CN103838803A - Social network community discovery method based on node Jaccard similarity - Google Patents
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Abstract
The invention discloses a social network community discovery method based on node Jaccard similarity. The method includes the steps that network data are preprocessed; according to a Jaccard similarity algorithm, the similarity of each pair of nodes is calculated; each node is regarded as a community initially; communities with the highest similarity are clustered; calculated communities with the highest similarity are clustered again according to the obtained communities till no community can be clustered in a network. Through calculation of the Jaccard similarity among the community nodes, a thought of hierarchical clustering is adopted for community division, and the social network community discovery method has the advantages that computer processing is easy and flexible through the method; in social networking calculation, the network communities needed by a user can be accurately discovered.
Description
technical field
The invention discloses a kind of social networks Combo discovering method based on node Jaccard similarity, belong to complex network technology, specifically a kind of community discovery technology of social networks.
Background technology
In recent years, the development of social networks was like a raging fire, and external well-known social network sites is as Facebook, Twitter and Google+ etc., and domestic have Renren Network, friend QQ to net etc.In a sense, social networks is the one mapping of real network.Research finds that a lot of real networks have community structure, by analyzing, can find the interested corporations of user according to user's request.People have done considerable research work to the corporations' partitioning algorithm in network now, have become one of current important subject research field.
In the time of research corporations partitioning algorithm, conventionally network is described with figure, the figure G=(V, E) being made up of node set V and limit set E can represent a network.It is as follows that conclusion figure is cut apart the algorithm of studying and grow up:
Kernighan-Lin algorithm is a kind of dichotomy based on greedy algorithm principle.Its ultimate principle is: define a gain function Q, Q be Liang Ge corporations inside limit number be connected the poor of limit number between Liang Ge corporations, find and make the maximum division methods of Q value afterwards.KL algorithm only adopts best candidate solution, and refusal is accepted all poor candidate solutions, and what therefore looked for is locally optimal solution rather than globally optimal solution.In addition the limitation of this dichotomy maximum is to know in advance the number of corporations and the scale of corporations, with preferably initial community structure of priori generation; This algorithm is very responsive to its initial solution, and bad initial solution often causes restraining slowly and poor final solution.KL is difficult to be applied in the real network analysis of the network size of not learning in advance as can be seen here.
Spectral bisection method based on Laplace proper value of matrix is employed at first in computer graphical is cut apart, and why it has good division effect in figure is cut apart, and is because the mathematical theory foundation take tight is as instructing.Its basic thought is: based on a symmetric matrix L that non-directed graph G is corresponding, determine the division of network according to different characteristic vector corresponding to its different characteristic value.From analyzing: can first it be divided into 2 corporations according to the little eigenwert of second of Laplace matrix corresponding to network in complex network is divided, again each corporations iteration is divided, obtain actual network until divide, in this iterative process, often occur wrong division again, effect is unsatisfactory; Spectral bisection method can only be divided network equally at every turn, if a network exists multiple corporations, just must antithetical phrase corporations repeatedly repeat to divide, but repeatedly divides and must depend on the correctness of dividing for the first time; Analysis of Complex network is more consuming time; So being not suitable for many corporations or multinode, this algorithm there is the complex network of ambiguity.
The algorithm developing based on hierarchical clustering has a lot, and this class algorithm is mainly divided into again two classes:
(1) solidifying clustering algorithm, this algorithm is from bottom to top, its thought is to be first independent corporations by the each node division in network, then based on corporations' polymeric rule, different little corporations is aggregated into larger corporations, until meet the demands; (2) division class methods, this algorithm is top-down, its thought is first whole network to be regarded as to corporations, then according to corporations' division rule, ceaselessly large corporations is divided into less corporations.
GN algorithm is a community discovery algorithm based on limit betweenness, is typical splitting method.The ultimate principle of GN algorithm is from network, progressively to remove the limit of betweenness maximum.The basic step of GN algorithm is as follows:
Step 1: the limit betweenness on all limits in calculation of complex network;
Step 2: all limit betweenness remove the highest limit of betweenness, limit in comparing cell;
Step 3: repeated execution of steps 1 and 2, until each node is exactly independently corporations.
The shortcoming that before although GN algorithm has overcome, algorithm only can two points, the definition of neither one amount, it is just most suitable at last that the corporations that can not judge network decompose any degree; And it is consuming time long to ask for this important step of limit betweenness, after removing the limit that limit betweenness is the highest, all to recalculate the limit betweenness of network at every turn.
Newman fast algorithm is a kind of typical agglomerative algorithm.Newman fast algorithm has been used for reference the thought of hierarchical clustering algorithm, based on coordinating to mix the standard that has defined a measurement network division quality, degree module.First algorithm is corporations by all node initializing in network, and when initial, corporations only comprise a node, in addition
kindividual corporations form
krank square formation
e=(
e ij ) be initialized as:
Wherein,
---nodes
degree;
Definition module degree
qincrement:
Algorithm, in the time carrying out corporations' merging, all selects to make the Liang Ge corporations of modularity increment maximum to carry out polymerization at every turn.After each polymerization, upgrade matrix
ein element, then select make the Liang Ge corporations of modularity increment maximum carry out polymerization, repeat above-mentioned steps until all corporations are all merged into corporations.Although this algorithm can better be found the community structure existing in real network, and do not need to know the number of corporations and the size of each corporations, due to consuming time large, the clearing amount of limit betweenness is large, and time complexity is O (n
3), therefore it is only suitable for medium scale network.
Summary of the invention
The method and system of a kind of social networks community discovery based on node Jaccard similarity provided by the invention, the method can be processed complex network, passes through simply, effectively calculates in computation process, and successively polymerization, finds corporations comparatively accurately.
For achieving the above object, the technical solution used in the present invention is as follows:
Based on a social networks Combo discovering method for node Jaccard similarity, comprise the following steps:
Step 1: social network data is carried out to pre-service, comprising: the user in social networks is abstracted into the node in network, obtains the set that comprises that all nodes form, the set that between two nodes, limit forms;
Step 2: the Jaccard similarity that calculates every two nodes in described social networks according to the pretreated result of step 1 by the computing method of Jaccard similarity;
The Jaccard similarity calculating method of described two nodes is as follows:
2-1 particularly, calculates the Jaccard similarity of arbitrary node i and node j in social network data: obtain first respectively with node i or interconnective each node of node j and comprise node i or the set of the node of j itself, both having gathered Vi or gathered Vj;
The Jaccard similarity of 2-2 computing node i and node j: set Vi and the common factor of Vj and the ratio of union, i.e. SIM (Vi, Vj)=(Vi ∩ Vj)/(Vi ∪ Vj);
Step 3: according to the similarity of all nodes of step 1 gained and every pair of node of step 2 gained, form a node similarity matrix;
Step 4: select described in step 3 the polymerization of carrying out of similarity maximum in node similarity matrix, obtain thus new corporations;
Step 5: calculate the Jaccard similarity between described social network data Zhong Liangge corporations;
Jaccard similarity calculating method between described Liang Ge corporations is as follows:
5-1 particularly, calculates in social network data the Jaccard similarity of the k of corporations and the l of corporations arbitrarily: first obtain from the arbitrary node m of the k of corporations with from the arbitrary node n of the l of corporations;
5-2 as described in the method computing node m of step 2 and the Jaccard similarity of node n;
5-3 repeats 5-1 step to 5-2 step and calculates the right similarity of all nodes from the k of corporations and the l of corporations composition respectively;
Every pair of node similarity of the k of corporations that 5-4 draws according to step 5-3 and the l of corporations is also obtained mean value according to result, the Jaccard similarity between Ji Liangge corporations;
Step 6: calculate the Jaccard similarity between all corporations in social network data according to the method for described step 5;
Step 7: according to the result of corporations in described social network data and the calculating of described step 6, form corporations' similarity matrix of each corporations in network;
Step 8: carry out polymerization according to the corporations of similarity maximum in corporations' similarity matrix described in step 7, form new corporations;
Step 9: repeating step five is to step 8, until whole network polymerization becomes corporations.
Wherein said step 3 obtains after told node similarity matrix, is corporations by each node initializing in corporations' network data; Jaccard similarity between Liang Ge corporations, the node that in described step 5,5-1 or 5-3 need obtain is to must be respectively from required Liang Ge corporations; Described social network data is carried out to pre-service, can obtain an adjacency matrix, the element in described adjacency matrix only has 1 and 0,1 to represent that the node of row and column representative is connected, and 0 represents that the node of row and column representative is not connected.
Compared with prior art the invention has the beneficial effects as follows:
Design object of the present invention is to find the community structure that is made up of user in social networks, find the corporations of the employee's composition that belongs to same company in social networks as excavated, belong to the corporations of classmate's formation of collective of same class, the corporations that same club member forms.Among social networks is mapped to network, then carry out corporations' division, can effectively divide the community structure in social networks; This method is also indifferent to the weight on limit or whether oriented, so the scope of application is wider; The similarity that the present invention is based on node is carried out corporations' division, and the accuracy rate that successively cluster is divided corporations is higher.
Accompanying drawing explanation
Fig. 1 is group dividing method of the present invention schematic network structure in an example;
Fig. 2 is the adjacency matrix of network in example;
Fig. 3 is the Jaccard similarity matrix between all nodes in network in example;
Fig. 4 is the corporations' division result after polymerization for the first time in example;
Fig. 5 is the corporations' similarity matrix after polymerization for the first time in example;
Fig. 6 is the corporations' division result after polymerization for the second time in example;
Dendrogram in Tu7Shi network corporations partition process.
Embodiment
For the present invention can be become apparent more, below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation:
A specific embodiment of the Combo discovering method that the present invention proposes, this example is based on an imaginary social networks.Suppose to exist such social networks: have 8 users, be respectively A, B, C, D, E, F, G and H, wherein A and B, C, D have friends, B and A, C, D have friends, and C and A, B, D have friends, and D and A, B, C, E have friends, E and D, F, G, H have friends, F and E, G, H have friends, and G and E, F, H have friends, and H and E, F, G have friends.
User in social networks is corresponded to the node in network, A, B, C, D, E, F, G and H are corresponded to respectively to 1,2,3,4,5,6,7 and 8, obtain node set V={1,2,3,4,5,6,7,8}.According to the limit in the friends generating network between node, after being processed by the step 1 of this algorithm, this social networks can obtain corresponding network, as shown in Figure 1.Can obtain this social networks adjacency matrix as shown in Figure 2 by above-mentioned cyberrelationship.
According to adjacency matrix, the right similarity of all nodes in computational grid.While adopting the similarity of Jaccard measuring similarity node i and j, by v
ibe designated as a set, set-inclusion with interconnective each node of node i and node i self, as v
1={ 1,2,3,4}.Now, set of computations v
iand v
jbetween Jaccard similarity can calculate the Jaccard similarity between node i and node j.Can obtain similarity matrix as Fig. 3 by the similarity of every pair of node.
Be 8 different corporations by 8 node initializing in this network, each corporations comprise a node, and corporations are numbered c1, c2 ..., c8, the matrix shown in Fig. 3 is also the similarity matrix of these 8 corporations.As seen from Figure 3, the similarity between the c1 of corporations, c2 and c3 is 1, and the similarity between the c6 of corporations, c7 and c8 is 1, be maximal value, therefore, the c1 of corporations, c2 and c3 are aggregated into a c9 of Ge Xin corporations, the c6 of corporations, c7 and c8 are aggregated into a new class c10.Polymerization result as shown in Figure 4 for the first time.
Now network is polymerized to 4 corporations, has calculated the Jaccard similarity between these four corporations, can obtain four similarity matrixs between corporations as shown in Figure 5.
Analyze the similarity matrix Fig. 5 of corporations, can find out that between the c4 of corporations and c9, similarity is 0.8, the similarity of the c5 of corporations and c10 is 0.8, their similarity is maximum, therefore, the c4 of corporations and c9 are polymerized to the new c11 of corporations, the c5 of corporations and c10 are polymerized to the c12 of corporations, the result after polymerization as shown in Figure 6.
After polymerization for the second time, in whole network, only had two interconnective corporations, therefore finally the c11 of Liang Ge corporations and c12 have been polymerized to a c13 of corporations, the dendrogram generating in algorithm polymerization process as shown in Figure 7.
Dotted line position cutting dendrogram from figure, now just corresponding two community structures, i.e. c11={1,2,3,4} and c12={5,6,7,8}.
Claims (4)
1. the social networks Combo discovering method based on node Jaccard similarity, comprises the following steps:
Step 1: social network data is carried out to pre-service, comprising: the user in social networks is abstracted into the node in network, obtains the set that comprises that all nodes form, the set that between two nodes, limit forms;
Step 2: the Jaccard similarity that calculates every two nodes in described social networks according to the pretreated result of step 1 by the computing method of Jaccard similarity;
The Jaccard similarity calculating method of described two nodes is as follows;
2-1 particularly, calculates the Jaccard similarity of arbitrary node i and node j in social network data: obtain first respectively with node i or interconnective each node of node j and comprise node i or the set of the node of j itself, both having gathered Vi or gathered Vj;
The Jaccard similarity of 2-2 computing node i and node j: set Vi and the common factor of Vj and the ratio of union, i.e. SIM (Vi, Vj)=(Vi ∩ Vj)/(Vi ∪ Vj);
Step 3: according to the similarity of all nodes of step 1 gained and every pair of node of step 2 gained, form a node similarity matrix;
Step 4: select described in step 3 the polymerization of carrying out of similarity maximum in node similarity matrix, obtain thus new corporations;
Step 5: calculate the Jaccard similarity between described social network data Zhong Liangge corporations;
Jaccard similarity calculating method between described Liang Ge corporations is as follows:
5-1 particularly, calculates in social network data the Jaccard similarity of the k of corporations and the l of corporations arbitrarily: first obtain from the arbitrary node m of the k of corporations with from the arbitrary node n of the l of corporations;
5-2 as described in the method computing node m of step 2 and the Jaccard similarity of node n;
5-3 repeats 5-1 step to 5-2 step and calculates the right similarity of all nodes from the k of corporations and the l of corporations composition respectively;
Every pair of node similarity of the k of corporations that 5-4 draws according to step 5-3 and the l of corporations is also obtained mean value according to result, the Jaccard similarity between Ji Liangge corporations;
Step 6: calculate the Jaccard similarity between all corporations in social network data according to the method for described step 5;
Step 7: according to the result of corporations in described social network data and the calculating of described step 6, form corporations' similarity matrix of each corporations in network;
Step 8: carry out polymerization according to the corporations of similarity maximum in corporations' similarity matrix described in step 7, form new corporations;
Step 9: repeating step five is to step 8, until whole network polymerization becomes corporations.
2. a kind of social networks Combo discovering method based on node Jaccard similarity according to claim 1, its feature comprises: described step 3 obtains after told node similarity matrix, is corporations by each node initializing in corporations' network data.
3. a kind of social networks Combo discovering method based on node Jaccard similarity of telling according to claim 1, its feature comprises: described social network data is carried out to pre-service, can obtain an adjacency matrix, element in described adjacency matrix only has 1 and 0,1 represents that the node of row and column representative is connected, and 0 represents that the node of row and column representative is not connected.
4. a kind of social networks Combo discovering method based on node Jaccard similarity according to claim 1, its feature comprises: the Jaccard similarity between Liang Ge corporations, the node that in described step 5,5-1 or 5-3 need obtain is to must be respectively from required Liang Ge corporations.
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