CN104657434B - A kind of social network structure construction method - Google Patents
A kind of social network structure construction method Download PDFInfo
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Abstract
The invention discloses a kind of social network structure construction method.This method is：1) the weighted links matrix and the user property matrix F of the social networks of interbehavior between the social networks graph model G=(V, L) based on social networks to be built, acquisition user；2) weighted links matrix and user property matrix are merged, builds an integrated information matrix N；3) it is right according to integrated information matrix N | | W | |0+ λ rank (W) seek minimum, obtain the link strength matrix W of the social networks；Minimum constraints is N=NW, diag (W)=0, W >=0；4) the link strength matrix W is obtained into G=(V, L as the weight information of side collection L in the social networks graph modelW), construct the network structure of the social networks.This method can be realized to the integrally-built modeling of social networks, so that true, the reliable measurement of correlation between any user in social networks is obtained, and solution efficiency is high.
Description
Technical field
The present invention relates to a kind of social network structure construction method, belong to technical field of software engineering.
Background technology
In recent years, with the drastically expansion of cyberspace, various informative social media is continued to bring out.Daily have number with
The user of ten million meter is gathered in (bibliography in miscellaneous social networks：D.Horowitz and S.D.Kamvar,
“The anatomy of a large-scale social search engine,”In Proc.of the 19th
International Conference on WorldWideWeb,2010,pp.431–440.).Social networks is developed rapidly
Layout enriches daily life, and there is provided colourful interactive medium.As content, user mutual and
The combination of Web2.0 technologies, social networks turns into carrying and maintains the important tie of interpersonal correlation.
Social networks generally represents that form is with graph model：G=(V, L), wherein set of node V (| V |=n) correspond to by n
The set that individual user is constituted, side collection L corresponds to the set (bibliography linked between user：W.Nooy,“Graph
theoretical approaches to social network analysis,”in Computational
Complexity:Theory,Techniques,and Applications,Springer,2012,pp.2864–2877.).It is logical
Cross opposite side collection L and be assigned to corresponding weight, form weighted links, can easily portray the correlation between user；Weight chain
Conventional adjacency matrix is connected to be expressed as：A∈Rn×n, each element aij∈ A represent user viAnd vj(vi,vj∈ V) between phase
Mutual relation (bibliography：J.Leskovec,K.J.Lang and M.Mahoney,“Empirical comparison of
algorithms for network community detection,”In Proc.of the 19th International
Conference on World Wide Web,2010,pp.631–640.).Two users in given social networks, can be with
Set out from different perspectives and describe and portray the correlation between user, for example：Whether certain user is indicated with " 0-1 " two-value data
Good friend or bean vermicelli for another user, with integer value data record user to the comment number of another user, reprint number, etc..
Corresponding to different customer relationships, the weight assignment method of weighted links matrix A also has diversity：Both can be by weight assignment
It whether there is direct correlation (good friend, bean vermicelli etc.) between user to represent for " 0-1 " two-value data, can also be by weight assignment
For integer Value Data to represent user between the interaction frequency (comment number, forwarding number etc.).As can be seen here, handed over from different user
Mutual behavior is set out, and can obtain a series of different weighted links matrix As1,A2,...,Ak, reflection of setting out from different perspectives respectively
Correlation between user.
Traditional social networks link strength computational methods are directly based upon above-mentioned weighted links matrix and obtained, and are substantially pair
The statistics of user interaction activity in original social networks, therefore it is referred to as " link strength based on statistics ".
Although traditional social networks link strength computational methods based on statistics are simple, its reliability, which lacks, protects
Card.
(1) link strength based on statistics is substantially directed to the simple of user mutual behavior in original social networks
Statistics and record, can not as between user correlation it is true, objectively respond and measure, link strength is related to user
Property directly has no positive connection.For example, the good friend user linked with certain user by weight " 1 ", although weight is all " 1 ", but
The correlation that it is not represented with the user is identical；For another example, comment on or reprint the more users of certain user's number of times and differ
It is fixed closer with the customer relationship.
(2) link strength based on statistics does not have completeness, and this method is only capable of in record data " observing " use
Family interactive information, intelligentized deduction and estimation can not be then carried out for the information for lacking or not yet getting；In other words, it is based on
The link strength of statistics can not effectively estimate the correlation between any user, so as to can not also describe social network structure
Overall picture.
The content of the invention
It is an object of the invention to provide a kind of social network structure construction method, wherein link strength estimation problem is determined
Justice, by organically blending for different information, integrated information matrix is learnt using automatic mode to optimize matrix reconstruction problem
The expression of sparse low-rank, realize to the integrally-built modeling of social networks, so as to obtain in social networks phase between any user
True, the reliable measurement of mutual relation.
Link strength estimation problem is defined as optimizing matrix reconstruction problem by the method the 1st, provided, utilizes automation side
The sparse low-rank expression of calligraphy learning matrix, is realized to the integrally-built modeling of social networks, so as to obtain any in social networks
True, the reliable measurement of correlation between user.
2nd, the method provided will be organically combined from the information of user mutual behavior and user's self attributes,
Holistic modeling under unified method frame, so as to realize the complementary enhancing of different information.
3rd, the method provided realizes the Efficient Solution of optimization problem using the mode of iteration alternative optimization, it is ensured that each
Step optimization has analytic solutions, so as to effectively improve solution efficiency, reduction computational complexity.
The technical scheme is that：
A kind of social network structure construction method, its step is：
1) interbehavior adds between the social networks graph model G=(V, L) based on social networks to be built, acquisition user
Weigh chain matrice A1,A2,...,AkAnd the user property matrix F of the social networks；Wherein, V is set of node, and L is side collection, Ak
Represent the weighted links matrix corresponding to kth kind user mutual behavior；
2) the weighted links matrix and the user property matrix are merged, builds an integrated information matrix N；
3) it is right according to the integrated information matrix N | | W | |0+ λ rank (W) seek minimum, obtain the link of the social networks
Intensity matrix W；Minimum constraints be N=NW, diag (W)=0, W >=0, | | | |0For L0 norms, rank () is to ask
The function of rank of matrix is taken, λ is to adjust the openness weight with low-rank of matrix W, and diag () is to ask for matrix diagonals line element
Function；
4) using the link strength matrix W as side collection L in the social networks graph model weight information, obtain G=(V,
LW), construct the network structure of the social networks.
Further, it is described according to the integrated information matrix N, right | | W | |0+ λ rank (W) seek minimum, obtain the social activity
The method of the link strength matrix W of network is：A reconstructed error variable E is introduced, will be right | | W | |0+ λ rank (W) ask minimum to turn
It is changed to pairSolve, minimum constraints is N=NW+E, W=W1, W=W2,diag(W)
=0, W >=0, | | | |1For L1 norms, | | | |*For Nuclear norms, λ1And λ2It is that adjustment matrix W is openness with low-rank
Weight.
Further, with augmented vector approach pairSolve, obtain the chain
Meet intensity matrix W.
Further, it is excellent in iteration using the method for alternative optimization in the augmented vector approach solution procedure
Each target variable is updated successively during change, other variables are considered as constant when often updating a variable.
Further, the method for the alternative optimization is：In iterative process each time, pass through optimal beggar respectively first
Problem solving method, updates matrix W1、W2And E；Then by optimizing subproblem method for solving, according to matrix W1、W2With E more
New W；Finally according to matrix W1、W2, E and W update Lagrange multiplier and parameter in augmented vector approach；Circulation changes
In generation, is until convergence.
Further, the integrated information matrix
Main contents of the present invention include：
1st, integrated information matrix is built
As it was noted above, based on social networks graph model G=(V, L), from different user mutual behaviors (such as mutual powder, comment,
Reprint etc.) set out, a series of different weighted links matrix As can be obtained1,A2,...,Ak∈Rn×n, it is anti-from different perspectives respectively
The correlation reflected between user, wherein k represent the quantity of user mutual behavior, AiRepresent to correspond to i-th kind of user mutual row
For weighted links matrix.In addition, from user's self attributes (such as sex, age, occupation, hobby), can be with structure
Build user property matrix：F∈Rm×n, wherein m is the dimension of user property characteristic vector, and n is total number of users.
In order to more effectively estimate social networks link strength, it is necessary to above- mentioned information combines, with more
Comprehensively obtain the correlation between user.
Weighted links matrix and user property matrix are combined by this method, build integrated information matrix：N∈R(n ×k+m)×n, formulation is expressed as follows：
Based on integrated information matrix N, the purpose of this method is to ask for link strength matrix W ∈ Rn×n, as in social networks
True, the reliable measurement of correlation between any user.
2nd, link strength estimation problem is modeled
According to homogeney principle, correlation comes from similitude, and a reliable link strength should be able to effectively reflect user
Between correlation so that the various information of user can effectively be expressed by the combination of the strong neighbour user of relevance.
Link strength estimation problem is modeled as the optimization reconstruction of integrated information matrix by this method, by learning automatically
The sparse low-rank expression of integrated information matrix is practised, effective estimation of social networks link strength is realized.The foundation of problem modeling is such as
Under：
(1) according to social networks homogeney, user's integrated information can pass through other users integrated information associated therewith
Linear combination is expressed.Therefore, integrated information matrix N can be weighed by the product of its own and link strength matrix W
Structure.
(2) in social networks, user is merely capable of keeping close relationship (i.e. more notable with a limited number of user
Relevance), and with most of other users be not present notable relevance.Therefore, the only relative only a few of link strength matrix W
Nonzero element, in other words, link strength matrix W have openness.
(3) can mutually it be expressed by linear combination between associated user, therefore, as a kind of special user property,
It is related (dependent) between the column vector of link strength matrix W.According to Matrix Properties, link strength matrix W has low-rank
Property.
According to above-mentioned analysis, link strength estimation problem can formulate and be expressed as optimization problem：
Wherein, object functionIn：||·||0It is the openness measurement of matrix for L0 norms；
Rank () is the function for asking for rank of matrix；λ is to adjust the openness weight parameter with low-rank of matrix W, can by technical staff
To set as needed；To object function | | W | |0+ λ rank (W) seek minimum, to ensure the openness of link strength matrix W
With low-rank.In constraints s.t.N=NW, diag (W)=0, W >=0：" s.t. " is the english abbreviation of constraints；N=NW
Represent that integrated information matrix N can be reconstructed by the product of its own and link strength matrix W；Diag () is to ask for square
The function of battle array diagonal entry, present invention contemplates that the link strength between different user, and diagonal entry wiiRepresent to use
Family viWith the relation of its own, therefore 0 is set to.
In order to ensure in the feasible solution of optimization problem, formula, constraints N=NW can be by introducing reconstructed error
Mode carries out relaxation, so that optimization problem adjustment is as follows：
Wherein, λ1And λ2It is to adjust the openness weight parameter with low-rank of matrix W.
In matrix reconstruction formula (3) object function, Frobenius normsAlthough using simple, by noise disturbance shadow
Sound is larger.For the robustness of ensuring method, this method explicitly introduces reconstructed error variable E, and uses L1 norms | | | |1With
Influence of noise is reduced, so that optimization problem adjustment is as follows：
Due to L0 norms | | | |0Minimum with rank of matrix rank () is the difficult problem of NP-, defined in formula
Optimization problem not Direct Solution.This method carries out relaxation to formula, uses L1 norms | | | |1Instead of L0 norms, use
Nuclear norms | | | |*Instead of rank of matrix, to realize the convex relaxationization of optimization problem, so that optimization problem adjustment is such as
Under：
Optimization problem defined in formula includes the minimum of L1 norms and Nuclear norms, and although object function is
Convex function but Non-smooth surface, therefore still can not direct solution.In order to solve the above problems, this method is further introduced into slack variable
With corresponding constraints so that optimization problem adjustment it is as follows：
3rd, duty Optimization
By a series of deformation process, optimization problem can be asked with augmented vector approach defined in formula
Solution, formulation is expressed as follows：
Wherein, Y1、Y2And Y3It is Lagrange multiplier, μ1、μ2And μ3It is positive parameter,<,>It is matrix inner products.
In order to improve solution efficiency, reduction computational complexity, the method that this method provides alternative optimization, in iteration optimization mistake
Each target variable is updated successively in journey, other variables are considered as constant when often updating a variable.
Duty Optimization updates including following 5 step：
(1) by optimizing subproblem, W is updated1：
Subproblem has analytic solutions, and form is as follows：
Wherein,
Sλ(X)=sign (X) max (X |-λ, 0) formula (10)
(2) by optimizing subproblem, W is updated2：
Subproblem has analytic solutions, and form is as follows：
Wherein,
Jλ(X)=USλ(S)VTFormula (13)
Wherein, USVTThe SVD that=X is matrix X is decomposed.
(3) by optimizing subproblem, E is updated：
Subproblem has analytic solutions, and form is as follows：
(4) by optimizing subproblem, W is updated：
Subproblem has analytic solutions, and form is as follows：
W*=(μ1I+μ2I+μ3NTN)-1G. formula (17)
Wherein, I represents unit matrix,
For constraints diag (W)=0, W >=0, post-process as follows：
(5) Y is updated1、Y2、Y3And μ1、μ2、μ3
By more than loop iteration 5 step renewal processes until augmented vector approach is restrained, you can obtain link strong
Spend matrix W ∈ Rn×n。
Social networks graph model G=(V, L are used as with WW) in side collection L weight information, can construct in social networks
The structural information of actualization, panorama, so as to obtain the overall picture of social networks.
Compared with prior art, the positive effect of the present invention is：
Social networks link strength method of estimation provided by the present invention, effective integration derives from user mutual behavior and use
The information of family self attributes, realizes the complementary enhancing of much information, link strength estimation problem is defined as into integrated information matrix
Optimization reconstruction, using automatic mode learn integrated information matrix sparse low-rank express, and using iteration alternating
The mode of optimization realizes the Efficient Solution of optimization problem, realizes integrally-built to social networks under unified approach framework build
Mould, so as to provide a kind of intelligent, efficient solution party for true, the reliable measurement of customer relationship in extensive social networks
Case.
Brief description of the drawings
Accompanying drawing is flow chart of the method for the present invention.
Embodiment
The principle and feature of the present invention are described below in conjunction with accompanying drawing, the given examples are served only to explain the present invention, and
It is non-to be used to limit the scope of the present invention.
Example social networks link strength method of estimation
The social networks link strength method of estimation flow that the present invention is provided is as follows：
By taking microblog data social network structure structure as an example：
Assuming that user's total amount is 100, then social networks graph model G=(V, L in microblog data) Point Set V correspond to should
The set of 100 users, the set when collection L corresponds to 100 users between any two, in order to build social network structure,
Need to calculate the link strength in each edge, to reflect the correlation between user, L subscript "" represent side collection L power
Weight is unknown, is to build the key that social network structure needs to solve.
Input：From 3 kinds of user mutual behaviors, (mutual powder, comment, reprinting) can obtain 3 different weighted links
Matrix：A1,A2,A3∈R100×100, the correlation reflected from different perspectives between user respectively；From user's self attributes (such as property
Not, age, occupation, hobby etc.) set out, user property matrix can be built：F∈R200×100, it is assumed herein that user property uses 200
The characteristic vector of dimension is represented；The condition of convergence could be arranged to solved link strength matrix：W∈R100×100In the r times and r
The L1 norm values of gained matrix difference are less than e after+1 iteration-10, i.e.,：||W(r+1)-W(r)||1＜ e-10。
Initialization：By weighted links matrix A1,A2,A3∈R100×100With user property matrix F ∈ R200×100It is combined,
Obtain integrated information matrix：N∈R500×100；For specification of variables initial value：E=W1=W2=W=Y1=Y2=Y3=0, μ1=μ2
=μ3=1.
Optimize：Loop iteration above-mentioned (1)-(5) step.
Output：The link strength matrix of optimization：W∈R100×100；Using W as side collection L weight, microblog data is constructed
Social networks graph model：G=(V, LW)。
Claims (5)
1. a kind of social network structure construction method, its step is：
1) the social networks graph model G=(V, L) based on social networks to be built, obtains the weighting chain of interbehavior between user
Connect matrix A1,A2,...,AkAnd the user property matrix F of the social networks；Wherein, V is set of node, and L is side collection, AkRepresent
Corresponding to the weighted links matrix of kth kind user mutual behavior；
2) the weighted links matrix and the user property matrix are merged, builds an integrated information matrix N；
3) it is right according to the integrated information matrix N | | W | |0+ λ rank (W) seek minimum, obtain the link strength square of the social networks
Battle array W；Minimum constraints be N=NW, diag (W)=0, W >=0, | | | |0For L0 norms, rank () is to ask for matrix
The function of order, λ is to adjust the openness weight with low-rank of matrix W, and diag () is the function for asking for matrix diagonals line element；
4) the link strength matrix W is obtained into G=(V, L as the weight information of side collection L in the social networks graph modelW), structure
Build out the network structure of the social networks；
Wherein, it is right according to the integrated information matrix N | | W | |0+ λ rank (W) seek minimum, and the link for obtaining the social networks is strong
Degree matrix W method be：A reconstructed error variable E is introduced, will be right | | W | |0+ λ rank (W) ask minimum to be converted to pairSolve, minimum constraints is N=NW+E, W=W1, W=W2,diag(W)
=0, W >=0, | | | |1For L1 norms, | | | |*For Nuclear norms, λ1And λ2It is that adjustment matrix W is openness with low-rank
Weight.
2. the method as described in claim 1, it is characterised in that with augmented vector approach pair
Solve, obtain the link strength matrix W.
3. method as claimed in claim 2, it is characterised in that in the augmented vector approach solution procedure, is used
The method of alternative optimization, is updated successively in iterative optimization procedure to each target variable, often by it during one variable of renewal
Its variable is considered as constant.
4. method as claimed in claim 3, it is characterised in that the method for the alternative optimization is：In iterative process each time
In, update matrix W by optimizing subproblem method for solving respectively first1、W2And E；Then solved by optimizing subproblem
Method, according to matrix W1、W2W is updated with E；Finally according to matrix W1、W2, E and W update drawing in augmented vector approach
Ge Lang multipliers and parameter；Loop iteration is until convergence.
5. the method as described in Claims 1-4 is any, it is characterised in that the integrated information matrix
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| CN105160546A (en) * | 2015-08-07 | 2015-12-16 | 北京思特奇信息技术股份有限公司 | Method and system for constructing and analyzing social network |
| CN106021290A (en) * | 2016-04-29 | 2016-10-12 | 中国科学院信息工程研究所 | Method for social network association excavation based on multi-scale geographic information |
| CN106022937B (en) * | 2016-05-27 | 2019-04-02 | 北京大学 | A kind of estimating method of social networks topological structure |
| CN107451255B (en) * | 2017-07-31 | 2020-05-19 | 陕西识代运筹信息科技股份有限公司 | User interest processing method and device based on attention relationship |
| CN107741953B (en) * | 2017-09-14 | 2020-01-21 | 平安科技（深圳）有限公司 | Method and device for matching realistic relationship of social platform user and readable storage medium |
| CN109446713B (en) * | 2018-11-14 | 2020-04-03 | 重庆理工大学 | Stability judgment method for extracted online social network data |
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