maximum value are the aging stability corporations in time-varying network.
In the present embodiment, vote network community division result as shown in Fig. 2, node size indicates corporations interior joints
Number even represents average weight when connecting between corporations in corporations in thickness.Ballot network maximum dynamic analog lumpiness be
0.1415, corresponding aging stability corporations are 4 corporations, and corporations' size is respectively 51 nodes, 45 nodes, 3 nodes and 1
A node.Vote network multiple moment adjacency matrix as shown in figure 3, obtained corporations are during this period of time stabilized.
For the above scheme convenient for the better implementation embodiment of the present invention, phase for implementing the above scheme is also provided below
Close device.
It please refers to shown in Fig. 4, the detection device of aging stability corporations in a kind of time-varying network provided in an embodiment of the present invention
400, it may include: time-varying network building module 401, fluctuation rate matrix computing module 402, dynamic analog lumpiness maximization module
403, aging stability corporations output module 404.
Time-varying network constructs module 401, and for obtaining the connection between different moments node, building includes N number of section
Point, the time-varying network at T time point, and network topological structure at various moments is indicated in the form of adjacency matrix set.
Rate matrix computing module 402 is fluctuated, for the stability bandwidth of the company's of calculating side right weight whithin a period of time, and uses stability bandwidth
Matrix stores the stability bandwidth for connecting side between all nodes pair.
Dynamic analog lumpiness maximizes module 403, for optimizing the dynamic analog lumpiness of network, finds the maximum of dynamic analog lumpiness
Value.
Aging stability corporations output module 404, for providing the corresponding community division of maximum dynamic analog lumpiness, i.e. time-varying net
The aging stability community structure of network.
By the previous embodiment description of this invention it is found that first obtain a period of time interior nodes between connection at any time
Between the case where changing, construct time-varying network, use the network structure at the set expression of adjacency matrix each moment；Calculate time-varying net
The fluctuation rate matrix of network；Regard the node in network as a corporations, for each node, calculates the node from current society
Corporations' bring network dynamic modularity increment where group is moved to neighbor node；If maximum modularity increment is positive,
By the corporations where node motion to respective neighbours node, otherwise do not change, traverses all nodes until the adjustment affiliated society of node
Group can not be such that dynamic analog lumpiness continues growing；Dynamic analog lumpiness is calculated based on new community structure；Regard new corporations as node,
The step of repeating above-mentioned adjustment node affiliated corporations, until dynamic analog lumpiness no longer increases, can get at this time time-varying network when
It imitates and stablizes corporations.The detection method and device of aging stability corporations in time-varying network provided by the present invention, and were confined in the past
Corporations' detection method of static network is compared, and corporations' detection method in time-varying network is given, it is contemplated that real system with
The key property of time change improves the accuracy and reliability of corporations' detection, to understand that the time-varying characteristics of network provide
New visual angle.It is dynamic by definition even side wave during the Aging Characteristic of corporations is introduced directly into corporations' detection for the first time by the present invention
Rate quantitative portrays the approach that network connection changes over time, and defines dynamic analog lumpiness based on stability bandwidth, gives discovery
The method of aging stability corporations and quantitative measurement aging stability corporations quality.Aging stability corporations proposed by the present invention detection method
The scene that is widely used in life with device and important use value such as pass through comparison sufferer and healthy individuals brain network
The difference of middle aging stability corporations realizes the diagnosis etc. objective and accurate to phrenoblabia class disease.
Those of ordinary skill in the art will appreciate that implement the method for the above embodiments be can be with
Relevant hardware is instructed to complete by program.Based on this understanding, technical solution of the present invention is substantially right in other words
The part that the prior art contributes can be embodied in the form of software products, which is stored in readable
In the storage medium taken, such as the floppy disk of computer, USB flash disk, mobile hard disk, read-only memory (ROM, Read-Only Memory),
Random access memory (RAM, Random Access Memory), magnetic or disk etc., including some instructions use so that
One computer installation (can be personal computer, server or network equipment etc.) executes each embodiment institute of the present invention
The method stated.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (6)
1. the detection method of aging stability corporations in a kind of time-varying network, which is characterized in that specific steps are as follows:
(1) the case where connection between a period of time interior nodes changes over time is obtained, time-varying network is constructed, uses adjacency matrix
Set expression each moment network structure；
(2) time-varying network obtained based on step (1) calculates the fluctuation rate matrix on even side, quantitatively the dynamic change journey on the company of portraying side
Degree；
(3) community structure is initialized, the dynamic analog lumpiness of time-varying network is calculated in conjunction with stability bandwidth；For quantitatively portraying time-varying network
In aging stability corporations；
(4) optimize the dynamic analog lumpiness of the step (3)；The corresponding community division of dynamic analog lumpiness maximum value is time-varying network
In aging stability corporations.
2. the method according to claim 1, wherein the time-varying network G in the step (1)dIndicate N number of node
Between company side the case where changing over time, specifically, Gd=(G (t), t=1 ... T), when wherein G (t)=(V, E (t)) is indicated
The corresponding network structure of t is carved, at total T time point, V is the set that N number of node is constituted, and each moment is all the same, and E (t) is t moment
The even set that side is constituted, changes at any time；The network structure at each moment is indicated with adjacency matrix, i.e. A (t)=[aij
(t)]N×NIf there is no even side, a between moment t node i and node jij(t)=0, otherwise aij(t) it is equal to and connects side
Weight, network G (t) is to have no right Undirected networks, so A (t) is symmetrical matrix.
3. the method according to claim 1, wherein the step (2) is indicated using stability bandwidth in a period of time
The degree of fluctuation of interior even side right weight, for quantitatively portraying the dynamic change of network；Connect side e between node i and jijStability bandwidth Vij
It calculates as follows:
Wherein, std () indicates standard deviation operator, Δij(t) company of expression side eijGrowth rate of the weight in moment t；Time-varying network
GdIn it is all even sides stability bandwidths form stability bandwidth matrix V=[Vij]N×N。
4. the method according to claim 1, wherein quantitatively being portrayed in the step (3) by dynamic analog lumpiness
Aging stability corporations in time-varying network；The specific manifestation of aging stability corporations are as follows: node about corporations membership not at any time
Between change, so in different moments network corresponding aging stability community structure be it is identical, with vector C=[C1,C2,…,CN]
Indicate corporations belonging to each node；Connection between different moments, same corporations' interior nodes than different corporations' nodes it
Between connection it is close；The dynamic change degree for connecting side between different corporations is more violent than the variation of same corporations Nei Lianbian；
The calculation method of dynamic analog lumpiness is as follows:
Wherein, si(t) be connected in moment t network with node i company's side right weight the sum of, ω (t) be it is all even sides weights it
With CiCorporations belonging to node i are indicated, if node i and j belong to the same corporations, δ (Ci,CjOtherwise)=1 is 0, mtFor
Company's number of edges mesh in t moment network；Dynamic analog lumpiness is to combine stability bandwidth, by Girvan-Newman modularity from static network
Expansion to time-varying network indicates the level of intimate of connection with the average weight of corporations Nei Lianbian, with the average stability bandwidth on even side
The dynamic change degree on the company of expression side.
5. the method according to claim 1, wherein method of the step (4) using optimization dynamic analog lumpiness
Find aging stability corporations；When changing the community division structure in network, dynamic analog lumpiness changes；Maximum dynamic module
Spend the aging stability corporations that corresponding community structure is exactly time-varying network.
6. the detection device of aging stability corporations in a kind of time-varying network, which is characterized in that construct module, wave including time-varying network
Dynamic rate computing module, dynamic analog lumpiness optimization module, aging stability corporations output module, in which:
The time-varying network constructs module, and for obtaining the connection between different moments node, building includes N number of node, T
The time-varying network at a time point, and network topological structure at various moments is indicated in the form of adjacency matrix set；
The stability bandwidth computing module for the stability bandwidth of the company's of calculating side right weight whithin a period of time, and is deposited with fluctuation rate matrix
Store up the stability bandwidth for connecting side between all nodes pair；
The dynamic analog lumpiness optimization module finds the maximum value of dynamic analog lumpiness for optimizing the dynamic analog lumpiness of network；
Aging stability corporations output module, for providing the corresponding community division of maximum dynamic analog lumpiness, i.e. time-varying network
Aging stability community structure.
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