CN106327345A - Social group discovering method based on multi-network modularity - Google Patents

Abstract

The invention discloses a social group discovering method based on multi-network modularity. A multi-network zero model is provided, and on the basis of the multi-network zero model, performance function multi-network modularity suitable for multi-network is further provided. On the basis of the multi-network modularity, a fast social group discovering method based on the multi-network modularity is provided, and the validity of the fast social group discovering method is verified. The social group discovering method is advantageous in that the multi-network zero model based on node redundancy is established by adopting a network configuration idea, and the zero model is guaranteed to be provided with the same node number, the same network number, and the same node redundancy distribution of the original network. The multi-network modularity is provided, and a new performance function used for measuring a multi-network social group structure is provided, and a new method for multi-network social group evaluation is provided. On the basis of the multi-network modularity, a fast social group discovering algorithm based on multi-network modularity maximization is provided, and time complexity of solving the maximum value of the multi-network modularity is reduced.

Description

A kind of Combo discovering method based on Multi net voting modularity

Technical field

The invention belongs to Multi net voting field, particularly to a kind of Multi net voting community structure and corporations' finding method.

Background technology

Multi net voting scientific research is the joint act of the formed system of the individuality communicated with each other, and explores between complex network General character and process their universal method.The source studied a question in Multi net voting science is various real networks, and it is produced The concept of general character, method combines and theoretical can analysis for various real networks refer to design offer macroscopic view in turn again Lead and and specific means.Such as, many real networks all have common property, i.e. a community structure.The most whole net Network is made up of some corporations.The connection between node within Mei Ge corporations is relatively very tight, but each corporations it Between connection ratio the most comparatively speaking sparse.

In Multi net voting science, need corporations are carried out quantitative analysis, propose the community structure of large-scale complex network Effectively mining algorithm.Meanwhile, when corporations' mining algorithm be applied to certain concrete real network analyze time, be necessary for examining Consider the practical significance corresponding to the feature of concrete network, corporations and be positioned at the specific function etc. of multiple corporations overlapping node. It is in recent years conventional that a kind of weigh corporations to divide the standard of quality be modularity, its basic idea be divide the network after corporations with Corresponding zero model compares, to weigh the quality that corporations divide.So-called zero model corresponding with a network, it is simply that refer to and This network has some same nature (such as identical limit number or identical degree distribution etc.) and completely random in other respects Random Graph model.It is considered as the important topological property of network due to degree distribution and real network often has heterogeneous Degree distribution, so at present when analyzing network community structure, it is common that network to be studied with have identical degree series with Machine figure also referred to as single order zero model compares.The modularity of one network is defined as corporations' internal edges number and the phase of this network The difference of corporations' internal edges number of zero model answered accounts for the ratio of limit, whole networking number.

Above-mentioned modularity definition is only applicable to the corporations of single network and divides, and the cyberrelationship of real world is often many Dimension.In complex networks system is analyzed, figure may often be such that the abstract representation that this kind of system is appropriate.Usually, individuality is represented as Summit, their mutual relation is represented as connecting the limit on summit.The up-to-date viewpoint of Network Science is that bag is regarded as in the limit in figure Set containing the various types of relations between individuality.There are work relationship, classmate's relation, family relation the most between men Deng.This is to retain the information diversity of relational network and representing the overall picture of this network deeper into ground.Research in the past few years Had been directed to the Multi-attributes of many networks of real world, people start to analyze in these networks any pair node it Between the annexation of multidimensional.Although research work before this have noticed the importance analyzing this kind of multidimensional network, but The holistic approach framework of multidimensional network is had not yet been formed.The general strategy of existing Multi net voting community discovery algorithm is to extract many nets The feature of network and PROBLEM DECOMPOSITION become known to the form of expression.The corporations under subproblem derivation Multi net voting after being decomposed by solution Divide.Therefore the community detecting algorithm of a large amount of Multi net voting depends on existing single network community detection algorithm.

More weak it is assumed that the division result of one corporation of assessment can according to connecting each other of corporations and its outside adjacent node With independent of remaining network.Therefore from one corporation of angular divisions of incorporator be effective.In view of Multi net voting In each figure represent communication mode independent between a kind of member, such as Email, phone etc..So one high-quality Corporations should remain able to the high speed information stream that ensures between its member after a kind of communication mode lost efficacy.Therefore society can be used The redundancy of group's interior joint is as the metric form of corporations' division result under Multi net voting.

Owing to corporations' division of Multi net voting is the much-talked-about topic of Research of network science in recent years, researchers propose various Group dividing method, and have been widely cited.

2006, M.E.J.Newman proposes Combo discovering method based on modularity, the author investigation matrix of figure Represent, and carry out community discovery based on modularity.First author describes traditional figure division methods, then proposes modularity Concept, and build modularity matrix, finally teach and carry out community discovery by modularity.

2010, Peter J.Mucha et al. proposed and carries out community discovery for multi-chip network, and author proposes existing mould Lumpiness algorithm is only applicable to single network condition, is not particularly suited for Multi net voting analysis, mainly have studied the mould under multi-chip network Lumpiness computational methods, the method can apply to the research of multiple features network, thus is research corporations in the range of more macroreticular Structure provides possibility.

Advised according to network various dimensions by Michele Berlingerio and Michele Cosci et al. in 2013 Characteristic divides corporations, and proposes the concept of corporations' redundancy to measure the multi-dimensional nature of corporations' interior joint annexation. Although Berlingerio proposes multidimensional network corporations based on corporations' redundancy and divides, the corporations' division for multidimensional network carries Supply a kind of new direction, but the method has not distinguished the dimension size of multi-dimensional relation, have ignored node in other words and connect pass The information value that the dimension size of system is brought.

Summary of the invention

The present invention solves above-mentioned technical problem, it is proposed that a kind of Multi net voting community structure and corporations based on this structure Discovery method；By defining the community structure of Multi net voting, and propose based on Multi net voting modularity maximized heterogeneous network society Group finds algorithm, is effectively found that the community structure in Multi net voting.

The technical solution used in the present invention is: a kind of Combo discovering method based on Multi net voting modularity, including:

S1, calculate Multi net voting modularity, specifically include following step by step:

S11, multiple adjacency matrix is used to represent Multi net voting, particularly as follows:

MN={A₁,A₂,…,A_i,…,A_M},i≤M；

Wherein, M represents network number, A_iRepresent the adjacency matrix of i-th network；

S12, determine node redundancy degree connection relationship matrix, the adjacency matrix of all-network is added and obtains node redundancy degree Connection relationship matrix；Expression formula is as follows:

$W=\underset{i}{\Σ}{A}_i,i\≤M;$

Wherein, W represents node redundancy degree connection relationship matrix, and every a line or each list in matrix W are shown and this node The number of times that occurs in a network of each bar limit being connected, i represents the sequence number of adjacency matrix, and i=1,2 ..., M；

S13, the node redundancy degree connection relationship matrix determined according to step S12, calculate node redundancy degree；Expression formula is such as Under:

$r_k^m=|w_{jk}=m+1|,w_{jk}\&Element;W,0\&le;m<M;$

Wherein, w_jkFor the element in multiple network node redundancy link relational matrix W, represent the company between node k and node j Edge fit number,Represent the m rank redundancy of node k；

S14, build Multi net voting 1 rank zero models according to node redundancy degree；

S15, Multi net voting 1 rank zero model built according to step S14, calculate Multi net voting modularity；

S2, according to step S1 calculated Multi net voting modularity, corporations in Multi net voting are divided；Specifically include with Under step by step:

S21, initial time node each in Multi net voting is considered as corporations；

Each node z in S22, traversal Multi net voting, finds out all nodes being attached thereto, and to each connected contact meter Operator node z adds the Multi net voting modularity increment of these node place corporations being connected；

S23, find out the corporations at Multi net voting modularity maximum of increments place, node z is added to these corporations；

S24, repetition step S22 are to step S23, until corporations' number no longer changes；

S25 as, the corporations marked off by step S22 to step S24 are regarded new node, repeat step S22 to step S24, during until the Multi net voting modularity increment of all new nodes is less than or equal to 0, terminates.

Further, described step S14 specifically include following step by step:

S141, according to the size of occurrence number, the limit in Multi net voting being divided into M class, the limit number correspondence exponent number of m class is m rank The limit number μ of redundancy^m,0≤m≤M；

S142, by Multi net voting m class limit random packet distribute to each network；

S143, general's distribution are to network A_iLimit random assortment to network A_iIn node j and node k, be calculated network A_i In node j and the acquisition limit probability of node k be:

$p_{A_i}(j,k)=\frac{r_j^m}{2{\mathrm{\&mu;}}^m}\&times;\frac{r_k^m}{2{\mathrm{\&mu;}}^m};$

Wherein,Represent the m rank redundancy of node j,Represent the m rank redundancy of node k；

S144, repetition step S142 are to step S143, until all of limit is allocated to network each node in network, Be calculated in M network, node j and node k become limit Probability p (j, k) be:

$p\left(j,k\right)=M\&times;\left(\frac{C_1^1}{C_M^1}\frac{r_j^0{r}_k^0}{{\left(2{\mathrm{\&mu;}}^0\right)}^2}+\frac{C_2^1}{C_M^2}\frac{r_j^1{r}_k^1}{{\left(2{\mathrm{\&mu;}}^1\right)}^2}+\mathrm{...}+\frac{C_{m+1}^1}{C_M^{m+1}}\frac{r_j^m{r}_k^m}{{\left(2{\mathrm{\&mu;}}^m\right)}^2}+\mathrm{...}+\frac{C_M^1}{C_M^M}\frac{r_j^{M-1}{r}_k^{M-1}}{{\left(2{\mathrm{\&mu;}}^{M-1}\right)}^2}\right).$

Further, described step S15 specifically include following step by step:

S151, according to step S144 obtain in M network, (j k), obtains the limit Probability p that becomes of node j and node k Multi net voting 1 rank zero model connects the desired amt P on limit, and ((j, k), and in Multi net voting, corporations are actual connects limit quantity E for j, k)=2 μ × p (j, k)=w_jk, μ represents all limits number sum；

S152, Multi net voting 1 rank zero model obtained according to step S151 connect the desired amt on limit, and corporations in Multi net voting Actual even limit quantity, obtains Multi net voting modularity；Particularly as follows: Multi net voting modularity=(in Multi net voting corporations actual connect limit quantity- Multi net voting 1 rank zero model connects the desired amt on limit), and withIt is normalized.

Further, the Multi net voting modularity expression formula described in step S152 is as follows:

$\begin{array}{c}{Q}_m=\frac{1}{2\mathrm{\&mu;}}{\mathrm{\&Sigma;}}_{jk}\&lsqb;E\left(j,k\right)-P\left(j,k\right)\&rsqb;\mathrm{\&delta;}\left(g_j,g_k\right)\\ =\frac{1}{2\mathrm{\&mu;}}{\mathrm{\&Sigma;}}_{jk}\&lsqb;w_{jk}-P\left(j,k\right)\&rsqb;\mathrm{\&delta;}\left(g_j,g_k\right)\end{array};$

Wherein, g_jRepresent the corporations belonging to node j, g_kRepresent the corporations belonging to node k, δ (g_j,g_k) represent impulse function, When node j and node k belongs to same corporations, then δ (g_j,g_k) it is 1, it is otherwise 0.

Further, Multi net voting modularity increment described in step S22, expression formula is:

${\mathrm{\&Delta;Q}}_{jk}=\frac{1}{2\mathrm{\&mu;}}\{{\mathrm{\&Sigma;}}_{z\&Element;g_k}\&lsqb;w_{jz}-P(j,z)\&rsqb;-{\mathrm{\&Sigma;}}_{z\&Element;g_j}\&lsqb;w_{jz}-P(j,z)\&rsqb;\};$

Wherein, any node during z represents Multi net voting.

Beneficial effects of the present invention: present applicant proposes zero model of Multi net voting, and further provide on its basis It is applicable to Multi net voting, the modularity of a kind of brand-new power function Multi net voting weighing Multi net voting community structure；And On the basis of Multi net voting modularity, it is proposed that quick Combo discovering method based on Multi net voting modularity, and demonstrate the method Effectiveness, the present processes has the advantage that

(1) multiple adjacency matrix is used to describe Multi net voting structure；

(2) thought of network configuration is used to construct Multi net voting zero model based on node redundancy degree, it is ensured that zero mould Type and former network have same node point number, network number, the distribution of node redundancy degree；

(3) proposing Multi net voting modularity, a kind of brand-new power function weighing Multi net voting community structure, for Multi net voting society Group's evaluation provides new method；

(4) on the basis of Multi net voting modularity, it is proposed that based on the maximized quick community discovery of Multi net voting modularity Algorithm, when real network is huge, reduces the maximum time complexity solving Multi net voting modularity, is effectively found that Community structure in Multi net voting.

Accompanying drawing explanation

The protocol procedures figure that Fig. 1 provides for the present invention.

Detailed description of the invention

For ease of skilled artisan understands that the technology contents of the present invention, below in conjunction with the accompanying drawings present invention is entered one Step explaination.

Being illustrated in figure 1 the protocol procedures figure of the application, the technical scheme of the application is: a kind of based on Multi net voting modularity Combo discovering method, including:

S1, calculate Multi net voting modularity, specifically include following step by step:

S11, using multiple adjacency matrix to represent Multi net voting, the Multi net voting in complex network refers to that node is identical, there is multiclass Type limit or multiple networks of multiple network yardstick, usual Multi net voting can be divided into for many relational networks, multiple dimensioned network, time Between rely on network etc..

The present invention represents a Multi net voting structure with multiple adjacency matrix, and for the ease of analyzing, the present invention only considers to have no right Undirected networks, weighting directed networks can be represented by weighted adjacent matrix, is equally applicable to this algorithm.In one network, The adjacency matrix of network is a N rank square formation, and wherein N refers to nodes number, points to from primary nodal point when existing in network The change of secondary nodal point, then in matrix, element value is 1, and otherwise value is 0.

According to adjacency matrix in network and the definition of Multi net voting, a Multi net voting MN is expressed as multiple adjacent by the present invention The set of matrix, particularly as follows:

MN={A₁,A₂,…,A_i,…,A_M},i≤M；

Wherein, M represents network number, A_iRepresent the adjacency matrix of i-th network；

S12, determine node redundancy degree connection relationship matrix, be specifically expressed as follows:

$W=\underset{j}{\&Sigma;}{A}_j,j\&le;M;$

Wherein, W represents node redundancy degree connection relationship matrix, and every a line or each list in matrix W are shown and this node The number of times that each bar limit being connected occurs in a network；J represents some node in Multi net voting.

S13, the node redundancy degree connection relationship matrix determined according to step S12, calculate node redundancy degree；Multi net voting saves The m rank redundancy of some jRepresent and be connected with node j, the quantity on the limit of m+1 time the most only occurs.Such asRepresent and joint Point j is connected, and the quantity on the limit of 1 time the most only occurs；Represent and be connected with node j that the number on the limit of 4 times occurs in a network Amount；Node redundancy degree expression formula is as follows:

r_i ^m=| w_ij=m+1 |, w_ij∈W,0≤m<M；

Wherein, w_ijFor the element in multiple network node redundancy link relational matrix W, represent the company between node i and node j Edge fit number, r_i ^mRepresent the m rank redundancy of node i.

Node redundancy degree illustrates node and repeats the number of degrees on even limit in Multi net voting, when Multi net voting deteriorates to single network, Node redundancy degreeRetrogression of nature is the number of degrees k of node_j, therefore, node redundancy degree applies to Multi net voting, weighs node degree The new parameter of number.

On the basis of node redundancy degree, the basic definition of binding modules degree of the present invention, first construct based on node superfluous Multi net voting zero model of remaining, then proposes a kind of new power function Multi net voting module weighing Multi net voting community structure Degree, will describe in detail in subsequent step.

S14, build Multi net voting 1 rank zero models according to node redundancy degree.

Multi net voting zero model: with the random Multi net voting that former Multi net voting has identical scale and same nature B.

Different according to constraints, Multi net voting zero model that can define different order is as follows:

(1) 0 rank zero model: there is same node point number N, limit number μ, the randomization network of network number M with former Multi net voting.

(2) 1 rank zero models: with former Multi net voting have same node point number N, network number M, node redundancy degree distribution P (r) with Machine network.

Zero model is strengthened on (3) 1 rank: have same node point number N, network number M, node redundancy degree distribution P with former Multi net voting The randomization network of (r), each nodes degree distribution P (k).

In the definition of Multi net voting zero model, there are 1 rank and strengthen the definition of zero model, this is because in 1 rank zero model, Redundancy distribution P (r) is identical has merely ensured that the overall degree distribution of multiple networks fusion posterior nodal point is identical, does not ensure each network In node degree distribution identical, this due in Multi net voting network number cause more than 1, therefore, add nodes degree Being distributed this constraint identical, zero model is strengthened on 1 rank that can be defined as Multi net voting.

First zero model of the application structure is a randomization network without community structure, and zero model order is more Height, its community structure is the most obvious, therefore can not select zero model of high exponent number.Meanwhile, in corporations divide, redundancy is got over The big singular association between node, the least for the contribution of its end points degree of being completely embedded, this community structure rule is at zero mould Should be reflected in type, therefore, the present invention uses 1 rank zero model to meet wanting of randomness and network redundancy characteristic simultaneously Asking, do not do specified otherwise, Multi net voting zero model in the present invention refers both to 1 rank zero model of Multi net voting.

The present invention uses the thought of network configuration to build Multi net voting 1 rank zero model, to ensure that zero model has with former network Same node point number N, network number M, node redundancy degree distribution P (r).Specifically include following steps:

S141, according to the size of occurrence number, the limit in Multi net voting being divided into M class, it is superfluous that the limit number of each class is defined as m rank The limit number μ of remaining^m,0≤m≤M；

S142, by Multi net voting m class limit random packet distribute to each network, i.e. the one group of m+1 bar occurring m+1 time Limit random assortment to each network, then network A_iIt is assigned to the Probability p on limit_m(A_i) it is:

$p_m\left(A_i\right)=\frac{C_{m+1}^1}{C_M^{m+1}};$

Wherein,Represent from m+1 element, take out the scheme sum that 1 element is combined, in like manner,Represent The scheme sum that m+1 element is combined is taken out from M element.

S143, general's distribution are to network A_iLimit distribute to network A_iIn node j and node k, it is considered to limit distribution to network and It is independent from the process of network allocation to node, is calculated network A_iIn node j and the acquisition limit probability of node k be:

$p_{A_i}(j,k)=\frac{r_j^m}{2{\mathrm{\&mu;}}^m}\&times;\frac{r_k^m}{2{\mathrm{\&mu;}}^m};$

Wherein,Represent the m rank redundancy of node j,Represent the m rank redundancy of node k；

S144, repetition step S142 are to step S143, until all of limit is allocated to network each node in network, Therefore, in one network node j and node k become limit Probability p (j, k) ' be:

$p{\left(j,k\right)}^{\&prime;}=\frac{C_1^1}{C_M^1}\frac{r_j^0{r}_k^0}{{\left(2{\mathrm{\&mu;}}^0\right)}^2}+\frac{C_2^1}{C_M^2}\frac{r_j^1{r}_k^1}{{\left(2{\mathrm{\&mu;}}^1\right)}^2}+\mathrm{...}+\frac{C_{m+1}^1}{C_M^{m+1}}\frac{r_j^m{r}_k^m}{{\left(2{\mathrm{\&mu;}}^m\right)}^2}+\mathrm{...}+\frac{C_M^1}{C_M^M}\frac{r_j^{M-1}{r}_k^{M-1}}{{\left(2{\mathrm{\&mu;}}^{M-1}\right)}^2};$

Then obtain in M network, node j and node k become limit Probability p (j, k) be:

$p\left(j,k\right)=M\&times;\left(\frac{C_1^1}{C_M^1}\frac{r_j^0{r}_k^0}{{\left(2{\mathrm{\&mu;}}^0\right)}^2}+\frac{C_2^1}{C_M^2}\frac{r_j^1{r}_k^1}{{\left(2{\mathrm{\&mu;}}^1\right)}^2}+\mathrm{...}+\frac{C_{m+1}^1}{C_M^{m+1}}\frac{r_j^m{r}_k^m}{{\left(2{\mathrm{\&mu;}}^m\right)}^2}+\mathrm{...}+\frac{C_M^1}{C_M^M}\frac{r_j^{M-1}{r}_k^{M-1}}{{\left(2{\mathrm{\&mu;}}^{M-1}\right)}^2}\right).$

It should be noted that in the distribution on limit, the application does not distinguish same node point j in heterogeneous networks, because During node redundancy degree calculates, there is the thought of the network integration, the redundancy of same node point j in heterogeneous networks is consistent, But in order to retain the independence of each network, the application considers each network when generating zero model and is assigned to the probability on limit, Due to network randomization, the final limit probability that averagely becomes becoming limit probability to be each nodes j and node k is multiplied by network Number, is not for same node point the most here and does the differentiation of heterogeneous networks.Actual limit number between the node that the application calculates, for joint Point limit number sum in each network, to highlight the contribution for node annexation of the repetition limit.

S15, Multi net voting 1 rank zero model built according to step S14, calculate Multi net voting modularity；Obtain according to step S144 To in M network, (j k), obtains Multi net voting 1 rank zero model and connects the expectation number on limit the limit Probability p that becomes of node j and node k Amount P (j, k)=2 μ × p (j, k), μ represents all limits number sum, and in Multi net voting corporations actual connect limit quantity E (j, k)= w_ij。

Then Multi net voting modularity=(in Multi net voting, actual limit quantity-Multi net voting 1 rank zero model that connects of corporations connects the expectation number on limit Amount), and withIt is normalized.Multi net voting modularity expression formula is as follows:

$\begin{array}{c}{Q}_m=\frac{1}{2\mathrm{\&mu;}}{\mathrm{\&Sigma;}}_{jk}\&lsqb;E\left(j,k\right)-P\left(j,k\right)\&rsqb;\mathrm{\&delta;}\left(g_j,g_k\right)\\ =\frac{1}{2\mathrm{\&mu;}}{\mathrm{\&Sigma;}}_{jk}\&lsqb;w_{jk}-P\left(j,k\right)\&rsqb;\mathrm{\&delta;}\left(g_j,g_k\right)\end{array};$

Wherein, g_jRepresent the corporations belonging to node j, g_kRepresent the corporations belonging to node k, δ (g_j,g_k) represent impulse function, When node j and node k belongs to same corporations, then δ (g_j,g_k) it is 1, it is otherwise 0.

It is found that when network number M is 1, Multi net voting deteriorates to list automatically from the power function of Multi net voting modularity Network, Multi net voting modularity deteriorates to single mixed-media network modules mixed-media degree that Newman proposes, and therefore Multi net voting modularity is to be carried by Newman The single mixed-media network modules mixed-media degree gone out extends to situation during Multi net voting, and 2010, the multi-chip network module that Peter J.Mucha proposes Degree is compared, and Multi net voting modularity does not accounts for connecting between actual and non-existent, more consideration Multi net voting lower node redundancies Several impacts on network structure, meet the original structure of Multi net voting, are more suitable for Multi net voting corporations than it and analyze.

S2, according to step S1 calculated Multi net voting modularity, corporations in Multi net voting are divided；The present invention uses Multi net voting modularity weighs the tightness degree of Multi net voting corporations contact, and when Multi net voting modularity maximum, the corporations of Multi net voting draw Divide result ideal.But owing to real network is huge, the maximum time complexity solving Multi net voting modularity is the highest, Being unfavorable in ultra-large network quickly finding corporations' result, therefore the present invention proposes a kind of based on Multi net voting modularity fast Speed community discovery algorithm.Specifically include following step by step:

S21, initial time node each in Multi net voting is considered as corporations；Then obtaining corporations' quantity is N.Wherein N is The quantity of Multi net voting interior joint.

Each node i in S22, traversal Multi net voting, finds out all nodes being attached thereto, and to each connected contact meter Operator node i adds the Multi net voting modularity increment of these node place corporations being connected；

Multi net voting modularity increment, expression formula is:

${\mathrm{\&Delta;Q}}_{jk}=\frac{1}{2\mathrm{\&mu;}}\{{\mathrm{\&Sigma;}}_{z\&Element;g_k}\&lsqb;w_{jz}-P(j,z)\&rsqb;-{\mathrm{\&Sigma;}}_{z\&Element;g_j}\&lsqb;w_{jz}-P(j,z)\&rsqb;\};$

Wherein, any node during z represents Multi net voting.

S23, find out the corporations at Multi net voting modularity maximum of increments place, node i is added to these corporations；

S24, repetition step S22 are to step S23, until corporations' number no longer changes；

S25, the corporations marked off by step S22 to step S24 regarding new node as, the connection within new corporations is made For node from ring, weight is the internal annexation summations of new corporations；Between connection between new corporations is as node Limit, the weight on limit is all node annexation summations in two new corporations.Repetition step S22 is to step S24, until owning When the Multi net voting modularity increment of new node is less than or equal to 0, terminate.

Those of ordinary skill in the art it will be appreciated that embodiment described here be to aid in reader understanding this Bright principle, it should be understood that protection scope of the present invention is not limited to such special statement and embodiment.For ability For the technical staff in territory, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, made Any modification, equivalent substitution and improvement etc., within should be included in scope of the presently claimed invention.

Claims (5)

1. a Combo discovering method based on Multi net voting modularity, it is characterised in that including:

S1, calculate Multi net voting modularity, specifically include following step by step:

S11, multiple adjacency matrix is used to represent Multi net voting, particularly as follows:

MN={A₁,A₂,…,A_i,…,A_M},i≤M；

Wherein, M represents network number, A_iRepresent the adjacency matrix of i-th network；

S12, determine node redundancy degree connection relationship matrix, the adjacency matrix of all-network is added and obtains node redundancy degree and connect Relational matrix；Expression formula is as follows:

$W=\underset{i}{\&Sigma;}{A}_i,i\&le;M;$

Wherein, W represents node redundancy degree connection relationship matrix, and every a line in matrix W or each list are shown and be connected with this node The number of times that occurs in a network of each bar limit, i represents the sequence number of adjacency matrix, and i=1,2 ..., M；

S13, the node redundancy degree connection relationship matrix determined according to step S12, calculate node redundancy degree；Expression formula is as follows:

$r_k^m=|w_{jk}=m+1|,w_{jk}\&Element;W,0\&le;m<M;$

Wherein, w_jkFor the element in multiple network node redundancy link relational matrix W, represent the connection limit between node k and node j Number,Represent the m rank redundancy of node k；

S14, build Multi net voting 1 rank zero models according to node redundancy degree；

S15, Multi net voting 1 rank zero model built according to step S14, calculate Multi net voting modularity；

S2, according to step S1 calculated Multi net voting modularity, corporations in Multi net voting are divided；Specifically include following point Step:

S21, initial time node each in Multi net voting is considered as corporations；

Each node z in S22, traversal Multi net voting, finds out all nodes being attached thereto, and each connected contact is calculated joint Point z adds the Multi net voting modularity increment of these node place corporations being connected；

S23, find out the corporations at Multi net voting modularity maximum of increments place, node z is added to these corporations；

S24, repetition step S22 are to step S23, until corporations' number no longer changes；

S25 as, the corporations marked off by step S22 to step S24 are regarded new node, repeat step S22 to step S24, directly When Multi net voting modularity increment to all new nodes is less than or equal to 0, terminate.

A kind of Combo discovering method based on Multi net voting modularity the most according to claim 1, it is characterised in that described step Rapid S14 specifically include following step by step:

S141, according to the size of occurrence number, the limit in Multi net voting being divided into M class, the limit number correspondence exponent number of m class is m rank redundancies The limit number μ of degree^m,0≤m≤M；

S142, by Multi net voting m class limit random packet distribute to each network；

S143, general's distribution are to network A_iLimit random assortment to network A_iIn node j and node k, be calculated network A_iIn The acquisition limit probability of node j and node k is:

$p_{A_i}(j,k)=\frac{r_j^m}{2{\mathrm{\&mu;}}^m}\&times;\frac{r_k^m}{2{\mathrm{\&mu;}}^m};$

Wherein,Represent the m rank redundancy of node j,Represent the m rank redundancy of node k；

S144, repetition step S142, to step S143, until all of limit is allocated to network each node in network, calculate Obtain in M network, node j and node k become limit Probability p (j, k) be:

$p(j,k)=M\&times;\left(\frac{C_1^1}{C_M^1}\frac{r_j^0{r}_k^0}{{\left(2{\mathrm{\&mu;}}^0\right)}^2}+\frac{C_2^1}{C_M^2}\frac{r_j^1{r}_k^1}{{\left(2{\mathrm{\&mu;}}^1\right)}^2}+\mathrm{...}+\frac{C_{m+1}^1}{C_M^{m+1}}\frac{r_j^m{r}_k^m}{{\left(2{\mathrm{\&mu;}}^m\right)}^2}+\mathrm{...}+\frac{C_M^1}{C_M^M}\frac{r_j^{M-1}{r}_k^{M-1}}{{\left(2{\mathrm{\&mu;}}^{M-1}\right)}^2}\right).$

A kind of Combo discovering method based on Multi net voting modularity the most according to claim 2, it is characterised in that described step Rapid S15 specifically include following step by step:

S151, according to step S144 obtain in M network, (j k), obtains many nets to the limit Probability p that becomes of node j and node k Network 1 rank zero model connect limit desired amt P (j, k)=2 μ × p (and j, k), and in Multi net voting corporations actual connect limit quantity E (j, K)=w_jk, μ represents all limits number sum；

S152, Multi net voting 1 rank zero model obtained according to step S151 connect the desired amt on limit, and in Multi net voting, corporations are actual Even limit quantity, obtains Multi net voting modularity；Particularly as follows: Multi net voting modularity=(in Multi net voting, corporations are actual connects limit quantity-many nets Network 1 rank zero model connects the desired amt on limit), and withIt is normalized.

A kind of Combo discovering method based on Multi net voting modularity the most according to claim 3, it is characterised in that step Multi net voting modularity expression formula described in S152 is as follows:

$\begin{array}{c}{Q}_m=\frac{1}{2\mathrm{\&mu;}}{\&Sigma;}_{jk}\&lsqb;E(j,k)-P(j,k)\&rsqb;\mathrm{\&delta;}(g_j,g_k)\\ =\frac{1}{2\mathrm{\&mu;}}{\&Sigma;}_{jk}\&lsqb;w_{jk}-P(j,k)\&rsqb;\mathrm{\&delta;}(g_j,g_k)\end{array};$

Wherein, g_jRepresent the corporations belonging to node j, g_kRepresent the corporations belonging to node k, δ (g_j,g_k) represent impulse function, work as joint When point j and node k belongs to same corporations, then δ (g_j,g_k) it is 1, it is otherwise 0.

A kind of Combo discovering method based on Multi net voting modularity the most according to claim 1, it is characterised in that step Multi net voting modularity increment described in S22, expression formula is:

${\mathrm{\&Delta;Q}}_{jk}=\frac{1}{2\mathrm{\&mu;}}\{{\mathrm{\&Sigma;}}_{z\&Element;g_k}\&lsqb;w_{jz}-P(j,z)\&rsqb;-{\mathrm{\&Sigma;}}_{z\&Element;g_j}\&lsqb;w_{jz}-P(j,z)\&rsqb;\};$

Wherein, any node during z represents Multi net voting.