CN110138619A - A kind of start node choosing method that realizing maximizing influence and system - Google Patents

A kind of start node choosing method that realizing maximizing influence and system Download PDF

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CN110138619A
CN110138619A CN201910448351.1A CN201910448351A CN110138619A CN 110138619 A CN110138619 A CN 110138619A CN 201910448351 A CN201910448351 A CN 201910448351A CN 110138619 A CN110138619 A CN 110138619A
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collection
transferred
curdist
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CN110138619B (en
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周旭
刘勇刚
姜文君
肖国庆
罗文晟
李肯立
李克勤
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Hunan University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/01—Social networking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/145—Network analysis or design involving simulating, designing, planning or modelling of a network

Abstract

The invention discloses a kind of start node choosing methods for realizing maximizing influence, its scene for influences a variety of in social networks while propagation, the consciousness of comforming is introduced into communication process, it proposes inversely for the propagation model for the consciousness of comforming using the method for sampling, start node choosing method and start node estimation method, it is reverse using sampling to network progress is influenced first, then according to inversely using the sample of sampling, iteratively calculate start node, until meeting required precision using income using estimation method judgement, otherwise sampling scale is doubled, repeat above step.The propagation model for consciousness of comforming is more scientific and truly modelled propagation process, start node choosing method can accurately and efficiently choose start node, and can adapt to large scale network structure, improves the timeliness of start node choosing method.

Description

A kind of start node choosing method that realizing maximizing influence and system
Technical field
The invention belongs to computer information technology fields, realize the initial of maximizing influence more particularly, to a kind of Node selection method and system.
Background technique
The life that the development of internet is not only provided convenience for the mankind, more changes human lives and working method.With The network applications rise such as Facebook, microblogging and mobile network's terminal it is universal, online social networks will be dispersed in differently Domain possesses heterogeneous beliefs, is under the jurisdiction of country variant and the people of tissue link together, and forms a huge information transportation net Network.Huge economy and society value is contained in the information propagation of large-scale social networks (such as can be used for advertisement marketing and political affairs Plan is promoted), therefore start node how is chosen to realize maximizing influence (Influence maximization, abbreviation IM), have become social networks technical field one important to study a question.
Existing start node selection method is mainly based upon independent cascade (Independent cascade, abbreviation IC) Model or linear threshold (Linear threshold, abbreviation LT) model use the method, heuristic based on analogue simulation Method or the method for reverse influence sampling determine the influence of start node.However, existing start node selection method institute The model used still has the technical issues of can not ignore: since it does not account for conformity behavior, so that the model established is not It is enough true, thus the influence value obtained is inaccurate, the start node for eventually leading to selection is not ideal enough.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the first of maximizing influence is realized the present invention provides a kind of Beginning node selection method and system, it is intended that solving model used by existing start node selection method due to not having Consider conformity behavior, so that the model established is not true enough, leads to the start node that the influence value obtained is inaccurate, selects not Enough ideal technical problems；In addition, the authenticity and science of the propagation model enhancing propagation model proposed in the present invention, also mention The scope of application of propagation model is risen；Finally, the start node selection method proposed in the present invention improves start node selection The timeliness of method.
To achieve the above object, according to one aspect of the present invention, it provides and a kind of realizes the initial of maximizing influence Node selection method, comprising the following steps:
(1) influence diagram is constructed according to established propagation model, and start node collection S is generated according to the influence diagram of buildingC, For propagating other influences for having competitive relation；
(2) according to preset precision parameter ε and δ, threshold value T is obtained using SSA algorithm0, to the influence diagram obtained in (1) into Row T0Secondary T reverse using sampling, and that all samplings are obtained0A sample is put into sample setIn；
(3) according to the sample set returned in step (2)Iteratively k is selected to use edge income from influence diagram Maximum node obtains the Biased estimator of the use of start node collection S as start node collectionWherein 0 < k < n；
(4) counter c10=0 is set, executes step (5) reverse number using sampling, and setting steps for indicating (3) the total of the start node collection S obtained in uses SUM2=0；
(5) inversely using sampling, calculate the start node collection S obtained in step (3) in this sampling to influence diagram Middle acquisition uses Ac10, and update the total using SUM of the start node collection S obtained in step (3)2=SUM2+Ac10；
(6) judge whether counter c10 is less than threshold value T2And the total of start node collection S uses SUM2Whether threshold value T is less than3, C10=c10+1, and return step (5) are if it is set, otherwise exportedAnd enter step (7)；
(7) Biased estimator of the start node collection S obtained in judgment step (3)It is first with being obtained in step (6) The unbiased esti-mator of beginning node collection SWhether meetIt is saved if it is satisfied, then directly output is initial Otherwise point set S updates sampling number T used in step (2) as a result, process terminates0=2*T0, and return step (2).
Preferably, influence diagram is represented as G=(V, E, p), and wherein V indicates the set of node, and E indicates the collection of directed edge Close, p indicates the function for the activation probability that all sides are preassigned, each edge have a pre-assigned activation Probability p (u, V) [0,1] ∈ indicates the probability of node u activation node v.
Preferably, the communication process of propagation model is as follows:
Firstly, different influences activates respective start node, at 0 moment to start communication process.Different influences can Select identical node as start node；
Then, in t moment, become state of activation at this moment in the node that the t-1 moment is activated, and attempt to activate The neighbor node not being activated, if activation trial and success, the node being activated will receive being had an impact for activation node, if Failed, then not to be activated node holding unactivated state is attempted in activation, and after this, the node in state of activation will According to comforming using probability defined in function, using one of its received influence, and adoption status is ultimately become；
That comforms is as follows using function h (u, I) definition probability:
Wherein, h (u, Ii) indicate node u using influence IiProbability,It is the set of had an impact composition, NA (u, Ii) Expression, which has activated node u and has propagated to it, influences IiNeighbor node.
Finally, communication process termination when not new node is activated.
Sample in step (2) is the data that single is inversely obtained using sampling, and including node set R, node set R In the set { d (u) | u ∈ R } of distance between each node w and other nodes, in node set R each node activation node Set { NA (u) | u ∈ R }, node w and the start node collection S of collectionCDistance dCWith node w by start node collection SCInterior joint institute The total degree Time of the influence activation of propagationC。
Preferably, single includes inversely following sub-step using the process of sampling in step (2):
(2-1) is randomly chosen a node w from influence diagram, and node w and itself distance d (w is arrangedc1)=0, by w It is put into node set R, and start node set S is setCWith node w distance dCVariable curDist=0 is arranged in=∞, CurDist indicate currently processed node at a distance from node w, abbreviation current distance；
(2-2) judges whether node w is start node collection SCIn element, if it is, record node w by competition shadow Ring the total degree Time of activationCWith start node set SCWith node w distance dc=0, it is transferred to step (2-17), is otherwise entered Step (2-3)；
Counter c1=1, current distance curDist=curDist+1 is arranged in (2-3), judges whether c1 value is greater than node w Enter neighbor node sum, if it is, being transferred to step (2-17), be otherwise transferred to step (2-4)；
(2-4) enters neighbor node w according to c1 of node wc1Activate the probability predicate node w of node wc1Activate node w Whether succeed, if it is, record node wc1With node w distance d (wc1)=curDist, by node wc1It is put into its activation section Point set NA (wc1), by node wc1It is put into node set V, and is transferred to step (2-5), be otherwise transferred to step (2-6)；
(2-5) judges node wc1It whether is start node collection SCIn element, if it is by start node set SC With node w distance dCIt is set as current distance curDist, and is transferred to step (2-6), is otherwise transferred to step (2-6)；
(2-6) judges that whether c1 value be equal to node w enters neighbor node sum, no if it is, be transferred to step (2-8) Then it is transferred to step (2-7)；
Counter c1=c1+1, and return step (2-4) is arranged in (2-7)；
(2-8) judges node set V and start node collection SCWhether have whether intersection or node set V are empty set, such as Fruit is then to calculate and record node w by node set V and SCThe total degree for the competitive influence activation that intersection interior joint is propagated TimeC, and it is transferred to step (2-17), otherwise all nodes in node set V are put into node set R, and be transferred to step (2-9)；
Counter c2=1 and current distance curDist=curDist+1 is arranged in (2-9)；
(2-10) selects the c2 node w from node set Vc2, and counter c3=1 is set, judge counter c3's Whether value is greater than node wc2Enter neighbor node sum, if it is, being transferred to step (2-14), be otherwise transferred to step (2-11)；
(2-11) judges node wc3Whether not in node set R, and according to node wc2C3 enter neighbor node wc3 Activate node wc2Probability predicate node wc3Activate node wc2Whether succeed, if it is, setting node wc3With node w away from From d (wc3) it is equal to curDist, by node wc2Activation node collection NA (wc2) in element be put into node wc3Activate node collection NA (wc3) in, by node wc3It is put into node set VnextIn, and it is transferred to step (2-12), otherwise it is transferred to step (2-13)；
(2-12) judges node wc3It whether is start node collection SCIn element, if it is be arranged start node set SC With node w distance dCEqual to curDist, and it is transferred to step (2-13), is otherwise directly transferred to step (2-13)；
(2-13) judges whether the value of counter c3 is greater than node wc2Enter neighbor node sum, if it is, being transferred to step Suddenly counter c3=c3+1, and return step (2-11) is otherwise arranged in (2-14)；
(2-14) judges whether counter c2 value is equal to the node total number in node set V, if yes then enter step (2- 15) counter c2=c2+1, and return step (2-10), are otherwise set；
(2-15) judges node set VnextWith start node collection SCWhether intersection or node set V are hadnextWhether be Empty set, if it is, obtaining node w by node set VnextWith SCTotal time of the competitive influence activation that intersection interior joint is propagated Number TimeC, and it is transferred to step (2-17), otherwise it is transferred to step (2-16)；
(2-16) uses node set VnextIn all nodes replacement node set V in all nodes, and by node collection All nodes closed in V are put into node set R, and return step (2-8)；
(2-17) obtain node set R, in node set R the distance between each node and node w set d (u) | u ∈ R }, in node set R the activation node collection of each node set { NA (u) | u ∈ R }, node w and start node collection SC's Distance dCAnd node w is by start node collection SCThe total degree Time for the influence activation that interior joint is propagatedC。
Preferably, the k mistake using the node of edge Income Maximum as start node collection is iteratively selected in step (3) Journey includes following sub-step:
(3-1) settingCounter c4=1 is set, and each node is in sample set in setting influence diagramOn The initial value always used is 0, and start node collection S is in sample setOn use summation SUM1=0；
Counter c5=1 is arranged in (3-2)；
(3-3) is from sample setThe c5 sample R of middle taking-upc5, counter c6=1 is set；
(3-4) is from sample Rc5The c6 node w of middle taking-upc6, judge in Rc5Interior joint wc6With node w distance d (wc6) Whether d is less thanC, if it is, setting node wc6In Rc5On be adopted as 1, node wc6It is total using plus 1, be then transferred to step (3-5)；Otherwise, node w is setc6In Rc5On be adopted asUpdate wc6In sample setOn it is total It is adopted as node wc6In sample setOn it is total using addingThen it is transferred to step (3-5)；Wherein NA(wc6) and TimeCIt is to respectively indicate sample Rc5In activation node collection and start node collection SCThe influence that interior joint is propagated swashs Sample R livingc5In node w total degree.
(3-5) judges whether counter c6 is less than | Rc5|, if it is, setting c6=c6+1, then return step (3- 4), otherwise it is transferred to step (3-6)；
(3-6) judges whether counter c5 is less thanIf it is, setting c5=c5+1, and return step (3-3), it is no Then it is transferred to step (3-7)；
(3-7) exists to nodes all in influence diagram according to each node using big root heapOn the size that always uses carry out Descending arrangement；
(3-8) judges counter C4Whether preset threshold k is less than, if it is, taking outOn always use maximum section Point wc4, by node wc4Start node collection S is added, SUM is set1=SUM1+A(wc4), wherein A (wc4) it is node wc4?On It is total to use, and the deletion of node w from big root heapc4, and step (3-9) is gone to, otherwise obtains start node set S and used with it Biased estimatorThen it is transferred to step (3-22).
(3-9) is from sample setMiddle take out all includes node wc4Sample, formed sample setAnd meter is set Number device c7=1；
(3-10) takes outIn the c7 sample Rc7, and judgement sample Rc7Whether it is marked as determining use, if It is to go to step (3-21), otherwise goes to step (3-11)；
(3-11) judges wc4With sample Rc7In node w distance d (wc4) whether it is less than Rc7In start node set SC With node w distance dC, if it is marker samples Rc7It is used to determine, and goes to step (3-12), otherwise go to step (3- 15)；
Counter c8=1 is arranged in (3-12)；
(3-13) takes out sample Rc7In the c8 node, update wc8In sample setOn be always adopted as node wc8 In sample setOn it is total using subtracting node wc8In Rc7On use, and more new node wc8Sequence in big root heap.
(3-14) judges whether counter c8 is less than | Rc7|, if it is, setting c8=c8+1, and go to step (3- 13) step (3-21), otherwise, is gone to；
Counter c9=1 is arranged in (3-15)；
(3-16) takes out sample Rc7In the c9 node wc9, judge wc9With sample Rc7In node w distance d (wc9) Whether R is less thanc7In start node set SCWith node w distance dC, step (3-17) is if it is gone to, step is otherwise gone to Suddenly (3-18)；
(3-17) more new node wc9In Rc7On be adopted as node wc9In Rc7On use subtract node wc4In Rc7On Using more new node wc9In sample setOn be always adopted as node wc9In sample setOn it is total using subtracting node wc4In Rc7On use；
(3-18) more new node wc9In sample setOn be always adopted as node wc9In sample setOn total use Subtract node wc9In Rc7On use, more new node wc9In Rc7On be adopted asWhereinFor swashing for set S interior joint The size of the union of movable joint point set, i.e., start node collection S is in Rc7On activation total degree, and more new node w againc9In sample SetOn be always adopted as node wc9In sample setOn it is total using add node wc9In Rc7Upper updated use；
Sequence of (3-19) the more new node wc9 in big root heap；
(3-20) judges whether counter c9 is less than | Rc7|, if it is, setting c9=c9+1, and go to step (3- 16) step (3-21), otherwise, is gone to；
(3-21) judges whether counter c7 is less thanIf it is, setting c7=c7+1, and go to step (3- 10) step (3-8), otherwise, is gone to；
(3-22) judges SUM1Whether threshold value T is greater than1, if it is, entering step (4), otherwise updating makes in step (2) Sampling number T0=2*T0, and return to (2).According to SSA algorithm, threshold value T1Calculation formula beWhereinε2=ε3=(1-1/e)-1ε/2。
Preferably, start node collection S's using f (S) is obtained using following formula:
Wherein, S is start node collection, and n is nodes sum, AiIt is the use income of i-th sampling,It is real The number of border sample,It isIn all samples average use.
Preferably, influence diagram is carried out inversely using sampling in step (5), and calculates the initial section obtained in step (3) What point set S was obtained in this sampling uses Ac10Process include following sub-step:
(5-1) is randomly chosen a node z from influence diagram, and node z is put into node set R, start node collection SCWith node z distance dC=∞, start node collection S and node z distance dS=∞, current distance curDist=0, it is initial to save Point set S uses A what this was sampledc10=0；
(5-2) judges whether node z is start node collection SCIn element, if it is dC=curDist is transferred to step Suddenly (5-3) otherwise enters step (5-3)；
(5-3) judges whether node z is element in start node collection S, if it is dS=curDist is transferred to step Suddenly (5-4) otherwise enters step (5-4)；
(5-4) judges dCWhether it is equal to curDist, is if it is transferred to step (5-5), otherwise enters step (5-6)；
(5-5) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWherein TimeCIt is the total degree that node z is activated by competitive influence, and is transferred to step (5-30), otherwise just Beginning node collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-6) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, turn Enter step (5-30), otherwise enters step (5-7)；
Counter c11=1, current distance curDist=curDist+1 is arranged in (5-7)；
(5-8) judges that whether c11 value be greater than node z enters neighbor node sum, if it is, be transferred to step (5-13), Otherwise it is transferred to step (5-9)；
(5-9) enters neighbor node z according to c11 of node zc11Activate the probability predicate node z of node zc11Activation section Whether point z succeeds, if it is, by node zc11It is put into it and activates node collection NA (zc11), by node zc11It is put into node set V In, and it is transferred to step (5-10), otherwise it is transferred to step (5-11)；
(5-10) judges node zc11It whether is start node collection SCIn element, if it is dC=curDist will be saved Point zc11Node collection Set is addedCIn, it is transferred to step (5-11), otherwise enters step (5-11)；
(5-11) judges node zc11It whether is element in start node collection S, if it is dS=curDist, it will Node zc11Node collection Set is addedSIn, it is transferred to step (5-12), otherwise enters step (5-12)；
(5-12) counter c11=c11+1, enters step (5-8)；
(5-13) judges dCWhether it is equal to curDist, is if it is transferred to step (5-14), otherwise enters step (5- 15)；
(5-14) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinIt is the total degree that node z is activated by competitive influence, InfsetCIt (u) is node collection SetCThe set for the competitive influence that interior joint is propagated, and is transferred to step (5-30), otherwise start node Collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-15) judges dSWhether curDist is equal to, if it is start node collection S uses A what this was sampledc10= 1, it is transferred to step (5-30), otherwise enters step (5-16)；
(5-16) if node set V is not empty set, and dSNot equal to curDist, and dCIt, then will section not equal to curDist All nodes in point set V are put into node set R, are transferred to step (5-17), are otherwise transferred to step (5-27)；
(5-17) be arranged counter c12=1, currently with node z distance curDist=curDist+1；
(5-18) judges the node total number whether c12 value is greater than in node set V, if yes then enter step (5-26), Otherwise return step (5-19)；
(5-19) selects the c12 node z from node set Vc12, and counter c13=1 is set；
(5-20) judges whether c13 value is greater than node zc12Enter neighbor node sum, if it is, being transferred to step (5- 25), otherwise it is transferred to step (5-21)；
(5-21) judges node zc13Whether not in node set R, and according to node zc12C13 enter neighbor node zc13Activate node zc12Probability predicate node zc13Activate node zc12Whether succeed, if it is, by node zc12Activation section Point set NA (wc2) in element be put into node zc13Activate node collection NA (wc3) in, by node zc13It is put into node set VnextIn, And it is transferred to step (5-22), otherwise it is transferred to step (5-24)；
(5-22) judges node zc13It whether is start node collection SCIn element, if it is dC=curDist will be saved Point zc13Node collection Set is addedCIn, it is transferred to step (5-23), otherwise enters step (5-23)；
(5-23) judges node zc13It whether is element in start node collection S, if it is dS=curDist will be saved Point zc13Node collection Set is addedSIn, it is transferred to step (5-24), otherwise enters step (5-24)；
(5-24) counter c13=c13+1, and return step (5-20)；
(5-25) counter c12=c12+1, and return step (5-18)；
(5-26) uses node set VnextIn all nodes replacement node set V in all nodes, and return step (5-16)；
(5-27) judges dCWhether it is equal to curDist, is if it is transferred to step (5-28), otherwise enters step (5- 29)；
(5-28) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinFor set S interior joint activation node collection and The size of collection, and it is transferred to step (5-30), otherwise start node collection S uses A what this was sampledc10=0, enter step (5- 30)；
(5-29) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, It is transferred to step (5-30), otherwise enters step (5-30)；
(5-30) returns to the use A of this samplingc10。
It is another aspect of this invention to provide that providing a kind of start node selecting system for realizing maximizing influence, wrap It includes:
First module for constructing influence diagram according to established propagation model, and generates just according to the influence diagram of building Beginning node collection SC, for propagating other influences for having competitive relation；
Second module, for obtaining threshold value T using SSA algorithm according to preset precision parameter ε and δ0, to the first module The influence diagram of acquisition carries out T0Secondary T reverse using sampling, and that all samplings are obtained0A sample is put into sample setIn；
Third module, the sample set for being returned according to the second moduleK use is iteratively selected from influence diagram The node of edge Income Maximum obtains the Biased estimator of the use of start node collection S as start node collectionIts In 0 < k < n；
Counter c10=0 is arranged in 4th module, for indicating to execute step (5) inversely using the number of sampling, and sets Set the total using SUM of the start node collection S of third module acquisition2=0；
5th module, for inversely calculate the start node collection S that third module obtains using sampling and exist to influence diagram What is obtained in this sampling uses Ac10, and the total of start node collection S for updating the acquisition of third module uses SUM2=SUM2+Ac10；
6th module, for judging whether counter c10 is less than threshold value T2And the total of start node collection S uses SUM2Whether Less than threshold value T3, c10=c10+1 is if it is set, and returns to the 5th module, otherwise exports the use of start node collection S Biased estimatorSubsequently into the 7th module；
7th module, the Biased estimator of the start node collection S for judging the acquisition of third moduleWith the 6th module The unbiased esti-mator of the start node collection S of acquisitionWhether meetIf it is satisfied, then directly defeated Out otherwise start node collection S updates the sampling number T that the second module uses as a result, process terminates0=2*T0, and return to the Two modules.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show Beneficial effect:
(1) propagation model of consciousness proposed by the present invention of comforming, it is contemplated that a variety of competitive relations for influencing to propagate, and for the first time It is used as decision-making foundation during conformity behavior is introduced using influencing, to enhance the reasonability and science of propagation model Property, the influence value of acquisition is accurate, therefore the start node of final choice is ideal enough；
(2) present invention for consciousness of comforming propagation model design it is reverse using the method for sampling, solve conventional inverse The problem of influencing sampling are not suitable for the method for sampling, so that inversely wider using the scope of application of the method for sampling more；
(3) incrementally more new node uses income for start node selection method of the invention, to reduce a large amount of It computes repeatedly, improves computational efficiency.
Detailed description of the invention
Fig. 1 is the flow chart for the start node choosing method that the present invention realizes maximizing influence；
Fig. 2 is the state transition diagram of the propagation model interior joint for the consciousness of comforming；
Fig. 3 shows an example of the propagation model of consciousness of the invention of comforming.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below Not constituting a conflict with each other can be combined with each other.
For the above-mentioned deficiency mentioned in background technique, present invention firstly provides a kind of propagation model of consciousness of comforming, For the propagation design of multiple competitive influences, the conformity behavior of people is introduced into communication process, for select finally to use It influences；Then, based on the propagation model for the consciousness of comforming, we have proposed the use maximization problems comformed；Finally, for comforming The propagation model design of consciousness inversely uses the method for sampling and start node selection method, and calculates and have in conjunction with SSA frame The start node set of quality assurance.
The technical term occurred in the present invention is explained in detail and is illustrated first below:
Comform: also referred to as conformity behavior refers to the personal influence by extraneous crowd behaviour, and in the consciousness of oneself, judge, recognize The behavior for according with public opinion or majority is shown in knowledge.
Using: the section for referring to the expectation of the quantity in social networks using certain node influenced or being influenced using certain The quantity of point.
That comforms uses function: for the scenes with emulative influence while propagation multiple in social networks, passing Broadcast probability function defined in modelThat comforms is met using probability function: 0≤h (u, Ii) ≤ 1 andTo provide probability ginseng using one such influence for the node selection in social networks Number, and node receive certain influence number it is more, using this kind influence probability it is bigger, embody node selection obey The behavior comformed.
Enter neighbor node: the information between the node in social networks, which is propagated, has directionality, therefore, the section in influence diagram Side between point also has direction.For arbitrary node v, if there is a directed edge (u, v), indicate that node u is directed toward node V, then, node u is that node v enters neighbor node.
Neighbor node out: with it is upper similarly, for arbitrary node u, if there is a directed edge (u, v), indicate that node u refers to To node v, then, node v is the neighbor node out of node u.
The propagation model for consciousness of comforming: which specify propagation rule of a variety of influences in influence diagram.Each section among these There are two types of behaviors for point: activating and uses, controls mainly activation probability function p (e) of both action and the use comformed is general Rate function h (u, I).
Activate probability function p (e) in the present invention there are three types of set-up mode, unified probability is arranged, and in-degree inverse weight is set Set selected with three values one setting.Unify probability set-up mode, identical activation probability is arranged in each edge in network, is commonly 0.1.The setting of in-degree inverse weight, by while activation probability be set as this while terminal in-degree inverse, i.e. p (u, v)=1/ | Nin(v) |, wherein side e=(u, v), v are the terminal on side, Nin(v) all of the side of v are directed to and enter neighbours.Three values select one Setting is that the activation probability for being set as side is randomly chosen from { 0.1,0.01,0.001 } three values.
That comforms is defined using the following h of probability function (u, I):
Wherein, h (u, Ii) indicate that node u uses IiProbability, Freq (Ii) indicate that u receives influence IiNumber.In reality Border uses following formula in calculating:
NA(u,Ii) indicate to have activated u and have propagated I to itiEnter neighbours.
That comforms is met using probability function: 0≤h (u, Ii)≤1 and
As shown in Figure 1, the present invention realize maximizing influence start node choosing method the following steps are included:
(1) influence diagram (Influence graph) is constructed according to established propagation model, and according to the influence diagram of building Generate start node collection SC, for propagating other influences (i.e. competitive influence) for having competitive relation；
Social networks is modeled as oriented influence diagram G=(V, E, p), and wherein V indicates the set of node, and E indicates oriented The set on side, p indicate the function for the activation probability that all sides are preassigned, and each edge has a pre-assigned activation general Rate p (u, v) ∈ [0,1] indicates the probability of node u activation node v.
For start node collection SCFor, it is assumed that there is q >=a kind influence in social networks, every kind influences all to correspond at the beginning of one The start node collection of beginning node collection, different influences can be overlapped, i.e. the start node that a node can be used as multiple influences. Start node collection SCCan be arranged by obtaining true start node from the network of reality, can also taking human as pass through inspiration The method setting (being such as arranged according to the out-degree of node) of formula.For example, being every kind of competitive influence as the number q=2 of competitive influence 50 start nodes are set, and it is the common start node of two kinds of competitive influences that maximum 25 nodes of out-degree, which may be selected, then again It is followed successively by two influences and distributes the maximum node of out-degree in remaining node, each node distributes a kind of influence.
Fig. 2 illustrates three kinds of state changes of the communication process interior joint of propagation model, and node is initially unactivated state, Become state of activation if by neighbor node successful activation, if un-activation will do not kept still by neighbor node successful activation State.When the node being activated receives the influence that one or more nodes are propagated, it will select and apply one of shadow It rings, state can become having used, and remains to communication process and terminate.
The communication process of propagation model is further illustrated below in conjunction with Fig. 3.In Fig. 3, circle indicates node, line with the arrow Indicate oriented side, the influence that digital representation this node in circle receives.Fan-shaped expression in circle is using corresponding shadow Loud probability, the line segment with the arrow of overstriking indicate the side for being try to activation, and dotted line indicates activation failure.
1) moment 0, different influences activates respective start node, to start communication process.Different influences may be selected Identical node is as start node.
In Fig. 3, t=0 moment, tri- nodes of a, b and c are activated as start node, and a, c are affected 1 and 4 respectively and swash Living, it is influence 2,3 and 4 respectively that node b is activated by three kinds of influences.
2) in moment t, the node being activated in t-1 becomes state of activation at this moment, and attempt activation not by The neighbor node of activation, if activation trial and success, the node being activated will receive activation the having an impact of node (same not The node being activated will likely be activated by the node of multiple states of activation, so that a variety of influences are received, it is same to influence May repeatedly be received by the same node), if failed, not to be activated node holding unactivated state is attempted in activation. After this, node in state of activation is by according to the probability defined using function comformed, using its received influence One of, and ultimately become adoption status.
That comforms uses function h (u, Ii) define probability it is as follows:
Wherein, h (u, Ii) indicate node u using influence IiProbability,It is the set of had an impact composition, Freq (Ii) Indicating that node u is received influences IiNumber.Following formula is used in actually calculating:
NA(u,Ii) indicate to have activated node u and have propagated to it to influence IiNeighbor node.
That comforms is met using probability function: 0≤h (u, Ii)≤1 andIn Fig. 3, the t=1 moment, A, tri- nodes of b and c become state of activation, and attempt activation tri- unactivated nodes of d, e and f respectively.Node c activates e Failure, node e are activated by two nodes of a and b, have received four kinds of influences of two nodes.Finally, tri- nodes of d, e and f will One kind is selected in the influence received from it respectively.Its interior joint e receives four kinds of influences, and every kind of influence receives only one It is secondary, so the probability used is all 1/4.In Fig. 3, at the t=2 moment, because node e is in, adoption status, node d cannot swash E living.Node g is activated by three nodes simultaneously, receives four kinds of influences, but is influenced 1 and 4 and had received twice, remaining receives one It is secondary.So it is higher using the probability for influencing 1 and 4, it is 2/6, remaining two kinds influences use probability for 1/6.
3) communication process termination when not new node is activated.
In Fig. 3, not new node can be activated after the t=2 moment, and communication process terminates.
(2) according to preset precision parameter ε and δ, threshold value T is obtained using SSA algorithm0, to the influence diagram obtained in (1) into Row T0Secondary T reverse using sampling, and that all samplings are obtained0A sample is put into sample setIn, wherein 0 < ε <, 1,0 < δ < 1；
Specifically, threshold value T0Calculation formula beWherein, function
N indicates the node total number in influence diagram,
In this step, sample refers to the data that single is inversely obtained using sampling, specifically includes: node set R, The set { d (u) | u ∈ R } of distance between each node w and other nodes, each node in node set R in node set R Activate set { NA (u) | u ∈ R }, node w and the start node collection S of node collectionCDistance dCWith node w by start node collection SC The total degree Time for the influence activation that interior joint is propagatedC。
Single includes inversely following sub-step using the process of sampling in this step:
(2-1) is randomly chosen a node w from influence diagram, and node w and itself distance d (w is arrangedc1)=0, by w It is put into node set R, and start node set S is setCWith node w distance dCVariable curDist=0 is arranged in=∞, CurDist indicate currently processed node at a distance from node w, abbreviation current distance；
(2-2) judges whether node w is start node collection SCIn element, if it is, record node w by competition shadow Ring the total degree Time of activationCWith start node set SCWith node w distance dc=0, it is transferred to step (2-17), is otherwise entered Step (2-3)；
Counter c1=1, current distance curDist=curDist+1 is arranged in (2-3), judges whether c1 value is greater than node w Enter neighbor node sum, if it is, being transferred to step (2-17), be otherwise transferred to step (2-4)；
(2-4) enters neighbor node w according to c1 of node wc1Activate the probability predicate node w of node wc1Activate node w Whether succeed, if it is, record node wc1With node w distance d (wc1)=curDist, by node wc1It is put into its activation section Point set NA (wc1), by node wc1It is put into node set V, and is transferred to step (2-5), be otherwise transferred to step (2-6)；
(2-5) judges node wc1It whether is start node collection SCIn element, if it is by start node set SC With node w distance dCIt is set as current distance curDist, and is transferred to step (2-6), is otherwise transferred to step (2-6)；
(2-6) judges that whether c1 value be equal to node w enters neighbor node sum, no if it is, be transferred to step (2-8) Then it is transferred to step (2-7)；
Counter c1=c1+1, and return step (2-4) is arranged in (2-7)；
(2-8) judges node set V and start node collection SCWhether have whether intersection or node set V are empty set, such as Fruit is then to calculate and record node w by node set V and SCThe total degree for the competitive influence activation that intersection interior joint is propagated TimeC, and it is transferred to step (2-17), otherwise all nodes in node set V are put into node set R, and be transferred to step (2-9)；
Counter c2=1 and current distance curDist=curDist+1 is arranged in (2-9)；
(2-10) selects the c2 node w from node set Vc2, and counter c3=1 is set, judge counter c3's Whether value is greater than node wc2Enter neighbor node sum, if it is, being transferred to step (2-14), be otherwise transferred to step (2-11)；
(2-11) judges node wc3Whether not in node set R, and according to node wc2C3 enter neighbor node wc3 Activate node wc2Probability predicate node wc3Activate node wc2Whether succeed, if it is, setting node wc3With node w away from From d (wc3) it is equal to curDist, by node wc2Activation node collection NA (wc2) in element be put into node wc3Activate node collection NA (wc3) in, by node wc3It is put into node set VnextIn, and it is transferred to step (2-12), otherwise it is transferred to step (2-13)；
(2-12) judges node wc3It whether is start node collection SCIn element, if it is be arranged start node set SC With node w distance dCEqual to curDist, and it is transferred to step (2-13), is otherwise directly transferred to step (2-13)；
(2-13) judges whether the value of counter c3 is greater than node wc2Enter neighbor node sum, if it is, being transferred to step Suddenly counter c3=c3+1, and return step (2-11) is otherwise arranged in (2-14)；
(2-14) judges whether counter c2 value is equal to the node total number in node set V, if yes then enter step (2- 15) counter c2=c2+1, and return step (2-10), are otherwise set；
(2-15) judges node set VnextWith start node collection SCWhether intersection or node set V are hadnextWhether be Empty set, if it is, obtaining node w by node set VnextWith SCTotal time of the competitive influence activation that intersection interior joint is propagated Number TimeC, and it is transferred to step (2-17), otherwise it is transferred to step (2-16)；
(2-16) uses node set VnextIn all nodes replacement node set V in all nodes, and by node collection All nodes closed in V are put into node set R, and return step (2-8)；
(2-17) obtain node set R, in node set R the distance between each node and node w set d (u) | u ∈ R }, in node set R the activation node collection of each node set { NA (u) | u ∈ R }, node w and start node collection SC's Distance dCAnd node w is by start node collection SCThe total degree Time for the influence activation that interior joint is propagatedC。
(3) according to the sample set returned in step (2)Iteratively k is selected to use edge income from influence diagram Maximum node obtains the Biased estimator of the use of start node collection S as start node collectionWherein 0 < k < n；
Because influence diagram is probability graph, activating and using has randomness, so, using the quantity of certain node influenced Also there is randomness.Therefore, multiple influences are in probability directed networks in communication process, definition use function f (S) for use by Expectation of the node collection S as the quantity of certain node influenced of start node collection.Because calculate start node collection S uses f It (S) is NP-Hard problem, so, f (S) is used using the sample estimation sampled in step (2), the calculation formula of use is as follows:
Wherein, S is start node collection, and n is nodes sum, AiIt is the use income of i-th sampling,It is real The number of border sample,It isIn all samples average use.
Using the income size of the measurement start node for being desirable to more rationally science of number of nodes.
In this step, iteratively select the k node using edge Income Maximum as start node from influence diagram Detailed process is as follows for collection:
(3-1) settingCounter c4=1 is set, and each node is in sample set in setting influence diagramOn The initial value always used is 0, and start node collection S is in sample setOn use summation SUM1=0；
Counter c5=1 is arranged in (3-2)；
(3-3) is from sample setThe c5 sample R of middle taking-upc5, counter c6=1 is set；
(3-4) is from sample Rc5The c6 node w of middle taking-upc6, judge in Rc5Interior joint wc6With node w distance d (wc6) Whether d is less thanC, if it is, setting node wc6In Rc5On be adopted as 1, node wc6It is total using plus 1, be then transferred to step (3-5)；Otherwise, node w is setc6In Rc5On be adopted asUpdate wc6In sample setOn it is total It is adopted as node wc6In sample setOn it is total using addingThen it is transferred to step (3-5)；Wherein NA(wc6) and TimeCIt is to respectively indicate sample Rc5In activation node collection and start node collection SCThe influence that interior joint is propagated swashs Sample R livingc5In node w total degree.
(3-5) judges whether counter c6 is less than | Rc5|, if it is, setting c6=c6+1, then return step (3- 4), otherwise it is transferred to step (3-6)；
(3-6) judges whether counter c5 is less thanIf it is, setting c5=c5+1, and return step (3-3), it is no Then it is transferred to step (3-7)；
(3-7) exists to nodes all in influence diagram according to each node using big root heapOn the size that always uses carry out Descending arrangement；
(3-8) judges counter C4Whether preset threshold k is less than, if it is, taking outOn always use maximum section Point wc4, by node wc4Start node collection S is added, SUM is set1=SUM1+A(wc4), wherein A (wc4) it is node wc4?On It is total to use, and the deletion of node w from big root heapc4, and step (3-9) is gone to, otherwise obtains start node set S and used with it Biased estimatorThen it is transferred to step (3-22).
(3-9) is from sample setMiddle take out all includes node wc4Sample, formed sample setAnd meter is set Number device c7=1；
(3-10) takes outIn the c7 sample Rc7, and judgement sample Rc7Whether it is marked as determining use, if It is to go to step (3-21), otherwise goes to step (3-11)；
(3-11) judges wc4With sample Rc7In node w distance d (wc4) whether it is less than Rc7In start node set SC With node w distance dC, if it is marker samples Rc7It is used to determine, and goes to step (3-12), otherwise go to step (3- 15)；
Counter c8=1 is arranged in (3-12)；
(3-13) takes out sample Rc7In the c8 node, update wc8In sample setOn be always adopted as node wc8 In sample setOn it is total using subtracting node wc8In Rc7On use, and more new node wc8Sequence in big root heap.
(3-14) judges whether counter c8 is less than | Rc7|, if it is, setting c8=c8+1, and go to step (3- 13) step (3-21), otherwise, is gone to；
Counter c9=1 is arranged in (3-15)；
(3-16) takes out sample Rc7In the c9 node wc9, judge wc9With sample Rc7In node w distance d (wc9) Whether R is less thanc7In start node set SCWith node w distance dC, step (3-17) is if it is gone to, step is otherwise gone to Suddenly (3-18)；
(3-17) more new node wc9In Rc7On be adopted as node wc9In Rc7On use subtract node wc4In Rc7On Using more new node wc9In sample setOn be always adopted as node wc9In sample setOn it is total using subtracting node wc4In Rc7On use.
(3-18) more new node wc9In sample setOn be always adopted as node wc9In sample setOn total use Subtract node wc9In Rc7On use, more new node wc9In Rc7On be adopted asWhereinFor swashing for set S interior joint The size of the union of movable joint point set, i.e., start node collection S is in Rc7On activation total degree, and more new node w againc9In sample SetOn be always adopted as node wc9In sample setOn it is total using add node wc9In Rc7Upper updated use.
Sequence of (3-19) the more new node wc9 in big root heap.
(3-20) judges whether counter c9 is less than | Rc7|, if it is, setting c9=c9+1, and go to step (3- 16) step (3-21), otherwise, is gone to；
(3-21) judges whether counter c7 is less thanIf it is, setting c7=c7+1, and go to step (3- 10) step (3-8), otherwise, is gone to；
(3-22) judges SUM1Whether threshold value T is greater than1, if it is, entering step (4), otherwise updating makes in step (2) Sampling number T0=2*T0, and return to (2).According to SSA algorithm, threshold value T1Calculation formula beWhereinε2=ε3=(1-1/e)-1ε/2, remaining change It measures identical with step (2).
Since there is nonnegativity, monotone nondecreasing and submodularity using function f (S).So being calculated using greedy strategy The sampling of S outWhereinIt is in sample setUpper optimal start node collection S+'s adopts Sample.
In the above process, respectively sample setIn sample R in all node u for sample R calculate use, so Add up use of each node in different sample R afterwards, and each node is in sample set in acquisition influence diagramOn always adopt With (3-1 to 3-6).Then according to node sample setOn total use, big root heap is established, according to node in sample set On always use size descending arrangement, heap top be the maximum node of total adopted value.Heap top node is selected, i.e., using maximum section Point, as new start node.Due to the overlapping of the range used between node, it is in same with the new start node chosen The use of node in sample R will be reduced, and need to be updated the income of these nodes and adjust in big heap of these nodes Position.It cyclically selects heap top node and updates the income of other nodes, until number of nodes is k (3-7 to 3-21).
(4) counter c10=0 is set, executes step (5) reverse number using sampling, and setting steps for indicating (3) the total of the start node collection S obtained in uses SUM2=0；
(5) inversely using sampling, calculate the start node collection S obtained in step (3) in this sampling to influence diagram Middle acquisition uses Ac10, and update the total using SUM of the start node collection S obtained in step (3)2=SUM2+Ac10。
Influence diagram is carried out inversely using sampling in this step, and calculates the start node collection S obtained in step (3) at this What is obtained in secondary sampling uses Ac10Process include following sub-step:
(5-1) is randomly chosen a node z from influence diagram, and node z is put into node set R, start node collection SCWith node z distance dC=∞, start node collection S and node z distance dS=∞, current distance curDist=0, it is initial to save Point set S uses A what this was sampledc10=0；
(5-2) judges whether node z is start node collection SCIn element, if it is dC=curDist is transferred to step Suddenly (5-3) otherwise enters step (5-3)；
(5-3) judges whether node z is element in start node collection S, if it is dS=curDist is transferred to step Suddenly (5-4) otherwise enters step (5-4)；
(5-4) judges dCWhether it is equal to curDist, is if it is transferred to step (5-5), otherwise enters step (5-6)；
(5-5) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWherein TimeCIt is the total degree that node z is activated by competitive influence, and is transferred to step (5-30), otherwise just Beginning node collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-6) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, turn Enter step (5-30), otherwise enters step (5-7)；
Counter c11=1, current distance curDist=curDist+1 is arranged in (5-7)；
(5-8) judges that whether c11 value be greater than node z enters neighbor node sum, if it is, be transferred to step (5-13), Otherwise it is transferred to step (5-9)；
(5-9) enters neighbor node z according to c11 of node zc11Activate the probability predicate node z of node zc11Activation section Whether point z succeeds, if it is, by node zc11It is put into it and activates node collection NA (zc11), by node zc11It is put into node set V In, and it is transferred to step (5-10), otherwise it is transferred to step (5-11)；
(5-10) judges node zc11It whether is start node collection SCIn element, if it is dC=curDist will be saved Point zc11Node collection Set is addedCIn, it is transferred to step (5-11), otherwise enters step (5-11)；
(5-11) judges node zc11It whether is element in start node collection S, if it is dS=curDist, it will Node zc11Node collection Set is addedSIn, it is transferred to step (5-12), otherwise enters step (5-12)；
(5-12) counter c11=c11+1, enters step (5-8)；
(5-13) judges dCWhether it is equal to curDist, is if it is transferred to step (5-14), otherwise enters step (5- 15)；
(5-14) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinIt is the total degree that node z is activated by competitive influence, InfsetCIt (u) is node collection SetCThe set for the competitive influence that interior joint is propagated, and is transferred to step (5-30), otherwise start node Collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-15) judges dSWhether curDist is equal to, if it is start node collection S uses A what this was sampledc10= 1, it is transferred to step (5-30), otherwise enters step (5-16)；
(5-16) if node set V is not empty set, and dSNot equal to curDist, and dCIt, then will section not equal to curDist All nodes in point set V are put into node set R, are transferred to step (5-17), are otherwise transferred to step (5-27)；
(5-17) be arranged counter c12=1, currently with node z distance curDist=curDist+1；
(5-18) judges the node total number whether c12 value is greater than in node set V, if yes then enter step (5-26), Otherwise return step (5-19)；
(5-19) selects the c12 node z from node set Vc12, and counter c13=1 is set；
(5-20) judges whether c13 value is greater than node zc12Enter neighbor node sum, if it is, being transferred to step (5- 25), otherwise it is transferred to step (5-21)；
(5-21) judges node zc13Whether not in node set R, and according to node zc12C13 enter neighbor node zc13Activate node zc12Probability predicate node zc13Activate node zc12Whether succeed, if it is, by node zc12Activation section Point set NA (wc2) in element be put into node zc13Activate node collection NA (wc3) in, by node zc13It is put into node set VnextIn, And it is transferred to step (5-22), otherwise it is transferred to step (5-24)；
(5-22) judges node zc13It whether is start node collection SCIn element, if it is dC=curDist will be saved Point zc13Node collection Set is addedCIn, it is transferred to step (5-23), otherwise enters step (5-23)；
(5-23) judges node zc13It whether is element in start node collection S, if it is dS=curDist, it will Node zc13Node collection Set is addedSIn, it is transferred to step (5-24), otherwise enters step (5-24)；
(5-24) counter c13=c13+1, and return step (5-20)；
(5-25) counter c12=c12+1, and return step (5-18)；
(5-26) uses node set VnextIn all nodes replacement node set V in all nodes, and return step (5-16)；
(5-27) judges dCWhether it is equal to curDist, is if it is transferred to step (5-28), otherwise enters step (5- 29)；
(5-28) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinFor set S interior joint activation node collection and The size of collection, and it is transferred to step (5-30), otherwise start node collection S uses A what this was sampledc10=0, enter step (5- 30)；
(5-29) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, It is transferred to step (5-30), otherwise enters step (5-30)；
(5-30) returns to the use A of this samplingc10。
(6) judge whether counter c10 is less than threshold value T2And the total of start node collection S uses SUM2Whether threshold value T is less than3, C10=c10+1, and return step (5) are if it is set, otherwise exportedAnd enter step (7)；
According to SSA algorithm, threshold value T2Calculation formula isThreshold value T3Calculation formula isVariable is identical with described in step (2) and (3-22) in formula.
(7) Biased estimator of the start node collection S obtained in judgment step (3)It is first with being obtained in step (6) The unbiased esti-mator of beginning node collection SWhether meetIt is saved if it is satisfied, then directly output is initial As a result, process terminates, process terminates point set S, otherwise updates sampling number T used in step (2)0=2*T0, and return Step (2).
To sum up, the propagation model of consciousness proposed by the present invention of comforming, it is contemplated that a variety of competitive relations for influencing to propagate, And for the first time by conformity behavior introduce using influence during be used as decision-making foundation, thus enhance propagation model reasonability and It is scientific.The method of sampling is used for the reverse of propagation model design for the consciousness of comforming, solves the reverse method of sampling of propagation It is not suitable for the problem of influencing sampling more, has widened the scope of application of such methods.Start node selection method incrementally updates Node uses income, largely computes repeatedly to reduce, improves computational efficiency.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include Within protection scope of the present invention.

Claims (9)

1. a kind of start node choosing method for realizing maximizing influence, which comprises the following steps:
(1) influence diagram is constructed according to established propagation model, and start node collection S is generated according to the influence diagram of buildingC, it is used for Propagate other influences for having competitive relation；
(2) according to preset precision parameter ε and δ, threshold value T is obtained using SSA algorithm0, T is carried out to the influence diagram obtained in (1)0 Secondary T reverse using sampling, and that all samplings are obtained0A sample is put into sample setIn；
(3) according to the sample set returned in step (2)Iteratively k is selected to use edge Income Maximum from influence diagram Node as start node collection S, and obtain the Biased estimator of the use of start node collection SWherein 0 < k < n；
(4) counter c10=0 is set, and the total of the start node collection S obtained in setting steps (3) uses SUM2=0；
(5) influence diagram inversely calculated the start node collection S obtained in step (3) using sampling and obtained in this sampling What is obtained uses Ac10, and update the total using SUM of the start node collection S obtained in step (3)2=SUM2+Ac10；
(6) judge whether counter c10 is less than threshold value T2And the total of start node collection S uses SUM2Whether threshold value T is less than3If It is that c10=c10+1 is set, and return step (5) otherwise exportsAnd (7) are entered step, wherein n table Show the node total number in influence diagram；
(7) Biased estimator of the start node collection S obtained in judgment step (3)With the initial section obtained in step (6) The unbiased esti-mator of point set SWhether meetIf it is satisfied, then directly exporting start node collection Otherwise S updates sampling number T used in step (2) as a result, process terminates0=2*T0, and return step (2), wherein ε1Indicate weight.
2. start node choosing method according to claim 1, which is characterized in that influence diagram be represented as G=(V, E, P), wherein the set of V expression node, E indicate the set of directed edge, and p indicates the letter for the activation probability that all sides are preassigned Number, each edge have pre-assigned activation Probability p (u, a v) ∈ [0,1], indicate the probability of node u activation node v.
3. start node choosing method according to claim 1, which is characterized in that the communication process of propagation model is as follows:
Firstly, different influences activates respective start node, at 0 moment to start communication process.Different influences may be selected Identical node is as start node；
Then, in t moment, become state of activation at this moment in the node that the t-1 moment is activated, and attempt activation not by The neighbor node of activation, if activation trial and success, the node being activated will receive being had an impact for activation node, if activation Attempt failed, then the node not being activated keeps unactivated state, and after this, the node in state of activation will be according to That comforms uses probability defined in function, using one of its received influence, and ultimately becomes adoption status.
That comforms uses function h (u, Ii) define probability it is as follows:
Wherein, h (u, Ii) indicate node u using influence IiProbability,It is the set of had an impact composition, NA (u, Ii) indicate Having activated node u and having propagated to it influences IiNeighbor node；
Finally, communication process termination when not new node is activated.
4. start node choosing method according to claim 1, which is characterized in that
Sample in step (2) is the data that single is inversely obtained using sampling, and including every in node set R, node set R The set { d (u) | u ∈ R } of distance between a node w and other nodes, the activation node collection of each node in node set R Set { NA (u) | u ∈ R }, node w and start node collection SCDistance dCWith node w by start node collection SCInterior joint is propagated Influence activation total degree TimeC。
5. start node choosing method as claimed in any of claims 1 to 4, which is characterized in that single in step (2) The secondary reverse process using sampling includes following sub-step:
(2-1) is randomly chosen a node w from influence diagram, and node w and itself distance d (w is arrangedc1)=0, w is put into In node set R, and start node set S is setCWith node w distance dCVariable curDist=0, curDist is arranged in=∞ Indicate currently processed node at a distance from node w, abbreviation current distance；
(2-2) judges whether node w is start node collection SCIn element, if it is, record node w swashed by competitive influence Total degree Time livingCWith start node set SCWith node w distance dc=0, it is transferred to step (2-17), is otherwise entered step (2-3)；
Counter c1=1, current distance curDist=curDist+1 is arranged in (2-3), judges whether c1 value is greater than entering for node w Neighbor node sum, if it is, being transferred to step (2-17), is otherwise transferred to step (2-4)；
(2-4) enters neighbor node w according to c1 of node wc1Activate the probability predicate node w of node wc1Whether activate node w Success, if it is, record node wc1With node w distance d (wc1)=curDist, by node wc1It is put into it and activates node collection NA(wc1), by node wc1It is put into node set V, and is transferred to step (2-5), be otherwise transferred to step (2-6)；
(2-5) judges node wc1It whether is start node collection SCIn element, if it is by start node set SCWith node The distance d of wCIt is set as current distance curDist, and is transferred to step (2-6), is otherwise transferred to step (2-6)；
(2-6) judge c1 value whether be equal to node w enter neighbor node sum, if it is, being transferred to step (2-8), otherwise turn Enter step (2-7)；
Counter c1=c1+1, and return step (2-4) is arranged in (2-7)；
(2-8) judges node set V and start node collection SCWhether have whether intersection or node set V are empty set, if so, It then calculates and records node w by node set V and SCThe total degree Time for the competitive influence activation that intersection interior joint is propagatedC, and It is transferred to step (2-17), otherwise all nodes in node set V are put into node set R, and is transferred to step (2-9)；
Counter c2=1 and current distance curDist=curDist+1 is arranged in (2-9)；
(2-10) selects the c2 node w from node set Vc2, and counter c3=1 is set, judge that the value of counter c3 is It is no to be greater than node wc2Enter neighbor node sum, if it is, being transferred to step (2-14), be otherwise transferred to step (2-11)；
(2-11) judges node wc3Whether not in node set R, and according to node wc2C3 enter neighbor node wc3Activation Node wc2Probability predicate node wc3Activate node wc2Whether succeed, if it is, setting node wc3With node w distance d (wc3) it is equal to curDist, by node wc2Activation node collection NA (wc2) in element be put into node wc3Activate node collection NA (wc3) in, by node wc3It is put into node set VnextIn, and it is transferred to step (2-12), otherwise it is transferred to step (2-13)；
(2-12) judges node wc3It whether is start node collection SCIn element, if it is be arranged start node set SCWith section The distance d of point wCEqual to curDist, and it is transferred to step (2-13), is otherwise directly transferred to step (2-13)；
(2-13) judges whether the value of counter c3 is greater than node wc2Enter neighbor node sum, if it is, being transferred to step (2- 14) counter c3=c3+1, and return step (2-11), are otherwise set；
(2-14) judges whether counter c2 value is equal to the node total number in node set V, if yes then enter step (2-15), Counter c2=c2+1, and return step (2-10) are otherwise set；
(2-15) judges node set VnextWith start node collection SCWhether intersection or node set V are hadnextIt whether is empty set, If it is, obtaining node w by node set VnextWith SCThe total degree for the competitive influence activation that intersection interior joint is propagated TimeC, and it is transferred to step (2-17), otherwise it is transferred to step (2-16)；
(2-16) uses node set VnextIn all nodes replacement node set V in all nodes, and will be in node set V All nodes be put into node set R, and return step (2-8)；
(2-17) obtain node set R, in node set R the distance between each node and node w set d (u) | u ∈ R }, in node set R the activation node collection of each node set { NA (u) | u ∈ R }, node w and start node collection SCAway from From dCAnd node w is by start node collection SCThe total degree Time for the influence activation that interior joint is propagatedC。
6. start node choosing method as claimed in any of claims 1 to 5, which is characterized in that in step (3) repeatedly It includes following sub-step that generation ground, which selects the k node using edge Income Maximum as the process of start node collection:
(3-1) settingCounter c4=1 is set, and each node is in sample set in setting influence diagramOn always adopt Initial value is 0, and start node collection S is in sample setOn use summation SUM1=0；
Counter c5=1 is arranged in (3-2)；
(3-3) is from sample setThe c5 sample R of middle taking-upc5, counter c6=1 is set；
(3-4) is from sample Rc5The c6 node w of middle taking-upc6, judge in Rc5Interior joint wc6With node w distance d (wc6) whether small In dC, if it is, setting node wc6In Rc5On be adopted as 1, node wc6It is total using plus 1, be then transferred to step (3-5)； Otherwise, node w is setc6In Rc5On be adopted asUpdate wc6In sample setOn be always adopted as Node wc6In sample setOn it is total using addingThen it is transferred to step (3-5)；Wherein NA (wc6) And TimeCIt is to respectively indicate sample Rc5In activation node collection and start node collection SCThe influence that interior joint is propagated activates sample Rc5In node w total degree.
(3-5) judges whether counter c6 is less than | Rc5|, if it is, setting c6=c6+1, then return step (3-4), no Then it is transferred to step (3-6)；
(3-6) judges whether counter c5 is less thanIf it is, setting c5=c5+1, and return step (3-3), otherwise turn Enter step (3-7)；
(3-7) exists to nodes all in influence diagram according to each node using big root heapOn the size that always uses carry out descending Arrangement；
(3-8) judges counter C4Whether preset threshold k is less than, if it is, taking outOn always use maximum node wc4, by node wc4Start node collection S is added, SUM is set1=SUM1+A(wc4), wherein A (wc4) it is node wc4?On it is total Using, and the deletion of node w from big root heapc4, and step (3-9) is gone to, otherwise obtain start node set S has with what it was used Estimation partiallyThen it is transferred to step (3-22).
(3-9) is from sample setMiddle take out all includes node wc4Sample, formed sample setAnd counter is set C7=1；
(3-10) takes outIn the c7 sample Rc7, and judgement sample Rc7Whether it is marked as determining use, if it is turns To step (3-21), step (3-11) is otherwise gone to；
(3-11) judges wc4With sample Rc7In node w distance d (wc4) whether it is less than Rc7In start node set SCWith section The distance d of point wC, if it is marker samples Rc7It is used to determine, and goes to step (3-12), otherwise go to step (3-15)；
Counter c8=1 is arranged in (3-12)；
(3-13) takes out sample Rc7In the c8 node, update wc8In sample setOn be always adopted as node wc8In sample This setOn it is total using subtracting node wc8In Rc7On use, and more new node wc8Sequence in big root heap；
(3-14) judges whether counter c8 is less than | Rc7|, if it is, setting c8=c8+1, and step (3-13) is gone to, it is no Then, step (3-21) is gone to；
Counter c9=1 is arranged in (3-15)；
(3-16) takes out sample Rc7In the c9 node wc9, judge wc9With sample Rc7In node w distance d (wc9) whether Less than Rc7In start node set SCWith node w distance dC, step (3-17) is if it is gone to, step is otherwise gone to (3-18)；
(3-17) more new node wc9In Rc7On be adopted as node wc9In Rc7On use subtract node wc4In Rc7On use, More new node wc9In sample setOn be always adopted as node wc9In sample setOn it is total using subtracting node wc4In Rc7 On use；
(3-18) more new node wc9In sample setOn be always adopted as node wc9In sample setOn it is total using subtracting Node wc9In Rc7On use, more new node wc9In Rc7On be adopted asWhereinFor swashing for set S interior joint The size of the union of movable joint point set, i.e., start node collection S is in Rc7On activation total degree, and more new node w againc9In sample SetOn be always adopted as node wc9In sample setOn it is total using add node wc9In Rc7Upper updated use；
Sequence of (3-19) the more new node wc9 in big root heap；
(3-20) judges whether counter c9 is less than | Rc7|, if it is, setting c9=c9+1, and step (3-16) is gone to, it is no Then, step (3-21) is gone to；
(3-21) judges whether counter c7 is less thanIf it is, setting c7=c7+1, and step (3-10) is gone to, it is no Then, step (3-8) is gone to；
(3-22) judges SUM1Whether threshold value T is greater than1, if it is, entering step (4), otherwise update used in step (2) Sampling number T0=2*T0, and return to (2).
7. start node choosing method as claimed in any of claims 1 to 6, which is characterized in that start node collection S Using f (S) be using following formula obtain:
Wherein, S is start node collection, and n is nodes sum, AiIt is the use income of i-th sampling,It is practical sample This number,It isIn all samples average use.
8. start node choosing method as claimed in any of claims 1 to 7, which is characterized in that right in step (5) Influence diagram carries out inversely using sampling, and calculates the use that the start node collection S obtained in step (3) is obtained in this sampling Ac10Process include following sub-step:
(5-1) is randomly chosen a node z from influence diagram, and node z is put into node set R, start node collection SCWith section The distance d of point zC=∞, start node collection S and node z distance dS=∞, current distance curDist=0, start node collection S A is used in this samplingc10=0；
(5-2) judges whether node z is start node collection SCIn element, if it is dC=curDist is transferred to step (5- 3) (5-3), is otherwise entered step；
(5-3) judges whether node z is element in start node collection S, if it is dS=curDist is transferred to step (5- 4) (5-4), is otherwise entered step；
(5-4) judges dCWhether it is equal to curDist, is if it is transferred to step (5-5), otherwise enters step (5-6)；
(5-5) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWherein TimeCIt is the total degree that node z is activated by competitive influence, and is transferred to step (5-30), otherwise just Beginning node collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-6) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, it is transferred to step Suddenly (5-30) otherwise enters step (5-7)；
Counter c11=1, current distance curDist=curDist+1 is arranged in (5-7)；
(5-8) judge c11 value whether be greater than node z enter neighbor node sum, if it is, being transferred to step (5-13), otherwise It is transferred to step (5-9)；
(5-9) enters neighbor node z according to c11 of node zc11Activate the probability predicate node z of node zc11Activating node z is No success, if it is, by node zc11It is put into it and activates node collection NA (zc11), by node zc11It is put into node set V, and It is transferred to step (5-10), is otherwise transferred to step (5-11)；
(5-10) judges node zc11It whether is start node collection SCIn element, if it is dC=curDist, by node zc11Node collection Set is addedCIn, it is transferred to step (5-11), otherwise enters step (5-11)；
(5-11) judges node zc11It whether is element in start node collection S, if it is dS=curDist, by node zc11Node collection Set is addedSIn, it is transferred to step (5-12), otherwise enters step (5-12)；
(5-12) counter c11=c11+1, enters step (5-8)；
(5-13) judges dCWhether it is equal to curDist, is if it is transferred to step (5-14), otherwise enters step (5-15)；
(5-14) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinIt is the total degree that node z is activated by competitive influence, InfsetCIt (u) is node collection SetCThe set for the competitive influence that interior joint is propagated, and is transferred to step (5-30), otherwise start node Collection S uses A what this was sampledc10=0, enter step (5-30)；
(5-15) judges dSWhether curDist is equal to, if it is start node collection S uses A what this was sampledc10=1, it is transferred to Step (5-30), otherwise enters step (5-16)；
(5-16) if node set V is not empty set, and dSNot equal to curDist, and dCNot equal to curDist, then by node collection All nodes closed in V are put into node set R, are transferred to step (5-17), are otherwise transferred to step (5-27)；
(5-17) be arranged counter c12=1, currently with node z distance curDist=curDist+1；
(5-18) judges the node total number whether c12 value is greater than in node set V, if yes then enter step (5-26), otherwise Return step (5-19)；
(5-19) selects the c12 node z from node set Vc12, and counter c13=1 is set；
(5-20) judges whether c13 value is greater than node zc12Enter neighbor node sum, it is no if it is, be transferred to step (5-25) Then it is transferred to step (5-21)；
(5-21) judges node zc13Whether not in node set R, and according to node zc12C13 enter neighbor node zc13 Activate node zc12Probability predicate node zc13Activate node zc12Whether succeed, if it is, by node zc12Activation node Collect NA (wc2) in element be put into node zc13Activate node collection NA (wc3) in, by node zc13It is put into node set VnextIn, and It is transferred to step (5-22), is otherwise transferred to step (5-24)；
(5-22) judges node zc13It whether is start node collection SCIn element, if it is dC=curDist, by node zc13Node collection Set is addedCIn, it is transferred to step (5-23), otherwise enters step (5-23)；
(5-23) judges node zc13It whether is element in start node collection S, if it is dS=curDist, by node zc13Node collection Set is addedSIn, it is transferred to step (5-24), otherwise enters step (5-24)；
(5-24) counter c13=c13+1, and return step (5-20)；
(5-25) counter c12=c12+1, and return step (5-18)；
(5-26) uses node set VnextIn all nodes replacement node set V in all nodes, and return step (5- 16)；
(5-27) judges dCWhether it is equal to curDist, is if it is transferred to step (5-28), otherwise enters step (5-29)；
(5-28) judges dSWhether curDist, the use that if it is start node collection S is sampled at this are equal toWhereinFor set S interior joint activation node collection and The size of collection, and it is transferred to step (5-30), otherwise start node collection S uses A what this was sampledc10=0, enter step (5- 30)；
(5-29) judges whether to be equal to curDist, and if it is start node collection S uses A what this was sampledc10=1, it is transferred to Step (5-30), otherwise enters step (5-30)；
(5-30) returns to the use A of this samplingc10。
9. a kind of start node selecting system for realizing maximizing influence characterized by comprising
First module for constructing influence diagram according to established propagation model, and generates initial section according to the influence diagram of building Point set SC, for propagating other influences for having competitive relation；
Second module, for obtaining threshold value T using SSA algorithm according to preset precision parameter ε and δ0, the first module is obtained Influence diagram carries out T0Secondary T reverse using sampling, and that all samplings are obtained0A sample is put into sample setIn；
Third module, the sample set for being returned according to the second moduleIteratively k are selected to use edge from influence diagram The node of Income Maximum obtains the Biased estimator of the use of start node collection S as start node collectionWherein 0 < k<n；
4th module, for counter c10=0 to be arranged, and the total of start node collection S that the acquisition of third module is arranged uses SUM2 =0；
5th module, for, inversely using sampling, calculating the start node collection S of third module acquisition at this to influence diagram progress What is obtained in sampling uses Ac10, and the total of start node collection S for updating the acquisition of third module uses SUM2=SUM2+Ac10；
6th module, for judging whether counter c10 is less than threshold value T2And the total of start node collection S uses SUM2Whether it is less than Threshold value T3, c10=c10+1 is if it is set, and returns to the 5th module, otherwise export the use of start node collection S has partially EstimationSubsequently into the 7th module, wherein n indicates the node total number in influence diagram；
7th module, the Biased estimator of the start node collection S for judging the acquisition of third moduleIt is obtained with the 6th module Start node collection S unbiased esti-matorWhether meetIf it is satisfied, then directly output is first Otherwise beginning node collection S updates the sampling number T that the second module uses as a result, process terminates0=2*T0, and return to the second mould Block, wherein ε1Indicate precision parameter.
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