CN103425738A - Network overlap community detection method based on fuzzy cooperative game - Google Patents

Abstract

The invention discloses a network overlap community detection method based on a fuzzy cooperative game. The method is implemented according to the following steps that step 1, an isolated node is selected randomly and initialized as a community C; step 2, gain of the community C is calculated after each neighbor node of the community C joins the community C; step 3, current community C belonging membership degree of each neighbor node of the community C is calculated; step 4, the node with the maximum value obtained by multiplying the membership degree with the community gain increment joins the current community C, and whether the node joins the community C is decided by the membership and the gain together; step 5, execution is conducted until gain of all nodes in neighbor points of the community is negative. If the gain of all nodes in Neigh_Community (C) of neighbor points of the community is not negative, the step 2 is returned, and follow-up steps are executed repeatedly and sequentially. Network overlap community detection is achieved by using new ideas, and network overlap community detection method accuracy is improved.

Description

Network overlapped community discovery method based on cooperative fuzzy games

Technical field

The invention belongs to network overlapped community discovery method technical field, relate to a kind of network overlapped community discovery method based on cooperative fuzzy games.

Background technology

Many complexity that exist in real world and huge system can be described with network, we are referred to as complex network.Complex network is the abstract of complication system, and the individuality in complication system is nodes, and the limit between node is according to certain relation of certain regular self-assembling formation or arteface between individuality.Comprising various types of complex networks in real world, the network formed as interlinked between the page in community network, technical network, biological networks, network, paper coauthorship network, reference citation network etc.In these real worlds, a large amount of complex networks is to be combined by many dissimilar nodes, the connection wherein existed between identical type node is many, and the connection of dissimilar node is relatively less, this specific character of complex network is called community structure.

The research of finding about community structure at present is own through making some progress, and many community structure discover methods have been proposed, apply more having: Kernighan-lin method, GN method, spectral bisection method, Extremal optimization method etc., yet, most community structure discover method all supposes that community does not overlap each other, this just means that a node can only belong to a community, but, in actual life, between community, is likely overlapping.For example, in the scientific research cooperative network, some scholars likely cooperate with people in a plurality of different fields simultaneously; In bio-networks, a certain protein likely with multiple other protein interaction, so just likely have some node to belong to a plurality of communities simultaneously; In community network, some interest people is widely likely participated in a plurality of different community activities.Find that the overlapping community structure in complex network contributes to us to understand better the topological structure of complex network, to the research of lap in community, contribute to us to open new thinking and solve the problems such as the propagation of network congestion, computer virus, public opinion and the propagation of popular virus.The accuracy rate of the existing discovery to overlapping Web Community is lower, especially for large scale network.

Summary of the invention

The object of the present invention is to provide a kind of network overlapped community discovery method based on cooperative fuzzy games, solve the prior art problem low for the accuracy rate of overlapping community discovery.

Technical scheme of the present invention is that the overlapping community discovery method based on cooperative fuzzy games comprises the following steps:

Step 1, select an isolated node to be initialized as the C of community at random;

Step 2, each neighbor node that calculates the C of community join the income of the C of community after the C of community;

Each neighbor node of step 3, the calculating C of community belongs to the degree of membership of the current C of community;

The node that step 4, selection degree of membership are multiplied by community's Increment of income maximum joins in the current C of community, by degree of membership and income, jointly determines whether node joins the C of community;

Step 5 is until stop when in the abutment points Neigh_Comunity of community (C), the income of all nodes is negative value; If, when in the abutment points Neigh_Comunity of community (C), the income of all nodes is not negative value, continues to return step 2 and repeat successively subsequent step.

Characteristics of the present invention also are:

In step 2, after node i adds the C of community, community's C revenue function shows as follows:

$\mathrm{revenge}\left(C\right)=f=\frac{{{\mathrm{deg}}^C}_{\mathrm{in}}}{{({{\mathrm{deg}}^C}_{\mathrm{in}}+{{\mathrm{deg}}^C}_{\mathrm{out}})}^{\mathrm{\α}}}---\left(1\right)$

In formula (1), C is the community divided, and α is controlling the size of community, common α value between 0.9 to 1.5, deg ^C _InThe inside number of degrees sum that means the node in community, i.e. the number twice of community's internal edges, deg ^C _outThe outside number of degrees sum that means the node in community, the i.e. number of external edge;

Node i adds the increment of the C of Hou， community of community income to be so:

Δrevenge(C)＝f _{C+i}-f _{C} （2）

If Δ revenge (C)>0, mean that node i adds the C of community income increase after the C of community so, if Δ revenge (C)<0 means that node i adds the income of the C of community after the C of community to reduce so.

In step 3, membership function specifically is expressed as:

membership _C(i)＝deg _C(i)-p _C(i)deg(i) （3）

Deg wherein _C(i) mean the number on the limit that node i is connected with other nodes in the C of this community, and the number of degrees that deg (i) is node i, p _C(i) mean the not limit in the C of community shared ratio in all limits of whole network that an end is connected with node i;

Due to each membership _C(i) all only relevant with the number of degrees of node i, it is obviously a local variable.For with degree of membership membership _C(i) definition of ∈ [0,1] is consistent, membership _C(i), within scope should remain on 0～1 scope, if therefore this value is less than 0, show that node i does not belong to the C of community fully, makes membership _C(i)=0, and do following normalized:

${\mathrm{\&lambda;}}_i=\frac{{\mathrm{membership}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}=\frac{{\mathrm{deg}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}-p_C\left(i\right)---\left(4\right)$

If λ _i<0, make λ _i=0.

The present invention has following beneficial effect:

1, the present invention selects an isolated node i to be initialized as the C of community at random, other communities of iterative solution; Until all nodes all at least are divided into a community, be divided into a plurality of communities at the node had, realized that the overlapping community of network divides.

2, the invention solves the overlapping community discovery problem of network, improved the accuracy rate of network overlapped community discovery.

The accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention is based on the network overlapped community discovery method of cooperative fuzzy games;

Fig. 2 is the Karate Network data set that the embodiment of the present invention adopts;

Fig. 3 is the Dolphin Network data set that the embodiment of the present invention adopts;

Fig. 4 is the Football Network data set that the embodiment of the present invention adopts;

Fig. 5 is embodiment of the present invention Karate Network data set division result;

Fig. 6 is embodiment of the present invention Dolphin Network data set division result;

Fig. 7 is embodiment of the present invention Football Network data set division result.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Step 1, select an isolated node to be initialized as the C of community at random;

Step 2, each neighbor node that calculates the C of community join the income of the C of community after the C of community;

After node i adds the C of community, community's C revenue function shows as follows:

$\mathrm{revenge}\left(C\right)=f=\frac{{{\mathrm{deg}}^C}_{\mathrm{in}}}{{({{\mathrm{deg}}^C}_{\mathrm{in}}+{{\mathrm{deg}}^C}_{\mathrm{out}})}^{\mathrm{\&alpha;}}}---\left(1\right)$

In formula (1), C is the community divided, and α is controlling the size of community, common α value between 0.9 to 1.5, deg ^C _InThe inside number of degrees sum that means the node in community, i.e. the number twice of community's internal edges, deg ^C _outThe outside number of degrees sum that means the node in community, the i.e. number of external edge.

Parameter alpha is being adjusted the size of community, and the community structure of the larger generation of α value is less, and namely the quantity of community is more, and the α value is less, and the community structure of generation is larger, if α is enough little, the community of generation is exactly network itself.Have been found that in most of the cases, α is less than 0.5, only produce a community, if α is greater than 2, regain minimum community.Generally, α equals at 1 o'clock, is the outside number of degrees of node and the ratio of the total number of degrees, and this weak structure definition with community is corresponding.

Node i adds the increment of the C of Hou， community of community income to be so:

Δrevenge(C)＝f _{C+i}-f _{C} （2）

If Δ revenge (C)>0, mean that node i adds the C of community income increase after the C of community so, if Δ revenge (C)<0 means that node i adds the income of the C of community after the C of community to reduce so.

Can see deg by formula (2) ^C _outValue less, show that other nodes in this community and network contact more sparse, this is consistent with the feature of community; Simultaneously, deg ^C _outValue less, the value of revenge (C) is larger so, shows that node joins behind community the income of community larger, community structural more obvious, if deg ^C _outValue be 0 o'clock, show that the node in current community and network does not contact, a community in network namely, then add any one node, all can make Δ revenge (C) be less than 0.

Each neighbor node of step 3, the calculating C of community belongs to the degree of membership of the current C of community;

Membership function specifically is expressed as:

membership _C(i)＝deg _C(i)-p _C(i)deg(i) （3）

Deg wherein _C(i) mean the number on the limit that node i is connected with other nodes in the C of this community, and the number of degrees that deg (i) is node i, p _C(i) mean the not limit in the C of community shared ratio in all limits of whole network that an end is connected with node i.

Due to each membership _C(i) all only relevant with the number of degrees of node i, it is obviously a local variable.For with degree of membership membership _C(i) definition of ∈ [0,1] is consistent, membership _C(i), within scope should remain on 0～1 scope, if therefore this value is less than 0, show that node i does not belong to the C of community fully, makes membership _C(i)=0, and do following normalized:

${\mathrm{\&lambda;}}_i=\frac{{\mathrm{membership}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}=\frac{{\mathrm{deg}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}-p_C\left(i\right)---\left(4\right)$

If λ _i<0, make λ _i=0.By calculating each node λ _iSize, just obtained the size of each node to the degree of membership of community structure.λ _iValue higher, illustrated that this node belongs to the degree of corresponding community structure larger, when with the common decision of income, whether adding current community, the possibility that this node joins current community is also larger; λ _iValue less, illustrated that this node belongs to the degree of corresponding community structure less, when with the common decision of income, whether adding current community, the possibility that this node joins current community is also less.

The node that step 4, selection degree of membership are multiplied by community's Increment of income maximum joins in the current C of community, by degree of membership and income, jointly determines whether node joins the C of community;

Step 5 is until stop when in the abutment points Neigh_Comunity of community (C), the income of all nodes is negative value; If, when in the abutment points Neigh_Comunity of community (C), the income of all nodes is not negative value, continues to return step 2 and repeat successively subsequent step.

Embodiment, the overlapping community discovery method of cooperative fuzzy games of the present invention, referring to Fig. 1, according to following steps, implement:

Step 1, select an isolated node to be initialized as the C of community at random;

For choosing of random node, the present invention is used as the choosing method of random seed by a degree centrad, point degree centrad be the most simply, index the most intuitively, it has represented that a node is positioned at the degree of the core position of figure, has portrayed the ability of other nodes development contacts relations in this node and figure.

Point degree centrad is divided into absolute center degree and relative centrad, and what the absolute point degree centrad of node i referred to is exactly the number of degrees of this point, for being described in the direct influence of static network node, uses C _ADiMean, that is:

C _ADi＝deg(i) （1）

Ask the node of some degree centrad value maximum of isolated node in network as random node, the present invention adopts the absolute center degree of a degree to ask isolated node, the exhausted degree centrad value of node is larger, node is described in this network and the node around it between the ability of establishing direct links stronger.

Step 2, each the neighbor node Neigh_Comunity (C) that calculates the C of community join the income of the C of community after the C of community;

The neighbours of community collection: the given C of community for certain, its neighbours be defined as with the C of community in node interconnect the set of other nodes in network, formula table is shown:

$\mathrm{Neigh}\_\mathrm{Comunity}\left(C\right)=\left\{v\right|(u,v)\&Element;E,u\&Element;C,v\&NotElement;C\}---\left(2\right)$

Wherein E is the limit in network, u, and v means the node in network, C means community;

The income of community is calculated by revenue function, and in cooperative fuzzy games, revenue function is a mapping, gives each participant's assign a value, tells and can in this cooperation, obtain how many incomes, define this revenue function as follows:

revenge:2 ^N→R （3）

Wherein 2 ^NBe the set of the subset of the node set N in network, the nonvoid subset C of N is called alliance, revenge (C) ∈ R, and to each C of alliance, real number revenge (C) is the absolute payment of effective distribution of the C of alliance.

For the method, after node i adds the C of community, community's C revenue function shows as follows:

$\mathrm{revenge}\left(C\right)=f=\frac{{{\mathrm{deg}}^C}_{\mathrm{in}}}{{({{\mathrm{deg}}^C}_{\mathrm{in}}+{{\mathrm{deg}}^C}_{\mathrm{out}})}^{\mathrm{\&alpha;}}}---\left(4\right)$

In formula, C is the community divided, and α is controlling the size of community, common α value between 0.9 to 1.5, deg ^C _InThe inside number of degrees sum that means the node in community, i.e. the number twice of community's internal edges, deg ^C _outThe outside number of degrees sum that means the node in community, the i.e. number of external edge.

Parameter alpha is finally being adjusted the size of community, and the community structure of the larger generation of α value is less, and namely the quantity of community is more, and the α value is less, and the community structure of generation is larger, if α is enough little, the community of generation is exactly network itself.Have been found that in most of the cases, α is less than 0.5, only produce a community, if α is greater than 2, regain minimum community.Generally, α equals at 1 o'clock, is the outside number of degrees of node and the ratio of the total number of degrees, and this weak structure definition with community is corresponding.

Node i adds the increment of the C of Hou， community of community income to be so:

Δrevenge(C)＝f _{C+i}-f _{C} （5）

If Δ revenge (C)>0, mean that node i adds the C of community income increase after the C of community so, if Δ revenge (C)<0 means that node i adds the income of the C of community after the C of community to reduce so.

Can see deg by formula (5) ^C _outValue less, show that other nodes in this community and network contact more sparse, this is consistent with the feature of community; Simultaneously, deg ^C _outValue less, the value of revenge (C) is larger so, shows that node joins behind community the income of community larger, community structural more obvious, if deg ^C _outValue be 0 o'clock, show that the node in current community and network does not contact, a community in network namely, then add any one node, all can make Δ revenge (C) be less than 0.

Each neighbor node Neigh_Comunity (C) of step 3, the calculating C of community belongs to the degree of membership of the current C of community;

Subordinate function is in order to determine that each node in network belongs to the degree of membership of different communities, the degree of this community of node preference namely, and to the n in certain network node N={1,2 ..., n} carries out the division of network overlapped community, uses membership _CThe value representation node participate in the degree of the C of community, that is:

membership _C:N→[0,1] （6）

In formula, membership _C(i)=1 participates in the C of community fully for node i, membership _C(i)=0 does not participate in the C of community fully for node i, and C is the alliance that the node in network is cooperated with each other and formed with the degree of participation interval between [0,1].

For method, be somebody's turn to do, membership function specifically is expressed as:

membership _C(i)＝deg _C(i)-p _C(i)deg(i) （7）

Deg wherein _C(i) mean the number on the limit that node i is connected with other nodes in the C of this community, and the number of degrees that deg (i) is node i, p _C(i) mean the not limit in the C of community shared ratio in all limits of whole network that an end is connected with node i.

Due to each membership _C(i) all only relevant with the number of degrees of node i, it is obviously a local variable.For with degree of membership membership _C(i) definition of ∈ [0,1] is consistent, membership _C(i), within scope should remain on 0～1 scope, if therefore this value is less than 0, show that node i does not belong to the C of community fully, makes membership _C(i)=0, and do following normalized:

${\mathrm{\&lambda;}}_i=\frac{{\mathrm{membership}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}=\frac{{\mathrm{deg}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}-p_C\left(i\right)---\left(8\right)$

If λ _i<0, make λ _i=0.By calculating each node λ _iSize, just obtained the size of each node to the degree of membership of community structure.λ _iValue higher, illustrated that this node belongs to the degree of corresponding community structure larger, when with the common decision of income, whether adding current community, the possibility that this node joins current community is also larger; λ _iValue less, illustrated that this node belongs to the degree of corresponding community structure less, when with the common decision of income, whether adding current community, the possibility that this node joins current community is also less.

The node that step 4, selection degree of membership are multiplied by community's Increment of income maximum joins in the current C of community, by degree of membership and income, jointly determines whether node joins the C of community;

Step 5 is until stop when in the abutment points Neigh_Comunity of community (C), the income of all nodes is negative value.If, when in the abutment points Neigh_Comunity of community (C), the income of all nodes is not negative value, continues to return step 2 and repeat successively subsequent step.

Find a community in the network by above-mentioned five steps, selected at random an isolated node i to be initialized as the C of community; Solve other community by said method; Repeat said process, until all nodes all at least are divided into a community.In this process, some nodes are divided into a plurality of communities, so the method has realized that the overlapping community of network divides.

The invention provides the overlapping community discovery method based on cooperative fuzzy games, determine suitable revenue function and subordinate function by the thought of original cooperative fuzzy games, solved the division of overlapping community according to the rule of fuzzy game, it is higher that accuracy rate is compared other algorithms.

In embodiment, select the validity of three kinds of different True Data collection checking this paper algorithms, and contrasted in accuracy rate with existing representative algorithm.These three kinds of data sets are respectively: karate karate club network, and shown in Fig. 2, this network comprises altogether 34 nodes and 78 limits, and wherein club each member means the node in network, and limit means the relation between this clubbite; BottlenoseDolphins dolphin network, shown in Fig. 3, this network is by 2 family's group compositions, 62 bottle-nosed dolphins altogether, this small-sized social network is comprised of 62 nodes and 159 limits; American university football league Football network, shown in Fig. 4, football team means the node in network, and between two teams, the match of regular season means the limit of network, and it comprises 115 nodes and 613 limits altogether.

For Zacharykarate club network, community's result that the algorithm of this paper is divided as shown in Figure 5, network is divided into to two communities, wherein blue and red node means two communities of community's partitioning algorithm, wherein the node of black means the overlapping point of community, overlapping point has four: 14,31,3,21, and wherein α equals 0.8.For Bottlenose dolphin network, the community structure of the dolphin network that this paper algorithm is divided as shown in Figure 6, network is divided into to two communities, as enter as shown in blue and redness, wherein the node of black means the overlapping point of community, overlapping point has five: 28,7,30,19,1, and wherein α equals 0.8.For the football network, when α equals 1.2, as shown in Figure 7, the method is divided into 11 communities to community to the overlapping community structure of division.

GCE algorithm commonly used, CPM algorithm, LEK algorithm and discover method of the present invention are compared, and experimental result is with reference to Fig. 5 to Fig. 7.Table 1 is accuracy rate (EQ) table of comparisons that adopts the network overlapped community discovery of algorithms of different.

The accuracy rate of the network overlapped community discovery of table 1, algorithms of different (EQ) table of comparisons

From table, can see, the EQ value of the EQ value-based algorithm calculated by algorithms of different in the Karate network is all higher than GCE algorithm and CPM algorithm, lower than the LEM algorithm; In the Dolphin network, the EQ value of discover method of the present invention is all higher than GCE algorithm and CPM algorithm, lower than the LEM algorithm; In the football network, the EQ value of discover method of the present invention is all higher than GCE algorithm and CPM algorithm, LEM algorithm.Therefore, invention has solved the overlapping community discovery problem of network, higher than prior art to the accuracy rate of network overlapped community discovery.

Claims (3)

1. the overlapping community discovery method based on cooperative fuzzy games, is characterized in that, comprises the following steps:

Step 1, select an isolated node to be initialized as the C of community at random;

Step 2, each neighbor node that calculates the C of community join the income of the C of community after the C of community;

Each neighbor node of step 3, the calculating C of community belongs to the degree of membership of the current C of community;

The node that step 4, selection degree of membership are multiplied by community's Increment of income maximum joins in the current C of community, by degree of membership and income, jointly determines whether node joins the C of community;

Step 5 is until stop when in the abutment points Neigh_Comunity of community (C), the income of all nodes is negative value; If, when in the abutment points Neigh_Comunity of community (C), the income of all nodes is not negative value, continues to return step 2 and repeat successively subsequent step.

2. the overlapping community discovery method based on cooperative fuzzy games as claimed in claim 1, is characterized in that, in step 2, after node i adds the C of community, community's C revenue function shows as follows:

$\mathrm{revenge}\left(C\right)=f=\frac{{{\mathrm{deg}}^C}_{\mathrm{in}}}{{({{\mathrm{deg}}^C}_{\mathrm{in}}+{{\mathrm{deg}}^C}_{\mathrm{out}})}^{\mathrm{\&alpha;}}}---\left(1\right)$

In formula (1), C is the community divided, and α is controlling the size of community, common α value between 0.9 to 1.5, deg ^C _InThe inside number of degrees sum that means the node in community, i.e. the number twice of community's internal edges, deg ^C _outThe outside number of degrees sum that means the node in community, the i.e. number of external edge;

Node i adds the increment of the C of Hou， community of community income to be so:

Δrevenge(C)＝f _{C+i}-f _{C} （2）

If Δ revenge (C)>0, mean that node i adds the C of community income increase after the C of community so, if Δ revenge (C)<0 means that node i adds the income of the C of community after the C of community to reduce so.

3. the overlapping community discovery method based on cooperative fuzzy games as claimed in claim 1 or 2, is characterized in that, in step 3, membership function specifically is expressed as:

membership _C(i)＝deg _C(i)-p _C(i)deg(i) （3）

Deg wherein _C(i) mean the number on the limit that node i is connected with other nodes in the C of this community, and the number of degrees that deg (i) is node i, p _C(i) mean the not limit in the C of community shared ratio in all limits of whole network that an end is connected with node i;

Due to each membership _C(i) all only relevant with the number of degrees of node i, it is obviously a local variable; For with degree of membership membership _C(i) definition of ∈ [0,1] is consistent, membership _C(i), within scope remains on 0～1 scope, if therefore this value is less than 0, show that node i does not belong to the C of community fully, makes membership _C(i)=0, and do following normalized:

${\mathrm{\&lambda;}}_i=\frac{{\mathrm{membership}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}=\frac{{\mathrm{deg}}_C\left(i\right)}{\mathrm{deg}\left(i\right)}-p_C\left(i\right)---\left(4\right)$

If λ _i<0, make λ _i=0.

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