CN105279187A - Edge clustering coefficient-based social network group division method - Google Patents

Abstract

The invention relates to an edge clustering coefficient-based social network group division method. Specifically, the method comprises the following steps: reading the social network data; constructing a social network planning which takes social network users as nodes and takes user relationships as edges; randomly endowing each user with a unique label value; updating the labels of the user nodes by adopting an edge clustering coefficient-based label propagation algorithm; and after several iteration, owning, by the tightly connected nodes, same specific label value. By adopting the social network group division method, the user groups are divided through improving the label propagation algorithm according to the edge clustering coefficient attribute of the user relationship graph, and the division result has preferable application value for the monitoring of network public opinions and the searching of commercial customers.

Description

A kind of community network group dividing method based on limit convergence factor

Technical field

The present invention relates to social networks technical field, particularly a kind of community network group dividing method based on limit convergence factor.

Background technology

From community network, how to excavate the information with Practical Benefit become a study hotspot in complex network.Be worth in theory or social utility and all have very important significance.Web Community usually close by function or that character is similar network node forms, by excavating the community structure in network, user can find rapidly and accurately the associated user having inner link with oneself, such as there is the user etc. of same or similar hobby, to fields such as network public-opinion monitoring, commercial user's excavations, all there is good using value.

Up to now, people have proposed many community discovery methods, 2002, the paper that Girvan and Newman delivers on PNAS is studied the community structure in community network and bio-networks, namely famous GN algorithm, it is an important milestone in community discovery technical development process, be a kind of very classical community discovery algorithm, be important reference model in community discovery technical research thus pulled open the prelude of community structure research.The topological characteristic that community structure generally has as network proposes by this paper first, and provides the community structure that a kind of Split type hierarchical clustering algorithm based on limit betweenness (edgebetweenness) carrys out recognition network.The basic thought of most of community discovery algorithm is all measure according to the cohesion of certain node, recursively merges network or divides, resolving into nested community's hierarchical structure.Traditional community division method is roughly divided into two classes: based on algorithm and the hierarchical clustering algorithm of graph theory.Wherein mainly contain Kemighan-Lin algorithm (referred to as K-L algorithm), spectral bisection method and clique percolation method etc. based on Laplce figure eigenwert based on the algorithm of graph theory, the shortcoming of these class methods to define iteration number of times; Hierarchical clustering algorithm can be divided into again two large classes: agglomerative algorithm and splitting-up method, and partitioning standards increases limit in a network or removes limit, and what increase limit is agglomerative algorithm, and what remove limit is splitting-up method.Typically represent algorithm and have Newman fast algorithm, GN algorithm etc., shortcoming be algorithm complex high, cannot define and when stop.

Visible, all there is many limitation in the algorithm of above classics, division result is unsatisfactory, and complexity is higher, is difficult to the requirement meeting large-scale live network community discovery.2007, the people such as Raghavan proposed label propagation algorithm, efficiently solved the problem that complexity is high, cannot restrain.Label propagation algorithm is a kind of semi-supervised learning method based on figure, think that contacting node closely can have an identical label value, its basic ideas are the label informations using the label information of flag node to predict unmarked node, and the node that last label value is identical is divided into a community.LPA has the features such as thinking is simple, extendability is strong, complexity is minimum, fastest.The time complexity of label propagation algorithm, close to linear O (m) (m is the number on limit), detects for fairly large community's (106-109 node), starts convergence after 5 iteration.In addition, label propagation algorithm neither needs to optimize predefined objective function, the prior imformation such as quantity and scale about community is not needed yet, the size of community is not also limited, therefore label propagation algorithm has become current application one of community discovery algorithm comparatively widely, is widely applied in the fields such as multimedia messages classification, virtual community excavation.

But although label propagation algorithm is simply efficient, the randomness that the label in algorithm is propagated causes the accuracy of algorithm poor, and division result is unstable, randomness is comparatively strong, and robustness has much room for improvement.In sum, all there is very large room for promotion in existing community discovery method in accuracy and time complexity.

Summary of the invention

The object of the present invention is to provide a kind of community network group dividing method based on limit convergence factor, the method is conducive to the degree of accuracy and the stability that improve Web Community's division.

For achieving the above object, technical scheme of the present invention is: a kind of community network group dividing method based on limit convergence factor, comprises the following steps:

Steps A: read social network data, constructing with social network user is node, and customer relationship is the social network diagram on limit;

Step B: vertex ticks: be the label value that each user node Random assignment one is unique, as the mark of community belonging to it;

Step C: preliminary community divides: carry out iteration renewal to the label on all summits in figure.After each iteration, the label value of node is updated to the label value that in the label of its adjacent node, quantity is maximum;

Step D: community divides refinement: if when having the quantity of multiple label value to be all maximal value, calculate the limit convergence factor on limit between node to be updated and adjacent node.The neighbor node label that limit convergence factor is large is preferentially propagated by selection.After several times iteration, the label variations in each user node neighbours tends towards stability;

Step e: all nodes with same label are classified as a community.

Further, in above-mentioned steps B, vertex ticks specifically comprises the following steps: be the label value that each user node Random assignment one is unique, i.e. C _n=L _n, C _nrepresent community belonging to node n, L _nrepresent the label value of node n.

Further, in above-mentioned steps C, preliminary community divides: social network diagram is abstracted into a simple non-directed graph G (N, E), wherein, N represents the set of node, and E represents the set on limit.W _nmrepresent the weight on the limit connecting n, m node, n, m ∈ N, uses C _nrepresent community belonging to node n, N ^ln () represents that in the neighbor node of node n ∈ N, label value is the node set of 1.Formula is as follows:

$C_n=\arg \underset{l}{\max }\underset{m\∈N^l\left(n\right)}{\mathrm{\Σ}}{W}_{\mathrm{nm}}$

Further, in above-mentioned steps D, community divides the so-called limit convergence factor of refinement detailed process, represent the aggregation extent of two nodes of fillet, its value is larger, the strength of joint representing two nodes that this edge connects is stronger, illustrates that these two nodes are larger in the possibility of same community.Concrete definition rule is as follows:

Suppose there is a limit E _ij, its summit is i and j, if wonder in network that how much other whether there is and have node k and i, j all adjacent, namely there is two other limit E _jk, E _ik, E _ijform three square rings (limit number is the closed path of 3).If three square ring comprise the limit that connects different community, then a certain bar in another two limits in this three square ring still connects the possibility of Liang Ge community will be very large.Therefore, the limit convergence factor on a limit is defined as the three square ring proportions comprising this limit:

$C_{\mathrm{ij}}=\frac{z_{\mathrm{ij}}+1}{\min (k_i-1,k_j-1)}$

Wherein, k _i, k _jthe degree of representation node i and j respectively, z _ijrepresent the actual leg-of-mutton number comprising this limit in network, the denominator in formula represents the triangle number of the maximum possible comprising this limit.

Further, in described step D, stopping criterion for iteration is that social networks reaches balance, and it is termination of iterations that number of tags no longer changes.

Compared to prior art, the invention has the beneficial effects as follows: compared to existing community discovery algorithm, under the prerequisite retaining conventional labels propagation algorithm advantage, stability and degree of accuracy are greatly enhanced.To sum up, algorithm of the present invention can detect community network efficiently.

Accompanying drawing explanation

Fig. 1 is the realization flow figure of the inventive method.

Fig. 2 changes the NMI value comparison diagram with label propagation algorithm (being represented by LPA) for adopting the inventive method (being represented by LPAc) community's number in baseline network 1000 nodes in the interior value along with hybrid parameter μ of [10,50] scope.

Fig. 3 changes the variance comparison diagram with the NMI value of label propagation algorithm (being represented by LPA) for adopting the inventive method (being represented by LPAc) community's number in baseline network 1000 nodes in the interior value along with hybrid parameter μ of [10,50] scope.

Fig. 4 changes the NMI value comparison diagram with label propagation algorithm (being represented by LPA) for adopting the inventive method (being represented by LPAc) community's number in baseline network 1000 nodes in the interior value along with hybrid parameter μ of [20,100] scope.

Fig. 5 changes the variance comparison diagram with the NMI value of label propagation algorithm (being represented by LPA) for adopting the inventive method (being represented by LPAc) community's number in baseline network 1000 nodes in the interior value along with hybrid parameter μ of [20,100] scope.

Fig. 6 for adopt the inventive method (being represented by LPAc) in baseline network 1000 nodes community's number [10,50] the Q module angle value comparison diagram of the interior change of the value along with hybrid parameter μ ∈ [0.50,0.65] of scope and label propagation algorithm (being represented by LPA).

Fig. 7 for adopt the inventive method (being represented by LPAc) in baseline network 1000 nodes community's number [10,50] the variance comparison diagram of the Q module angle value of the interior change of the value along with hybrid parameter μ ∈ [0.50,0.65] of scope and label propagation algorithm (being represented by LPA).

Fig. 8 for adopt the inventive method (being represented by LPAc) in baseline network 1000 nodes community's number [20,100] the Q module angle value comparison diagram of the interior change of the value along with hybrid parameter μ ∈ [0.375,0.575] of scope and label propagation algorithm (being represented by LPA).

Fig. 9 for adopt the inventive method (being represented by LPAc) in baseline network 1000 nodes community's number [20,100] the variance comparison diagram of the Q module angle value of the interior change of the value along with hybrid parameter μ ∈ [0.375,0.575] of scope and label propagation algorithm (being represented by LPA).

Embodiment

Below in conjunction with accompanying drawing, by embodiment, the present invention is further detailed explanation.

Fig. 1 is the realization flow figure of a kind of community network group dividing method based on limit convergence factor of the present invention.As shown in Figure 1, said method comprising the steps of:

Steps A: read social network data, constructing with social network user is node, and customer relationship is the social network diagram on limit.

As for micro blog network, using each microblog users as the node of in community network, using the interaction between user as community network limit, such as, mutually comment on or mutually pay close attention to.If the community one by one in micro blog network so can be excavated, microblog users are joined and has with self in the groupuscule group of same or similar hobby, to network public-opinion monitoring and the commercial user field such as to excavate, all there is good using value.

In the present embodiment, adopt baseline network at hybrid parameter μ ∈ [0,0.80] between, (Δ μ=0.025) generates nodes is the community network of 1000, and hybrid parameter μ represents the obvious degree of the community structure of community network, and the less community structure of μ value is more obvious.Community's number is divided into two groups, is respectively [10,50] and [20,100].

Step B: vertex ticks: be the label value that each user node Random assignment one is unique, as the mark of community belonging to it.

Concrete, in above-mentioned steps B, vertex ticks specifically comprises the following steps: be the label value that each user node Random assignment one is unique, i.e. C _n=L _n, C _nrepresent community belonging to node n, L _nrepresent the label value of node n.

Step C: preliminary community divides: carry out iteration renewal to the label on all summits in figure.After each iteration, the label value of node is updated to the label value that in the label of its adjacent node, quantity is maximum.

Concrete, in above-mentioned steps C, preliminary community divides: social network diagram is abstracted into a simple non-directed graph G (N, E), wherein, N represents the set of node, and E represents the set on limit.W _nmrepresent the weight on the limit connecting n, m node, n, m ∈ N, uses C _nrepresent community belonging to node n, N ^ln () represents that in the neighbor node of node n ∈ N, label value is the node set of 1.Be defined as:

$C_n=\arg \underset{l}{\max }\underset{m\∈N^l\left(n\right)}{\mathrm{\Σ}}{W}_{\mathrm{nm}}$

Step D: community divides refinement: if when having the quantity of multiple label value to be all maximal value, calculate the limit convergence factor on limit between node to be updated and adjacent node.The neighbor node label that convergence factor is large is preferentially propagated by selection.After several times iteration, the label variations in each user node neighbours tends towards stability.

Concrete, in above-mentioned steps D, community divides the so-called limit convergence factor of refinement detailed process, represent the aggregation extent of two nodes of fillet, its value is larger, the strength of joint representing two nodes that this edge connects is stronger, illustrates that these two nodes are larger in the possibility of same community.Concrete definition rule is as follows:

Suppose there is a limit E _ij, its summit is i and j, if wonder in network that how much other whether there is and have node k and i, j all adjacent, namely there is two other limit E _jk, E _ik, E _ijform three square rings (limit number is the closed path of 3).If three square ring comprise the limit that connects different community, then a certain bar in another two limits in this three square ring still connects the possibility of Liang Ge community will be very large.Therefore, the limit convergence factor on a limit is defined as the three square ring proportions comprising this limit:

$C_{\mathrm{ij}}=\frac{z_{\mathrm{ij}}+1}{\min (k_i-1,k_j-1)}$

Concrete, k _i, k _jthe degree of representation node i and j respectively, z _ijrepresent the actual leg-of-mutton number comprising this limit in network, the denominator in formula represents the triangle number of the maximum possible comprising this limit.

Concrete, in described step D, stopping criterion for iteration is that social networks reaches balance, and it is termination of iterations that number of tags no longer changes.

Step e: all nodes with same label are classified as a community.

In the present embodiment investigate adopt the present invention is based on nodes be in the node base pseudo-crystalline lattice of 1000 community's number respectively [10,50] and [20,100] in scope, along with value change and the Experimental comparison of label propagation algorithm division result at Stability and veracity of hybrid parameter μ, the present embodiment adopts the size of NMI (normalizedmutualinformation) value and Q module degree to pass judgment on the accuracy of community division result, NMI is the judging basis of the degree of closeness of judgment experiment division result and actual legitimate reading, and rule is as follows:

$\mathrm{NMI}(A,B)=\frac{-2\underset{i=1}{\overset{c_A}{\mathrm{\Σ}}}\underset{j=1}{\overset{c_B}{\mathrm{\Σ}}}{N}_{\mathrm{ij}}\log \left(\frac{N_{\mathrm{ij}}N}{N_i{N}_j}\right)}{\underset{i=1}{\overset{c_A}{\mathrm{\Σ}}}{N}_i\log \left(\frac{N_i}{N}\right)+\underset{j=1}{\overset{c_B}{\mathrm{\Σ}}}{N}_j\log \left(\frac{N_j}{N}\right)}$

Wherein, define a confusion matrix N, line number represents true community, and columns representative finds community, N _ijthe node represented in true community i is finding node number shared in community j, c _arepresent the quantity of true community, c _brepresentative has found the quantity of community, N _irepresent matrix N _ijthe summation that middle i is capable, N _jrepresent the summation of j row.

Q module degree is a function evaluating community discovery algorithm partition community quality, and it is that network is split into k community, the symmetric matrix E=e of a structure k*k by a kind of evaluation function supposition be widely used at present _ij(1≤i, j≤k).Element e in this matrix _ijnode in expression connection i community and the limit between the node in j community account for the ratio on all limits in network, the element e on diagonal of a matrix _iirepresent the ratio accounting for whole limit in network on the limit of i inside, community.Matrix trace Tr (E) represents that the limit connecting same community internal node accounts for the ratio in network between all limits, and obviously, community's quality of matrix trace larger expression algorithm partition is higher.The element sum a of the i-th row (or i-th row) in matrix _irepresenting has at least each bar limit of the node of one end in community i to account for the ratio on all limits in network.Suppose that these limits are random connections, the expectation value of ratio that so these limits are connected with the node in community i is a _i ².Be defined as:

$Q=\underset{i}{\mathrm{\Σ}}(e_{\mathrm{ii}}-{a_i}^2)=\mathrm{Tr}\left(E\right)-\left|\right|E^2\left|\right|$

Wherein, wherein || E ²|| represent the element number in matrix E.

Stability is embodied by the variance yields size of NMI value and Q module degree.

A kind of community network group dividing method based on limit convergence factor of the present invention, community's partition process is divided into and reads social network data, vertex ticks, the division of preliminary community, community's division refinement four-stage, first social network data is read, structure is node with social network user, and customer relationship is the social network diagram on limit; Be the unique label value of each user node Random assignment one according to social network diagram, as the mark of community belonging to it, after users all in network marked label value, at random iteration renewal carried out to the label on all summits in figure.After each iteration, the label value of node is updated to the label value that in the label of its adjacent node, quantity is maximum.If when there being the quantity of multiple label value to be all maximal value, calculate the limit convergence factor on limit between node to be updated and adjacent node.The neighbor node label that wherein convergence factor is large is preferentially propagated by selection.After several times iteration, the label variations in each user node neighbours tends towards stability.Finally, all nodes with same label are classified as a community.Described method is by introducing the concept of the convergence factor on limit, calculate the limit convergence factor between node to be updated and its neighbor node, the node label that prioritizing selection limit convergence factor is large is propagated, the value of limit convergence factor shows that more greatly the strength of joint of two nodes that this edge connects is stronger, and two nodes are larger in the possibility of same community.Thus the randomness avoiding label propagation algorithm is on the impact of community division result accuracy.In order to prove the advantage of the inventive method, the baseline network Zhong Liangge community scale (community's number is respectively between [10,50] and [20,100]) choosing 1000 nodes being similar to micro blog network herein carries out simulated experiment.Fig. 2 adopts the inventive method and label propagation algorithm to carry out NMI value accuracy Experimental comparison, when getting a specific μ value, algorithm of the present invention and label propagation algorithm being run 1000 times respectively, calculating its average N MI value.Can find out in figure that the NMI value of algorithm of the present invention is totally greater than label propagation algorithm.Therefore visible, the accuracy of the inventive method is better than label propagation algorithm.In same Fig. 4, in order to prove the broad applicability of algorithm further, when when community, number is taken at [20,100] interval, the order of accuarcy that the inventive method divides community is also better than label propagation algorithm.In Fig. 3 and Fig. 5, the NMI variance yields of the inventive method is totally better than label propagation algorithm, shows that the quality being divided community by the inventive method is stablized than label propagation algorithm.Fig. 6 and Fig. 8 is respectively when community's number is [10,50] and [20,100] time in scope (Δ μ=0.0125), the modularity Q changing value curve of the inventive method in effect comparatively significantly interval, and contrast with label propagation algorithm.Result shows in this interval, and the Q module degree of the inventive method is also better than traditional label propagation algorithm, illustrates that the quality of the inventive method division community is also better.Fig. 7 and Fig. 9 is the variance calculated value curve of above modularity Q value, the variance result of the inventive method is overall less, conclusion proves that the stability of the inventive method has had significant improvement on label propagation algorithm basis, and the inventive method does not need the priori of community's number, and to network structure self-adaptation.To sum up, the method makes the performance such as the accuracy of community discovery algorithm, stability, division quality is upgraded, and effectively can excavate the community structure in social networks, can be applicable to data mining and the field of information processing of multiple varying number scale.

The foregoing is only preferred embodiment of the present invention, all carry out in invention jurisdictions mandate limited range change, amendment, all belong to protection scope of the present invention.

Claims (5)

1., based on a community network group dividing method for limit convergence factor, it is characterized in that, said method comprising the steps of:

Steps A: read social network data, constructing with social network user is node, and customer relationship is the social network diagram on limit;

Step B: vertex ticks: be the label value that each user node Random assignment one is unique, as the mark of community belonging to it;

Step C: preliminary community divides: carry out iteration renewal to the label on all summits in figure, after each iteration, the label value of node is updated to the label value that in the label of its adjacent node, quantity is maximum;

Step D: community divides refinement: if when having the quantity of multiple label value to be all maximal value, calculate the limit convergence factor on limit between node to be updated and adjacent node, the neighbor node label that limit convergence factor is large is preferentially propagated by selection; After several times iteration, the label variations in each user node neighbours tends towards stability;

Step e: all nodes with same label are classified as a community.

2. a kind of community network group dividing method based on limit convergence factor according to claim 1, is characterized in that,

In above-mentioned steps B, be the label value that each user node Random assignment one is unique, i.e. C _n=L _n, C _nrepresent community belonging to node n, L _nrepresent the label value of node n.

3. a kind of community network group dividing method based on limit convergence factor according to claim 1, is characterized in that,

In above-mentioned steps C, the label value detailed process label value of node being updated to quantity in the label of its adjacent node maximum is: social network diagram is abstracted into a simple non-directed graph G (N, E), wherein, N represents the set of node, and E represents the set on limit; W _nmrepresent the weight on the limit connecting n, m node, n, m ∈ N, uses C _nrepresent community belonging to node n, N ^ln () represents that in the neighbor node of node n ∈ N, label value is the node set of 1, formula is as follows:

。

4. a kind of community network group dividing method based on limit convergence factor according to claim 1, is characterized in that:

In above-mentioned steps D, so-called limit convergence factor, represents the aggregation extent of two nodes of fillet, its value is larger, the strength of joint representing two nodes that this edge connects is stronger, and illustrate that these two nodes are larger in the possibility of same community, concrete definition rule is as follows:

Suppose there is a limit E _ij, its summit is i and j, if wonder in network that how much other whether there is and have node k and i, j all adjacent, namely there is two other limit E _jk, E _ik, E _ijform three square rings (limit number is the closed path of 3); If three square ring comprise the limit that connects different community, then a certain bar in another two limits in this three square ring still connects the possibility of Liang Ge community will be very large; Therefore, the limit convergence factor on a limit is defined as the three square ring proportions comprising this limit:

Wherein, k _i, k _jthe degree of representation node i and j respectively, z _ijrepresent the actual leg-of-mutton number comprising this limit in network, the denominator in formula represents the triangle number of the maximum possible comprising this limit.

5. a kind of community network group dividing method based on limit convergence factor according to claim 1, is characterized in that:

In described step D, stopping criterion for iteration is that social networks reaches balance, and it is termination of iterations that number of tags no longer changes.