CN109471995A - A kind of hyperbolic embedding grammar of complex network - Google Patents
A kind of hyperbolic embedding grammar of complex network Download PDFInfo
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Abstract
The present invention provides a kind of hyperbolic embedding grammars of complex network, the figure that complex network is constituted is mapped into the hyperbolic space that curvature is -1 based on Poincare disk model, obtain the hyperbolic map of complex network insertion, the connection probability between node coordinate and node in hyperbolic map including each node, according to the connection property of each node in the degree and weight and hyperbolic map between the Node Contraction in Complex Networks, the node coordinate in hyperbolic map is estimated by the method for logarithm maximum likelihood, according to the original connection relationship of each node, and then obtain the network after the complex network insertion hyperbolic space.Method of the invention may be implemented to retain more network informations, reduce error, improve the technical effect of information analysis accuracy.
Description
Technical field
The present invention relates to data minings and Complex Networks Analysis technical field, and in particular to a kind of hyperbolic of complex network is embedding
Enter method.
Background technique
With the rapid development of mobile Internet, have become the important society of modern society using it as the information network of representative
Hand over tool one of.To meet wilderness demand and good user experience of the user in mobile Internet, it is based on mobile Internet
Data analysis become data mining and Complex Networks Analysis field hot issue.
User, can to the efficiently and accurately analysis of internet behavior in the complicated multiplicity of the online internet behavior of mobile interchange
Keep the data growth rate of social more " intelligence " and now mobile Internet too fast, the excavation and processing of effective information become
Stubborn problem, and a large amount of data operation also has very high requirement to the computing capability of computer.And mobile Internet
Essence is a kind of complex network, and real-life complex network possesses self-organizing, self similarity, worldlet, the characteristics such as uncalibrated visual servo,
Its node degree obeys power-law distribution.Set of the complex network as a large amount of interaction nodes, can be expressed as the form of figure.Figure be by
What the company side on vertex set and connection vertex formed.Currently, usually way is, using figure embedding grammar by true complex network
It is embedded into theorem in Euclid space, and is handled using the method for graph theory.
Present invention applicant is in implementing the present invention, it may, discovery at least has the following technical problems in the prior art:
By the way that complex network is embedded into theorem in Euclid space and then is handled, although certain effect can be played, this method is
It establishes on the basis of losing the network information, with the increase of data and the refinement of information, complex network is embedded into European
Space will lose big accuracy of measurement, lose a large amount of important informations, cause a large amount of error.
From the foregoing, it will be observed that the technical problem that the method for the prior art is larger due to the imperfect and existing error of information.
Summary of the invention
In view of this, the present invention provides the hyperbolic embedding grammars and device of a kind of complex network, to solve or extremely
The method of the small part solution prior art technical problem larger due to the imperfect and existing error of information.
The present invention provides a kind of hyperbolic embedding grammars of complex network characterized by comprising
Step S1: the figure that complex network is constituted is obtained；
Step S2: mapping to the hyperbolic space that curvature is -1 for the figure that complex network is constituted based on Poincare disk model,
The hyperbolic map for obtaining complex network insertion, include in hyperbolic map each node node coordinate and node between connection probability, root
According to the connection property of each node in the degree and weight and hyperbolic map between the Node Contraction in Complex Networks, greatly seemingly by logarithm
Right method estimates the node coordinate in hyperbolic map, according to the original connection relationship of each node, and then obtains complex network
Network after being embedded in the hyperbolic space.
In one implementation, the node total number n of the complex network, side information between complex network node and
Connect the weight on side between nodeWherein wijIndicate the weight for connecting side between node i and node j, i=
1 ..., n, j=1 ..., n, in the absence of even side, weight 0, and wii=1 permanent establishment, step S1 are specifically included:
Complex network adjacency matrix is generated according to the side information between nodeWherein xijIt indicates
With the presence or absence of even side, i=1 ..., n, j=1 ..., n between node i and node j, if there is even Bian Zewei 1, there is no connect
Bian Zewei 0, and xii=1 permanent establishment；
Above-mentioned complex network is constituted into figure G (V, E), wherein V indicates the set of Node Contraction in Complex Networks, and E indicates complex web
Connect the set on side between network interior joint.
In one implementation, step S2 is specifically included:
Step S2.1: according to the node total number and Poincare disk model of complex network, hyperbolic disc radius R is calculated；
Step S2.2: setting the number of iterations k, according to maximum likelihood method for solving first jiao of each node seat according to a preliminary estimate
Mark θ and first degree of relevant parameter κ, wherein the first angular coordinate θ is that the figure that complex network is constituted is embedded in after the hyperbolic space according to a preliminary estimate
Coordinate, to characterize company's side situation between each node, the degree by counting each node obtains first degree of relevant parameter κ
?；
Step S2.3: according to the first angular coordinate θ and first degree of relevant parameter κ according to a preliminary estimate, intensity relevant parameter is calculated
σ, wherein intensity relevant parameter σ connects the weight on side to characterize each node；
Step S2.4: according to the first angular coordinate θ and the first intensity relevant parameter σ according to a preliminary estimate, second degree of correlation is calculated
Parameter κ '；
Step S2.5: according to intensity relevant parameter σ and second degree of relevant parameter κ ', calculate second jiao of each node seat
Mark θ ', wherein the second angular coordinate is each node coordinate adjusted；
Step S2.6: judging whether the number of iterations reaches setting value k, if not up to, S2.3 is thened follow the steps, wherein walking
Angular coordinate and degree relevant parameter in rapid S2.3 to estimate are step S2.4 and the updated parameter of step S2.5；
Step S2.7: whether the precision of the second angular coordinate θ ' of Rule of judgment estimation has restrained, if do not restrained,
Step S2.3 is gone to, wherein the angular coordinate and degree relevant parameter in step S2.3 to estimate are step S2.4 and step S2.5
Updated parameter；
Step S2.8: the third angular coordinate θ of each node is estimated using maximum likelihood method essencei, wherein third angular coordinate
For each node the hyperbolic space actual coordinate；
Step S2.9: according to node total number n, disc radius R, power law parameter α and temperature T, the diameter of each node is calculated
Coordinate ri；
Step S2.10: according to the third angular coordinate θ of nodeiWith diameter coordinate ri, obtain the hyperbolic of all complex network nodes
Space coordinate (r, θ), all hyperbolic space nodes constitute the network after insertion.
In one implementation, in step S2.1, the specific calculation of hyperbolic disc radius R is as follows:
Wherein, n is the node total number of weighted input complex network, and β is power law index, according to the classics of accumulative degree distribution
Algorithm estimation, α is adjustment parameter, for adjusting power law index β, wherein the relationship between β and α is the α+1 of β=2, and T is temperature ginseng
Number, for adjusting hyperbolic space basis geometry, | E | connect the total number on side for node of graph.
In one implementation, step S2.2 is specifically included:
Any two node u is obtained, v, diameter coordinate is respectively ruAnd rv, wherein the meter of the difference of the angular coordinate of two nodes
Calculate formula are as follows:
Wherein, Θ () indicates that direct ratio function, Θ (1) are invariant,WithIt is directly proportional, r0=
Min { R, R-ru- 2log (Δ θ (u, v)) ± Θ (1) }, R is the hyperbolic disc radius calculated in step S2.1；
Obtain two common neighbours' quantity c of node u, vuvCalculation formula:
The calculation formula of the difference of the angular coordinate of two nodes is converted, the maximum likelihood function of Δ θ (u, v) is obtained:
Estimated to obtain Δ θ (u, v) according to the maximum likelihood function of Δ θ (u, v), and gives the definition of the angular coordinate of first node
For the random value between 0 to 2 π, it is left the angular coordinate of node according to the angular coordinate of first node and the difference Δ θ (u, v) of angular coordinate
It calculates, to obtain the first angular coordinate of each node.
In one implementation, step S2.3 is specifically included:
The probability distribution of acquisition hyperbolic Random Graph and default weight equationWherein, probability
It is distributed as ε distribution f (ε), and<ε>=1；
Weight w is obtained according to default weight equationijVery big log-likelihood function；
Based on the first angular coordinate θ, first degree of relevant parameter κ, weight w is utilizedijObtain the first very big log-likelihood function meter
Calculate σ.
In one implementation, step S2.4 is specifically included:
Obtain the connection Probability p (κ between nodei, κj, dij)；
According to connection Probability p (κi, κj, dij) and default weight equationObtain second greatly
Log-likelihood function；
Based on the first angular coordinate θ and intensity relevant parameter σ, second degree of correlation is calculated using the second very big log-likelihood function
Parameter κ '.
In one implementation, step S2.5 is specifically included:
Second degree estimated using maximum likelihood method according to step S2.3 the intensity relevant parameter σ estimated and step S2.4
Relevant parameter κ trains one group of angular coordinate adjusted valueMakeAs the second angular coordinate θ ' after reevaluating.
In one implementation, angular coordinate adjusted valueMethod of adjustment specifically include:
It was [0,2 π] according to disk one week, [0,2 π] is used as an independent variable axis, value is x θ thereon, and dependent variable is
Angular coordinate adjusted value；
Section is equally divided into N parts, the boundary value for obtaining each section is
Using maximum likelihood method each section boundary training one group of angular coordinate adjusted value set expression beTool
Body are as follows: at each interval border, there are lower bound x θlbThe angular coordinate adjusted value at placeWith upper bound x θubThe angular coordinate adjusted value at place
By each θ of step S2.2 rough estimateiIt is adjusted according to adjusted value, in each interval border, each angle of rotation of joint
Coordinate θ is according to known adjusted valueCarry out addition adjustment；
In each section, each node angular coordinate is carried outAddition adjustment, adjustment
The second angular coordinate θ ' of one group of new estimation is obtained afterwards.
In one implementation, step S2.9 is specifically included:
The diameter coordinate r of node is obtained according to following calculation formulai:
Wherein, deg (i) indicates company's side sum of node i, and n is node total number, and R is disc radius, and α is power law parameter,
T is temperature parameter.
Said one or multiple technical solutions in the embodiment of the present application at least have following one or more technology effects
Fruit:
The invention proposes a kind of embedding grammar of complex network, the connection that can use the hyperbolic Random Graph provided is general
Rate obtains the connection relationship between each node, and then obtains the network after the complex network insertion hyperbolic space, due to that can incite somebody to action
Complex network is embedded into compared to in theorem in Euclid space " bigger " hyperbolic space, retains complex network band so as to more complete
Some essential informations improve precision, reduce the error that information indicates, solve the method for the prior art since information is imperfect and
The larger technical problem of existing error.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is the present invention
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 is a kind of flow chart of the hyperbolic embedding grammar of complex network in the embodiment of the present invention；
Fig. 2 is the flow chart that the coordinate of the node in the hyperbolic space is obtained in method shown in Fig. 1.
Specific embodiment
The embodiment of the invention provides a kind of hyperbolic embedding grammars of complex network, and by that will have the right, complex network insertion is double
Bent space, to complex network can be handled and be analyzed in the case where retaining more networks information.
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
Embodiment one
A kind of hyperbolic embedding grammar of complex network is present embodiments provided, referring to Figure 1, this method comprises:
Step S1: the figure that complex network is constituted is obtained；
Specifically, the node total number n of the complex network connects side between the side information and node between complex network node
WeightWherein wijIndicate the weight for connecting side between node i and node j, i=1 ..., n, j=
1 ..., n, in the absence of even side, weight 0, and wii=1 permanent establishment, step S1 are specifically included:
Complex network adjacency matrix is generated according to the side information between nodeWherein xijIt indicates
With the presence or absence of even side, i=1 ..., n, j=1 ..., n between node i and node j, if there is even Bian Zewei 1, there is no connect
Bian Zewei 0, and xii=1 permanent establishment；
Above-mentioned complex network is constituted into figure G (V, E), wherein V indicates the set of Node Contraction in Complex Networks, and E indicates complex web
Connect the set on side between network interior joint.
Step S2: mapping to the hyperbolic space that curvature is -1 for the figure that complex network is constituted based on Poincare disk model,
The hyperbolic map for obtaining complex network insertion, include in hyperbolic map each node node coordinate and node between connection probability, root
According to the connection property of each node in the degree and weight and hyperbolic map between the Node Contraction in Complex Networks, greatly seemingly by logarithm
Right method estimates the node coordinate in hyperbolic map, according to the original connection relationship of each node, and then obtains complex network
Network after being embedded in the hyperbolic space.
Specifically, figure is mapped to the double of curvature K=-1 by the figure G (V, E) that complex network is constituted in the embodiment of the present invention
It is bent spatially, due to the hyperbolic space description and visualization all there is certain difficulty, thus in the present embodiment using huge plus
Lay disk model is described, and the point in the hyperbolic space is expressed as polar form (r, θ), and r indicates diameter coordinate, the i.e. point
To the distance of disk origin；θ indicates angular coordinate, the i.e. angle of the point and horizontal axis.Assuming that there are two nodes for the hyperbolic space
Respectively (rs, θs) and (rt, θt), the hyperbolic distance of point-to-point transmission indicates at this time are as follows:
Dist (s, t)=arccosh (cosh2rscosh2rt-sinh2rsinh2rtcos(θs-θt))
Hyperbolic Random Graph is closed in the collection for all figures that size is n defines probability distribution, and there are the figure G roots of n node
It is sampled according to the probability distribution.On hyperbolic space Poincare disk model, disc radius is defined as R=2logn+C, wherein C is
Adjustment generates the parameter of the average degree of figure, and each node v is according to probability density functionSampling point
With a node (r, θ), α is the parameter for adjusting power law index β, the α+1 of β=2.Thus two node u, v connected probability are as follows:
Wherein, temperature parameter T adjusts the potential geometry of the hyperbolic space.So generating hyperbolic Random Graph depends on 4 parameters,
Respectively node number n, disc radius R, power rate parameter alpha and temperature parameter T.It is mapped to for arbitrarily inputting figure G=(V, E)
Hyperbolic space pointDefine log-likelihood function:
In order to which the hyperbolic insertion of complex network, each section after the default insertion hyperbolic space of the embodiment of the present invention is better achieved
There are three parameters that are mutually related: θ for point, κ and σ, wherein θ indicates the angular coordinate of figure insertion hyperbolic space posterior nodal point, and κ and σ are
Two hidden variables, for adjusting hyperbolic space embedded coordinate (r, θ).κ corresponds to the expecting degree of node, each node can
Distribute an expecting degreeI.e. continuous power-law distributionIn stochastic variable κ, wherein γ
> 2 is target degree distribution exponent, κ0For minimum expectation degree, according to probability density function ρ (κ), distance is two the nodes u, v of d
Possess hidden variable κ and κ ', connection probability is represented byWhereinIn order to be embedded in weighting network, σ
It is associated with each node, since with node to connect side right weight related by σ, so referred to as intensity relevant parameter, each node can distribute one
A expectation strengthIt is corresponding with κ.The joint probability density distribution function ρ (κ, σ) of κ and σ=ρ (κ) ρ (σ | κ) control section
Relationship between point degree and node strength.
If there are node is to be connected with j for D dimension space, can be indicated between the two connecting nodes according to hidden variable κ and σ
Connect the weight on side:
Wherein v is figure parameters v > 0, and α is 0≤α of dimensional parameter < D, and ∈ is taken from noise probability density function f (∈)
Positive stochastic variable, function f (∈) obey gamma distribution,Indicate the distance between α dimension lower node i and j.
In one embodiment, Fig. 2 is referred to, step S2 is specifically included:
Step S2.1: according to the relevant parameter of the node total number of complex network and Poincare disk model, hyperbolic is calculated
Disc radius R.
Specifically, relevant parameter includes power law index, adjustment parameter, temperature parameter.
In one implementation, in step S2.1, the specific calculation of hyperbolic disc radius R is as follows:
Wherein, n is the node total number of weighted input complex network, and β is power law index, according to the classics of accumulative degree distribution
Algorithm estimation, α is adjustment parameter, for adjusting power law index β, wherein the relationship between β and α is the α+1 of β=2, and T is temperature ginseng
Number, for adjusting hyperbolic space basis geometry, | E | connect the total number on side for node of graph.
Step S2.2: setting the number of iterations k tentatively estimates according to hyperbolic disc radius R and default maximum likelihood method for solving
Count the first angular coordinate θ and first degree of relevant parameter κ of each node, wherein the first angular coordinate θ is that the figure that complex network is constituted is embedding
Enter coordinate according to a preliminary estimate, first degree of relevant parameter κ after the hyperbolic space to pass through to characterize company's side situation between each node
The degree for counting each node obtains.
Specifically, step S2.2 is specifically included:
Any two node u is obtained, v, diameter coordinate is respectively ruAnd rv, wherein the meter of the difference of the angular coordinate of two nodes
Calculate formula are as follows:
Wherein, Θ () indicates that direct ratio function, Θ (1) are invariant,WithIt is directly proportional, r0=
Min { R, R-ru- 2log (Δ θ (u, v)) ± Θ (1) }, R is the hyperbolic disc radius calculated in step S2.1；
Obtain two common neighbours' quantity c of node u, vuvCalculation formula:
The calculation formula of the difference of the angular coordinate of two nodes is converted, the maximum likelihood function of Δ θ (u, v) is obtained:
Estimated to obtain Δ θ (u, v) according to the maximum likelihood function of Δ θ (u, v), and gives the definition of the angular coordinate of first node
For the random value between 0 to 2 π, it is left the angular coordinate of node according to the angular coordinate of first node and the difference Δ θ (u, v) of angular coordinate
It calculates, to obtain the first angular coordinate of each node.
Specifically, can be according to known network structure, the degree for counting each node obtains first degree of each node
Relevant parameter κi, wherein i=1 ..., n.
Step S2.3: according to the first angular coordinate θ and first degree of relevant parameter κ according to a preliminary estimate, intensity relevant parameter is calculated
σ, wherein intensity relevant parameter σ connects the weight on side to characterize each node.
Specifically, step S2.3 is specifically included:
The probability distribution of acquisition hyperbolic Random Graph and default weight equationWherein, probability
It is distributed as ε distribution f (ε), and<ε>=1；
Weight w is obtained according to default weight equationijVery big log-likelihood function；
Based on the first angular coordinate θ, first degree of relevant parameter κ, weight w is utilizedijThe first very big log-likelihood function, calculate
σ。
Specifically, weight w can be obtained according to default weight equationijDistribution are as follows:
Then it is independently distributed according to each even side of the definition of complex network, weight w can be obtainedijThe likelihood function of distribution:
Then logarithm is asked to obtain log-likelihood function above-mentioned likelihood function are as follows:
Local derviation is asked to obtain on log-likelihood function both sides again:
Since f (ε) is the exponential distribution that mean value is 1, the formula after local derviation can will be asked to be further simplified as following form:
It then can use maximum likelihood method for solving at this time to estimate to obtain intensity relevant parameter σ.
Step S2.4: according to the first angular coordinate θ and intensity relevant parameter σ according to a preliminary estimate, second degree of relevant parameter is calculated
κ′。
Specifically, step S2.4 is specifically included:
Obtain the connection Probability p (κ between nodei, κj, dij)；
According to connection Probability p (κi, κj, dij) and default weight equationObtain second greatly
Log-likelihood function；
Based on the first angular coordinate θ and intensity relevant parameter σ, second degree of correlation is calculated using the second very big log-likelihood function
Parameter κ '.
In the specific implementation process, weight wijDistribution are as follows:
It is independently distributed according to each even side of the definition of complex network, then weight wijThe likelihood function of distribution are as follows:
Wherein, θ () is to describe direct ratio function in step 2, and logarithm is asked to obtain log-likelihood L':
Wherein
To simplify the calculation, if log-likelihood function is expressed as L '=L1+L2:
Local derviation is asked to obtain on log-likelihood function both sides:
It calculates
Wherein
It calculates
Since f (ε) is the exponential distribution that mean value is 1, can be further simplified as follows:
In summary it calculates and finally obtains log-likelihood function
Estimate to obtain second degree of relevant parameter κ ' using maximum likelihood method for solving.
Step S2.5: according to intensity relevant parameter σ and second degree of relevant parameter κ ', calculate second jiao of each node seat
Mark θ ', wherein the second angular coordinate is each node coordinate adjusted.
Specifically, step S2.5 is specifically included: being joined using maximum likelihood method according to the intensity correlation that step S2.3 estimates
Second degree of relevant parameter κ, one group of angular coordinate adjusted value of training of number σ and step S2.4 estimationMakeAfter reevaluating
The second angular coordinate θ '.
Wherein, angular coordinate adjusted valueMethod of adjustment specifically include:
It was [θ, 2 π] according to disk one week, [θ, 2 π] is used as an independent variable axis, value is x θ thereon, and dependent variable is
Angular coordinate adjusted value；
Section is equally divided into N parts, the boundary value for obtaining each section is
Using maximum likelihood method each section boundary training one group of angular coordinate adjusted value set expression beTool
Body are as follows: at each interval border, there are lower bound x θlbThe angular coordinate adjusted value at placeWith upper bound x θubThe angular coordinate adjusted value at place
By each θ of step S2.2 rough estimateiIt is adjusted according to adjusted value, in each interval border, each angle of rotation of joint
Coordinate θ is according to known adjusted valueCarry out addition adjustment；
In each section, each node angular coordinate is carried outAddition adjustment, adjustment
The second angular coordinate θ ' of one group of new estimation is obtained afterwards.
Step S2.6: judging whether the number of iterations reaches setting value, if not up to, S2.3 is thened follow the steps, wherein walking
Angular coordinate and degree relevant parameter in rapid S2.3 to estimate are step S2.4 and the updated parameter of step S2.5.
Specifically, setting value K can be configured according to the actual situation, in solution procedure, to the number of iterations into
Row record, and current the number of iterations is compared with setting value.Angular coordinate and intensity relevant parameter in each iterative process
All it is adjusted.
Step S2.7: whether the precision of the second angular coordinate θ ' of Rule of judgment estimation has restrained, if do not restrained,
Step S2.3 is gone to, wherein the angular coordinate and degree relevant parameter in step S2.3 to estimate are step S2.4 and step S2.5
Updated parameter.
Step S2.8: the third angular coordinate θ of each node is estimated using maximum likelihood method essencei, wherein third angular coordinate
For each node the hyperbolic space actual coordinate.
In the specific implementation process, each node in the method essence estimation hyperbolic space of very big log-likelihood function is utilized
Third angular coordinate θi, wherein i=1 ..., n.
Step S2.9: according to node total number n, disc radius R, power law parameter α and temperature T, the diameter of each node is calculated
Coordinate ri。
Specifically, step S2.9 is specifically included:
The diameter coordinate r of node is obtained according to following calculation formulai:
Wherein, deg (i) indicates the company's side sum being connected with node i, and n is node total number, and R is disc radius, and α is
Power law parameter, T are temperature parameter.
Step S2.10: according to the third angular coordinate θ of nodeiWith diameter coordinate ri, obtain the coordinate of all hyperbolic space nodes
(r, θ), all hyperbolic space nodes constitute the network after insertion.
Specifically, the embodiment of the present invention is by being embedded into the hyperbolic space, available hyperbolic space section for complex network
The coordinate (r, θ) of point, it is each node in complex network that hyperbolic space node coordinate is corresponding, can describe complex network section
A kind of mapping relations of point, and then can handle complex network problem according to node coordinate, such as feature information extraction, each
Association etc. between node.
The concrete application of the method provided in order to illustrate the embodiments of the present invention more clearly is given below by specific example
To be discussed in detail, for the complex network having the right, node total number be 1000,1000 nodes link information and each side
Weight provided by txt document, directly as input, the number of iterations is rule of thumb provided.
First according to the txt document of input, weight matrix is generatedAnd adjacency matrixThen step S2.1~S2.10 is executed, then can be exported as the hyperbolic space section of 1000 nodes
Point coordinate.
Method provided by the invention has the following advantages that or advantageous effects:
The invention proposes a kind of embedding grammar of complex network, the connection that can use the hyperbolic Random Graph provided is general
Rate obtains the connection relationship between each node, and then obtains the network after the complex network insertion hyperbolic space, due to that can incite somebody to action
Complex network is embedded into compared to in theorem in Euclid space " bigger " hyperbolic space, retains complex network band so as to more complete
Some essential informations improve precision, reduce the error that information indicates, solve the method for the prior art since information is imperfect and
The larger technical problem of existing error.
Although preferred embodiments of the present invention have been described, it is created once a person skilled in the art knows basic
Property concept, then additional changes and modifications can be made to these embodiments.So it includes excellent that the following claims are intended to be interpreted as
It selects embodiment and falls into all change and modification of the scope of the invention.
Obviously, those skilled in the art can carry out various modification and variations without departing from this hair to the embodiment of the present invention
The spirit and scope of bright embodiment.In this way, if these modifications and variations of the embodiment of the present invention belong to the claims in the present invention
And its within the scope of equivalent technologies, then the present invention is also intended to include these modifications and variations.
Claims (10)
1. a kind of hyperbolic embedding grammar of complex network characterized by comprising
Step S1: the figure that complex network is constituted is obtained；
Step S2: the figure that complex network is constituted is mapped to by the hyperbolic space that curvature is -1 based on Poincare disk model, is obtained
The hyperbolic map of complex network insertion, include in hyperbolic map each node node coordinate and node between connection probability, according to institute
The connection property for stating each node in the degree and weight and hyperbolic map between Node Contraction in Complex Networks, passes through logarithm maximum likelihood
Method estimates the node coordinate in hyperbolic map, according to the original connection relationship of each node, and then obtains complex network insertion
Network after the hyperbolic space.
2. the method as described in claim 1, which is characterized in that the node total number n of the complex network, complex network node
Between side information and node between connect the weight on sideWherein wijIt indicates to connect between node i and node j
The weight on side, i=1 ..., n, j=1 ..., n, in the absence of even side, weight 0, and wii=1 permanent establishment, step S1 tool
Body includes:
Complex network adjacency matrix is generated according to the side information between nodeWherein xijIndicate node i
With the presence or absence of even side, i=1 ..., n, j=1 ..., n between node j, if there is even Bian Zewei 1, there is no even Bian Ze
It is 0, and xii=1 permanent establishment；
Above-mentioned complex network is constituted into figure G (V, E), wherein V indicates the set of Node Contraction in Complex Networks, and E is indicated in complex network
Connect the set on side between node.
3. method according to claim 2, which is characterized in that step S2 is specifically included:
Step S2.1: according to the node total number and Poincare disk model of complex network, hyperbolic disc radius R is calculated；
Step S2.2: setting the number of iterations k, according to the first angular coordinate θ of maximum likelihood method for solving each node according to a preliminary estimate
With first degree of relevant parameter κ, wherein the first angular coordinate θ is that the figure that complex network is constituted is embedded in after the hyperbolic space according to a preliminary estimate
Coordinate, to characterize company's side situation between each node, the degree by counting each node obtains first degree of relevant parameter κ；
Step S2.3: according to the first angular coordinate θ and first degree of relevant parameter κ according to a preliminary estimate, calculating intensity relevant parameter σ,
In, intensity relevant parameter σ connects the weight on side to characterize each node；
Step S2.4: according to the first angular coordinate θ and the first intensity relevant parameter σ according to a preliminary estimate, second degree of relevant parameter is calculated
κ′；
Step S2.5: according to intensity relevant parameter σ and second degree of relevant parameter κ ', calculate the second angular coordinate of each node
θ ', wherein the second angular coordinate is each node coordinate adjusted；
Step S2.6: judging whether the number of iterations reaches setting value k, if not up to, thening follow the steps S2.3, wherein step
Angular coordinate and degree relevant parameter in S2.3 to estimate are step S2.4 and the updated parameter of step S2.5；
Step S2.7: whether the precision of the second angular coordinate θ ' of Rule of judgment estimation has restrained, if do not restrained, goes to
Step S2.3, wherein the angular coordinate and degree relevant parameter in step S2.3 to estimate are that step S2.4 and step S2.5 updates
Parameter afterwards；
Step S2.8: the third angular coordinate θ i of each node is estimated using maximum likelihood method essence, wherein third angular coordinate is each
Actual coordinate of a node in the hyperbolic space；
Step S2.9: according to node total number n, disc radius R, power law parameter α and temperature T, the diameter coordinate of each node is calculated
ri；
Step S2.10: according to the third angular coordinate θ of nodeiWith diameter coordinate ri, obtain the hyperbolic space of all complex network nodes
Coordinate (r, θ), all hyperbolic space nodes constitute the network after insertion.
4. method as claimed in claim 3, which is characterized in that in step S2.1, the specific calculation of hyperbolic disc radius R
It is as follows:
Wherein, n is the node total number of weighted input complex network, and β is power law index, according to the classic algorithm of accumulative degree distribution
Estimation, α is adjustment parameter, for adjusting power law index β, wherein it is temperature parameter that the relationship between β and α, which is β=2 α+1, T,
For adjusting hyperbolic space basis geometry, | E | connect the total number on side for node of graph.
5. method as claimed in claim 3, which is characterized in that step S2.2 is specifically included:
Any two node u is obtained, v, diameter coordinate is respectively ruAnd rv, wherein the calculating of the difference of the angular coordinate of two nodes is public
Formula are as follows:
Wherein, Θ () indicates that direct ratio function, Θ (1) are invariant,WithIt is directly proportional, r0=min
{ R, R-ru- 2log (Δ θ (u, v)) ± Θ (1) }, R is the hyperbolic disc radius calculated in step S2.1；
Obtain two common neighbours' quantity c of node u, vuvCalculation formula:
The calculation formula of the difference of the angular coordinate of two nodes is converted, the maximum likelihood function of Δ θ (u, v) is obtained:
Estimated to obtain Δ θ (u, v) according to the maximum likelihood function of Δ θ (u, v), and is defined as 0 to the angular coordinate of first node
Random value between 2 π, the angular coordinate for being left node are counted according to the angular coordinate of first node and the difference Δ θ (u, v) of angular coordinate
It calculates, to obtain the first angular coordinate of each node.
6. method as claimed in claim 3, which is characterized in that step S2.3 is specifically included:
The probability distribution of acquisition hyperbolic Random Graph and default weight equationWherein, probability distribution is
ε is distributed f (ε), and<ε>=1；
Weight w is obtained according to default weight equationijVery big log-likelihood function；
Based on the first angular coordinate θ, first degree of relevant parameter κ, weight w is utilizedijIt obtains the first very big log-likelihood function and calculates σ.
7. method as claimed in claim 3, which is characterized in that step S2.4 is specifically included:
Obtain the connection Probability p (κ between nodei, κj, dij)；
According to connection Probability p (κi, κj, dij) and default weight equationObtain the second very big logarithm
Likelihood function；
Based on the first angular coordinate θ and intensity relevant parameter σ, second degree of relevant parameter is calculated using the second very big log-likelihood function
κ′。
8. method as claimed in claim 3, which is characterized in that step S2.5 is specifically included:
The intensity relevant parameter σ estimated using maximum likelihood method according to step S2.3 to step S2.4 estimates second degree it is related
Parameter κ trains one group of angular coordinate adjusted valueMakeAs the second angular coordinate θ ' after reevaluating.
9. method according to claim 8, which is characterized in that angular coordinate adjusted valueMethod of adjustment specifically include:
It was [0,2 π] according to disk one week, [0,2 π] is used as an independent variable axis, value is x θ thereon, and dependent variable is angle seat
Mark adjusted value；
Section is equally divided into N parts, the boundary value for obtaining each section is
Using maximum likelihood method each section boundary training one group of angular coordinate adjusted value set expression beSpecifically:
At each interval border, there are lower bound x θlbThe angular coordinate adjusted value at placeWith upper bound x θubThe angular coordinate adjusted value at place
By each θ of step S2.2 rough estimateiIt is adjusted according to adjusted value, in each interval border, each node angular coordinate θ
According to known adjusted valueCarry out addition adjustment；
In each section, each node angular coordinate is carried outAddition adjustment, after adjustment
To the second angular coordinate θ ' of one group of new estimation.
10. method as claimed in claim 3, which is characterized in that step S2.9 is specifically included:
The diameter coordinate r of node is obtained according to following calculation formulai:
Wherein, deg (i) indicates company's side sum of node i, and n is node total number, and R is disc radius, and α is power law parameter, and T is
Temperature parameter.
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