CN104657434B - A kind of social network structure construction method - Google Patents
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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 invention relates to a social network structure construction method, and belongs to the technical field of software engineering.
Background
In recent years, with the rapid expansion of network space, social media in diverse forms are emerging. Tens of millions of users are gathered In a wide variety of social networks each day (references: d.horowitz and s.d.kamvar, "The animal of large-scale social search engine," In proc.of The 19th international Conference on world wide web,2010, pp.431-440.). The rapid development layout of the social network enriches the daily life of people and provides a colorful interaction medium. As a combination of content, user interaction, and web2.0 technology, social networking becomes an important link to carry and maintain interpersonal relationships.
Social networks are generally represented by a graph model in the form G (V, L), where a node set V (V |) corresponds to a set of n users, an edge set L corresponds to a set of links between users (reference: w. nooy, "graphical Applications to social network analysis," in computational complexity: Theory, Techniques, and Applications, Springer,2012, pp.2864-2877.) by assigning corresponding weights to the set L to form weighted links, which can easily depict the relationships between users, and the weighted links are generally represented by an adjacency matrix a ∈ Rn×nEach element aij∈ A represents user viAnd vj(vi,vj∈ V) (reference: J.Leskovec, K.J.Lang and M.Mahoney, "actual compliance of network communication protection," In Proc.of the 19th International compliance on World Wide Web,2010, pp.631-640.). given two users In a social network, the interrelationship between the users can be described and characterized from different angles, e.g., whether a user is a fan or a fan of another user is indicated by "0-1" binary data, the number of comments, the number of reprints, etc. of a user to another user is indicated by integer data, etc. for different user relationships, the method of assigning weights to link matrix A also has diversity, i.e., assigning weights to "0-1" binary data to indicate whether there are direct associations between users (friends, fans, etc.), or assigning weights to integer data to different user relationships to indicate the number of comments, forwarding numbers, etc., whereby a series of interactions between users can be obtained from different interaction matrices1,A2,...,AkAnd reflecting the mutual relation among the users from different angles respectively.
The traditional social network link strength calculation method is directly obtained based on the weighted link matrix, is essentially statistics of user interaction activities in the original social network, and is called as 'statistical-based link strength'.
Although the traditional social network link strength calculation method based on statistics is simple, the reliability of the traditional social network link strength calculation method is lack of guarantee.
(1) The link strength based on statistics is directly derived from simple statistics and records of user interaction behaviors in an original social network in nature, and cannot be used as a real and objective reflection and measurement of the mutual relation between users, and the link strength is directly not necessarily connected with the relevance of the users. For example, friend users who are linked with a user by a weight of "1" are not all "1" in weight, but do not represent the same relevance to the user; for another example, users who comment on or reprint a user more often do not necessarily have a closer relationship to the user.
(2) The statistical-based link strength is not complete, the method can only record 'observed' user interaction information in data, and can not intelligently infer and estimate missing or unacquired information; in other words, the statistical-based link strength does not effectively estimate the interrelationships between any users, and thus does not describe the overall appearance of the social network structure.
Disclosure of Invention
The invention aims to provide a social network structure construction method, wherein a link strength estimation problem is defined as an optimization matrix reconstruction problem, and the modeling of the overall structure of the social network is realized by organically fusing different information and learning the sparse low-rank expression of a comprehensive information matrix by an automatic method, so that the real and reliable measurement of the mutual relation between any users in the social network is obtained.
1. The provided method defines the link strength estimation problem as an optimization matrix reconstruction problem, realizes modeling of the overall structure of the social network by utilizing an automatic method to learn the sparse low-rank expression of the matrix, and thus obtains the true and reliable measurement of the mutual relation between any users in the social network.
2. The provided method organically combines the information derived from the user interaction behavior and the user self attribute, and integrally models under a unified method framework, thereby realizing the complementary enhancement of different information.
3. The method provided by the invention realizes the efficient solution of the optimization problem by using an iterative alternate optimization mode, and ensures that each step of optimization has an analytic solution, thereby effectively improving the solution efficiency and reducing the operation complexity.
The technical scheme of the invention is as follows:
a social network structure construction method comprises the following steps:
1) obtaining a weighted link matrix A of interaction behaviors between users based on a social network graph model G (V, L) of a social network to be constructed1,A2,...,AkAnd a user attribute matrix F for the social network; wherein V is a node set, L is an edge set, AkRepresenting a weighted link matrix corresponding to the kth user interaction behavior;
2) combining the weighted link matrix and the user attribute matrix to construct a comprehensive information matrix N;
3) according to the comprehensive information matrix N, count | | | W | | count0Minimizing the + lambda rank (W) to obtain a link strength matrix W of the social network; the minimum constraint is N NW, diag (W) 0, W ≧ 0, | · | | ceiling0Is L0 norm, rank () is the function to find matrix rank, λ is the weight to adjust the sparsity and low rank of matrix W, diag () is the function to find diagonal elements of matrix;
4) taking the link strength matrix W as the weight information of the edge set L in the social network graph model to obtain G ═ V, LW) And constructing a network structure of the social network.
Further, the information matrix N may be used to count | | W | | calcei0The minimization is performed by + λ rank (W), and the method for obtaining the link strength matrix W of the social network comprises the following steps: introducing a reconstruction error variable E to count W | |0+ λ rank (W) minimizationIs converted into a pairSolving, the minimization constraint condition is N-NW + E, W-W1,W＝W2,diag(W)＝0,W≥0，||·||1Is L1 norm, | · | | non-woven*Is a Nuclear norm, λ1And λ2Is the weight for adjusting the sparsity and low rank of the matrix W.
Further, using the augmented Lagrange multiplier methodAnd solving to obtain the link strength matrix W.
Furthermore, in the solution process of the augmented Lagrange multiplier method, an alternating optimization method is adopted, each target variable is updated in sequence in the iterative optimization process, and other variables are regarded as constants when one variable is updated.
Further, the alternating optimization method comprises the following steps: in each iteration process, firstly, the matrix W is updated through an optimization subproblem solving method1、W2And E; then solving the problem through an optimization subproblem method according to the matrix W1、W2And E updating W; finally according to the matrix W1、W2E and W update Lagrange multipliers and parameters in the augmented Lagrange multiplier method; and (5) circularly iterating until convergence.
Further, the comprehensive information matrix
The main content of the invention comprises:
1. integrated information matrix construction
As described above, based on the social network graph model G ═ V, L, starting from different user interaction behaviors (such as mutual whitewashing, comment, reprinting, etc.), a series of different weighted link moments can be obtainedArray A1,A2,...,Ak∈Rn×nReflecting the interrelationship between the users from different angles respectively, wherein k represents the number of user interaction behaviors, AiIn addition to the weighted link matrix representing the corresponding i-th user interaction behavior, a user attribute matrix F ∈ R may be constructed based on the user's own attributes (e.g., gender, age, occupation, hobbies, etc.)m×nWhere m is the dimension of the user attribute feature vector and n is the total number of users.
In order to estimate the social network link strength more effectively, it is necessary to combine the above information organically to more fully acquire the mutual relationship between users.
The method combines the weighted link matrix and the user attribute matrix to construct a comprehensive information matrix N ∈ R(n ×k+m)×nThe formulation is as follows:
based on the comprehensive information matrix N, the method aims to obtain a link strength matrix W ∈ Rn×nAs a true, reliable measure of the interrelationship between any users in a social network.
2. Link strength estimation problem modeling
According to the principle of homogeneity, the correlation is derived from similarity, and a reliable link strength can effectively reflect the correlation between users, so that various information of the users can be effectively expressed by the combination of the neighboring users with strong correlation.
The method models the link strength estimation problem as the optimal reconstruction problem of the comprehensive information matrix, and realizes effective estimation of the link strength of the social network by automatically learning the sparse low-rank expression of the comprehensive information matrix. The basis for problem modeling is as follows:
(1) according to social network homogeneity, user integrated information can be expressed through linear combination with other user integrated information related to the user integrated information. Thus, the integrated information matrix N can be reconstructed by multiplying itself by the link strength matrix W.
(2) In a social network, a user can only maintain close relationships (i.e., more significant associations) with a limited number of users, while there are no significant associations with most other users. Therefore, the link strength matrix W has only a relatively few non-zero elements, in other words, the link strength matrix W has sparsity.
(3) The related users can be mutually expressed by linear combination, so that the column vectors of the link strength matrix W are related (non-independent) as a special user attribute. The link strength matrix W has low rank property according to the matrix characteristics.
From the above analysis, the link strength estimation problem can be formulated as an optimization problem as follows:
wherein the objective functionThe method comprises the following steps: i | · | purple wind0Is the L0 norm, which is a measure of the sparsity of the matrix; rank () is a function to find the matrix rank; λ is a weight parameter for adjusting the sparsity and low rank property of the matrix W, which can be set by a technician as required; to the target function | | W | | non-woven gas0The + λ rank (W) is minimized to ensure sparsity and low rank of the link strength matrix W. Constraint s.t.n ═ NW, diag (W) ═ 0, where W ≧ 0: "s.t." is an english abbreviation for constraint; n — NW denotes that the integrated information matrix N can be reconstructed by multiplying itself by the link strength matrix W; diag (-) is a function of the diagonal elements of the matrix, the invention takes into account the link strengths between different users, and the diagonal element wiiRepresenting a user viIn relation to itself, and thereforeIt is set to 0.
In order to ensure a feasible solution of the optimization problem, in the formula, the constraint N — NW can be relaxed by introducing a reconstruction error, so that the optimization problem is adjusted as follows:
wherein λ is1And λ2Is a weight parameter for adjusting the sparsity and low rank of the matrix W.
Frobenius norm in the objective function of the matrix reconstruction formula (3)Although simple to use, it is greatly affected by noise disturbance. In order to ensure the robustness of the method, the method explicitly introduces a reconstruction error variable E and uses an L1 norm | · | | non-calculation1To reduce the noise impact, the optimization problem is adjusted as follows:
because L0 norm | · | | non-woven0And the minimization of the matrix rank () is an NP-hard problem, the optimization problem defined by the formula is not directly solvable. The method relaxes the formula and adopts L1 norm | · | | non-conductive1Replacing the L0 norm with the Nuclear norm | | · | | non |*Instead of the matrix rank, convex relaxation of the optimization problem is achieved, whereby the optimization problem is adjusted as follows:
the optimization problem defined by the formula includes minimization of the L1 norm and the Nuclear norm, and the objective function is a convex function but not smooth and therefore still cannot be solved directly. In order to solve the above problem, the method further introduces a relaxation variable and a corresponding constraint condition, so that the optimization problem is adjusted as follows:
3. optimization problem solving
Through a series of deformation processes, the optimization problem defined by the formula can be solved by using an augmented Lagrange multiplier method, and the formula is expressed as follows:
wherein, Y1、Y2And Y3Is the Lagrange multiplier, mu1、μ2And mu3Is a positive parameter of the number of bits,<·，·>is the matrix inner product.
In order to improve the solving efficiency and reduce the operation complexity, the method provides an alternative optimization method, each target variable is sequentially updated in the iterative optimization process, and other variables are regarded as constants when one variable is updated.
The optimization problem solution includes the following 5-step update:
(1) updating W by optimizing sub-problems1：
The subproblem has an analytical solution, of the form:
wherein,
Sλ(X) ═ sign (X) · (X | - λ,0). formula (10)
(2) Updating W by optimizing sub-problems2：
The subproblem has an analytical solution, of the form:
wherein,
Jλ(X)＝USλ(S)VTequation (13)
Wherein, the USVTX is the SVD decomposition of matrix X.
(3) Updating E by optimizing the subproblem:
the subproblem has an analytical solution, of the form:
(4) updating W by optimizing the subproblem:
the subproblem has an analytical solution, of the form:
W*＝(μ1I+μ2I+μ3NTN)-1G. formula (17)
Wherein, I represents a unit array,
for the constraint condition diag (W) is 0, W is more than or equal to 0, the post-treatment is as follows:
(5) updating Y1、Y2、Y3And mu1、μ2、μ3
The link strength matrix W ∈ R can be obtained by circularly iterating the updating process of the 5 steps until the augmented Lagrange multiplier method is convergedn×n。
Using W as the social network graph model G ═ (V, L)W) The weight information of the edge set L can construct realistic and panoramic structural information in the social network, so that the overall appearance of the social network is obtained.
Compared with the prior art, the invention has the following positive effects:
the social network link strength estimation method provided by the invention effectively fuses information derived from user interaction behaviors and user attributes, realizes complementary enhancement of various information, defines the link strength estimation problem as an optimization reconstruction problem of a comprehensive information matrix, learns sparse low-rank expression of the comprehensive information matrix by using an automatic method, realizes efficient solution of the optimization problem by using an iterative alternative optimization mode, and realizes modeling of the overall structure of the social network under a unified method frame, thereby providing an intelligent and efficient solution for real and reliable measurement of user relationships in a large-scale social network.
Drawings
The attached figure is a flow chart of the method of the invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
Example social network link strength estimation method
The social network link strength estimation method provided by the invention comprises the following steps:
taking the construction of the social network structure of microblog data as an example:
assuming that the total amount of users in the microblog data is 100, the social network graph model G is (V, L)？) The midpoint set V corresponds to the set of 100 users, the edge set L corresponds to the set of edges between every two 100 users, in order to construct a social network structure, the link strength on each edge needs to be calculated to reflect the interrelation between the users, and the superscript of L? "the weight representing the edge set L is unknown, and is the key to solve for constructing the social network structure.
Inputting: starting from 3 user interaction behaviors (mutual power, comment and reprint), 3 different weighted link matrixes can be obtained: a. the1,A2,A3∈R100×100Reflecting the mutual relation between users from different angles, and constructing user attribute matrix F ∈ R from user's own attributes (such as sex, age, occupation, hobby, etc.)200×100Here, it is assumed that the user attribute is represented by a feature vector of 200 dimensions, and the convergence condition can be set to the solved link strength matrix W ∈ R100×100The L1 norm value of the resulting matrix difference after the r and r +1 iterations is less than e-10Namely: i W(r+1)-W(r)||1＜e-10。
Initialization: link the weights to the matrix A1,A2,A3∈R100×100And a user attribute matrix F ∈ R200×100Combined to obtain a comprehensive information matrix N ∈ R500×100(ii) a Setting initial values for variables: e ═ W1＝W2＝W＝Y1＝Y2＝Y3＝0,μ1＝μ2＝μ3＝1。
Optimizing: and (5) circularly iterating the steps (1) to (5).
Outputting an optimized link strength matrix W ∈ R100×100(ii) a And taking W as the weight of the edge set L to construct a microblog data social network graph model: g ═ V, LW)。
Claims (5)
1. A social network structure construction method comprises the following steps:
1) obtaining a weighted link matrix A of interaction behaviors between users based on a social network graph model G (V, L) of a social network to be constructed1,A2,...,AkAnd a user attribute matrix F for the social network; wherein V is a node set, L is an edge set, AkRepresenting a weighted link matrix corresponding to the kth user interaction behavior;
2) combining the weighted link matrix and the user attribute matrix to construct a comprehensive information matrix N;
3) according to the comprehensive information matrix N, count | | | W | | count0Minimizing the + lambda rank (W) to obtain a link strength matrix W of the social network; the minimum constraint is N NW, diag (W) 0, W ≧ 0, | · | | ceiling0Is L0 norm, rank () is the function to find matrix rank, λ is the weight to adjust the sparsity and low rank of matrix W, diag () is the function to find diagonal elements of matrix;
4) taking the link strength matrix W as the weight information of the edge set L in the social network graph model to obtain G ═ V, LW) Constructing a network structure of the social network;
wherein, according to the comprehensive information matrix N, counting | | | W | | ceiling0The minimization is performed by + λ rank (W), and the method for obtaining the link strength matrix W of the social network comprises the following steps: introducing a reconstruction error variable E to count W | |0The minimization of + λ rank (W) is converted into a pairSolving, the minimization constraint condition is N-NW + E, W-W1,W＝W2,diag(W)＝0,W≥0，||·||1Is L1 norm, | · | | non-woven*Is a Nuclear norm, λ1And λ2Is the weight for adjusting the sparsity and low rank of the matrix W.
2. The method of claim 1, wherein the pair of augmented lagrange multipliers is usedAnd solving to obtain the link strength matrix W.
3. The method according to claim 2, wherein in the augmented lagrange multiplier solution process, an alternating optimization method is adopted, each target variable is sequentially updated in an iterative optimization process, and each time one variable is updated, other variables are regarded as constants.
4. The method of claim 3, wherein the method of alternating optimization is: in each iteration process, firstly, the matrix W is updated through an optimization subproblem solving method1、W2And E; then solving the problem through an optimization subproblem method according to the matrix W1、W2And E updating W; finally according to the matrix W1、W2E and W update Lagrange multipliers and parameters in the augmented Lagrange multiplier method; and (5) circularly iterating until convergence.
5. The method of any of claims 1 to 4, wherein the integrated information matrix
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| 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 |
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