CN106997562A - The mapping method of the vertex classification of tape symbol network - Google Patents

Abstract

The invention discloses a kind of mapping method of the vertex classification of tape symbol network, label matrix Y is drawn according to labeled summit first；Obtain final preference matrix P, the transition matrix Q for needing to optimize, and the matrix w needed for grader；Q is fixed respectively^p,Qⁿ, P, three therein of w obtain Q^p,Qⁿ, P, w Optimized Iterative formula；According to obtained Optimized Iterative formula to Q^p,Qⁿ, P, w is iterated renewal simultaneously；According to the Q after iteration^p,Qⁿ, P, w optimal value makes prediction to the classification belonging to summit not labeled in tape symbol network；The mapping method iterative convergence speed of the present invention is fast, and accuracy rate is high.

Description

The mapping method of the vertex classification of tape symbol network

Technical field

The invention belongs to vertex classification method field in social networks, particularly a kind of vertex classification of tape symbol network Mapping method.

Background technology

With a series of rapid emergence of community network websites, such as Facebook, Twitter, LinkedI, Epinions Etc..In order to ensure the experience of user, substantial amounts of energy has all been put among the research of social mechanism.Traditional community network The main community network such as Facebook that only considered no symbol (symbol on the side i.e. in network is all for just) of analysis with MySpace, these networks can be turned into graph model, and its interior joint just represents user subject, and the side of positive Weight just represents reality With the presence or absence of relation and the importance size of this relation between body.Recently, to the research of the oriented community network of tape symbol Just progressively rise, in the community network of tape symbol, the relation between user both can be positive (to show the letter between user Appoint) or negative (showing that the relation between user is distrust).Such as, user can root in Epinions networks Determine to trust or distrust other users according to their evaluation, in Slashdot networks, this is primarily upon related to technology On the website of news, users can mutually click on according to the comment to article and (not liked as friend's (liking) or enemy Vigorously).The oriented community network of these tape symbols can be represented with asymmetric adjacency matrix, if element therein is 1, then the relation of the two inter-entity is just, if element is -1, then the relation for just illustrating the two inter-entity be it is negative, 0 Then represent missing.

From nearest some research work analysis, it is seen that the link born in network have than positive link more added with The surcharge of meaning.Such as, the minus strand of sub-fraction connects the forecasting accuracy that can improve that symbol is positive link, and improves The performance of commending system in social networks.Similarly, in Epinions networks, the relation between user (is trusted or not believed Appoint) user can be helped to find the high-quality reliable comment that they need.So in the network of tape symbol, link prediction Problem and the sign prediction problem of link are all important problems.In sign prediction problem, local and global knot in network Structure feature is usually used to prediction and there is the symbol linked between two nodes of link.The prediction of symbol has in social networks Many potential application values.Such as, the degree of belief prediction between user may be used as a similarity in commending system Method.In some cases, the symbol linked in network may be determined that sign prediction problem can recognize this by malicious user A little behaviors and purify network.Generally speaking, for tape symbol network a total of two major class of sign prediction problem method, one Class is to use machine learning techniques, another kind of to be an attempt to not go to give a forecast by study.In the side based on machine learning framework In method, it is necessary first to extract a number of significant architectural feature, be then predicted using specific grader. Another kind of algorithm is attempted to be predicted with existing theory of social science, so as to avoid the process of study.Such as Say, social equilibrium is theoretical and social status theory can be for the symbol in prediction network.The principle of these method behinds is Network is constantly evolved, and it can become increasingly to balance or increasingly support status theory.The result of this two major classes method Generally can not directly it be compared, because the use of the amount of calculation of the method based on machine learning being very big and complicated, cost It is larger, and the calculating based on balance theory and status theory is generally simpler.When network is larger, the method based on machine learning May no longer it be applicable.The thought of community mining can also be used for the chain in the forecasting problem of symbol in tape symbol network, i.e., each class It is positive to connect, and the link between class is negative, and whole network is balance in structure.These current methods only focus on chain The research of symbol is connect, and the classification to summit in tape symbol network is not made prediction, and how to design one kind in tape symbol network In to predict the method for summit generic be current subject matter.

The content of the invention

Technical problem solved by the invention is to provide a kind of mapping method of the vertex classification of tape symbol network, to solve The problem of certainly existing method vertex classification algorithm can not carry out vertex classification in tape symbol network.

The technical solution for realizing the object of the invention is：

A kind of mapping method of the vertex classification of tape symbol network, is comprised the following steps that：

Step 1, label matrix Y is drawn according to labeled summit；

Step 2, final preference matrix P, the transition matrix Q for needing to optimize, and the matrix w needed for grader are obtained；

Step 3, Q is fixed respectively^p,Qⁿ, P, three therein of w obtain Q^p,Qⁿ, P, w Optimized Iterative formula；

Step 4, according to obtained Optimized Iterative formula to Q^p,Qⁿ, P, w is iterated renewal simultaneously；

Step 5, according to the Q after iteration^p,Qⁿ, P, w optimal value, to belonging to summit not labeled in tape symbol network Classification is made prediction.

The present invention compared with prior art, its remarkable advantage：

(1) mapping method of the vertex classification of tape symbol network is drawn according to the summit being labeled in tape symbol network Initial vertex label matrix, is used as the reliable basis followed by optimization.

(2) network is divided into the sub-network being made up of respectively positive side and negative side, it is to avoid the symbol problem in calculating process.

(3) be that each summit in tape symbol network defines a preference vector, i.e., each summit in network oneself Belong to each class and all there is this preference probability, it is proposed that the adjacency matrix of sub-network is corresponding with its in tape symbol network The method that preference matrix has mapping matrix, the forecasting problem for not being labeled summit generic in tape symbol network is converted into Ask the problem of causing the optimal preference matrix of object function and corresponding transition matrix.

(4) this method can not only make prediction to not being labeled summit generic in tape symbol network, and method Iterative convergence speed is fast, and accuracy rate is high.

The present invention is described in further detail below in conjunction with the accompanying drawings.

Brief description of the drawings

Fig. 1 is overall procedure schematic diagram of the present invention.

Fig. 2 for tape symbol vertex classification mapping algorithm on data set Slashdot and Epinions run when matrix Q^p,Qⁿ, P, w average rate of convergence.

Embodiment

The present invention is realized to labeled in tape symbol network using the mapping method of the vertex classification of tape symbol network Classification belonging to summit is made prediction, and is comprised the following steps that：

Step 1, label matrix Y is drawn according to labeled summit；

According to the adjacency matrix A of tape symbol, each summit may carry class-mark, if C={ c₁,c₂,...,c_mFor m The tag set of class, c₁..., c_mFor m label of class；If u^L={ u₁,u₂,...,u_n' it is the individual summits of n ' being labeled Set；n’<N, n are the number on the summit in network, u^nL=u u^LIt is for by the individual not labeled vertex sets of n-n ', i.e., individual in n The labeled individual summits of n ' are removed in summit；With Y ∈ R^n×mRepresent to set u^LLabel matrix；

Y_ik=1 represents summit u_iIt has been marked as class c_k, otherwise Y_ik=0, Y_ikIt is the member of the i-th row kth row in label matrix Y Element.

Step 2, final preference matrix P, the transition matrix Q for needing to optimize, and the matrix w needed for grader are obtained；

2.1st, network is divided into sub-network：Positive line set G^pWith negative side set Gⁿ；

Network G=(V, E) is defined as by positive line set G^p=(V, E^p) and negative side set Gⁿ=(V, Eⁿ) two sub-networks Constitute.

Wherein, V is the set on all summits in network, and E is the set on side in network, E^pIt is that all symbols are positive side Set, EⁿIt is that all symbols are the set (E on the side born^p∪Eⁿ=E)；

2.2nd, two sub-networks are obtained and distinguish corresponding adjacency matrix A^pAnd Aⁿ；

A^pFor positive line set G^pAdjacency matrix；

AⁿFor negative side set GⁿAdjacency matrix；

Wherein A=A^p-Aⁿ, | A | it is A absolute value matrix.

2.3rd, user preference matrix P, positive edge adjacency matrix A are defined^pTransition matrix Q between user preference matrix P^p, with And negative side adjacency matrix AⁿTransition matrix Q between user preference matrix Pⁿ；

If P_i=(p_i1,p_i2,...,p_im) it is summit u_iPreference vector, Pi is the element of user preference matrix P the i-th row The vector of composition；Wherein p_ij(1≤j≤m) represents summit u_iBelong to class c_jPreference probability；

If positive line set G^pAdjacency matrix A^pThere is transition matrix Q between user preference matrix P^p,

If negative side set GⁿAdjacency matrix AⁿThere is transition matrix Q between user preference matrix Pⁿ；

So that A^pAnd PQ^pAs close possible to AⁿAnd PQⁿAs close possible to, P is n*m rank matrixes,

Wherein, Q^pAnd QⁿIt is m*n rank matrixes.

2.4th, defining classification device Pw, and draw the function to be optimized；

If grader is Pw, wherein w is m*m rank matrixes, for u^LIn summit u_i, P_iW=y_i, i.e., to uⁿIn summit, y_i=P_iW is summit u_iClass label vector, take y_iLargest component is y_ik, then u_iBelong to kth class c_k.Wherein y_iFor class label matrix The vector of Y the i-th row element composition；

According to user preference matrix P, the transition matrix Q and matrix w of adjacency matrix and user preference matrix draw excellent Function F (the Q of change^p,Qⁿ, P, w), i.e.,

Wherein,It is to prevent the regular terms of overfitting phenomenon, be Iterative optimization procedure behind convenience, note n*n rank diagonal matrix D=diag (d₁,d₂,...,d_n), d_iDefinition be：

Then (1) formula can be rewritten as：

Wherein, β, λ and α are parameter of the span between 0 to 1.

Step 3, Q is fixed respectively^p,Qⁿ, P, three therein of w obtain Q^p,Qⁿ, P, w Optimized Iterative formula；

3.1st, fixed Qⁿ, P, w, draw Q^pOptimized Iterative formula；

Due to Qⁿ, P, w value fix, constant can be regarded as, to the function F (Q to be optimized^p,Qⁿ, P, optimization w) is equivalent to excellent Change such as minor function：

Using gradient descent method to Q^pOptimization is iterated, Qⁿ, P, w regard constant as, to Q^pLocal derviation is asked to obtain

According to the definition of Frobenius norms, for matrix B=[b of a m*n rank_ij]_m*n, matrix B^TIt is matrix B Transposition；For B Frobenius functions；

Then known by definition

Wherein tr (B^TB) it is square formation B^TThe sum of B diagonal entry, referred to as square formation B^TB trace (mark).

So being changed as follows

Expansion, is obtained according to the property of mark

According to the Rule for derivation of mark, it can obtain

OrderFollowing renewal rule is derived by KKT conditions

Similarly：

3.2nd, fixed Q^p, P, w, draw QⁿOptimized Iterative formula；

As fixed Q^p, P, w, optimize QⁿWhen, obtain following iterative formula

3.3rd, fixed Q^p、Qⁿ, w, show that P Optimized Iterative is public；

As fixed Q^p、Qⁿ, w, optimization P when, obtain following iterative formula

3.4th, fixed Q^p、Qⁿ, P, draw w Optimized Iterative formula：

As fixed Q^p、Qⁿ, P, optimization w when obtain following iterative formula

Step 4, according to obtained Optimized Iterative formula to Q^p,Qⁿ, P, w is iterated renewal simultaneously；

First, to Q^p,Qⁿ, P, w tax initial values, initial value can be random number.It is right according to four iterative formulas of formula (8)-(11) Q^p,Qⁿ, P, the iteration that w value is synchronized updates, until convergence.

Step 5, according to the Q after iteration^p,Qⁿ, P, w optimal value, to belonging to summit not labeled in tape symbol network Classification is made prediction；

According to the Q after iteration^p,Qⁿ, P, the optimal of w be worth to i-th (1 in last label matrix Y, wherein label matrix Y ≤ i≤n) the row number j (1≤j≤m) where the maximum score value of row is summit u_iAffiliated classification c_j, i.e., according to label matrix Y just Classification belonging to summit not labeled in tape symbol network can be made prediction.

The present invention weighs the accuracy of classification using Micro-F1 indexs.I.e.Wherein p is essence The grand average value of exactness, r is the grand average value of recall rate.The value of the accuracy accurate number of times of prediction divided by forecast sample Sum, recall rate is with the quantity for predicting class interior joint in accurate number of times divided by overall data.

As shown in table 1, it is Epinions and Slashdot data sets, Slashdot websites master to test used data set The news related to technology is paid close attention to, users can be mutually clicked on according to the comment to article as friend's (liking) or enemy People (does not like).Epinions is a product scoring website, while being also a trust network, user can be according to theirs Evaluate to determine to trust or distrust other users.Because data set is huger, the method that we take random sampling, often The secondary node that x% is chosen in labeled node, 1-x% node is chosen in not labeled node, experiment is used as Data set sample, for each x value, we do 10 experiments, take the average value of 10 experimental results.In view of data It is openness, we choose relatively small x value, and this experiment have chosen { 5,10,15 }.And by the experimental result of acquirement with 3 classical vertex classification algorithm Random, ICA, GReg is made comparisons, in table 1, and the vertex classification mapping method of tape symbol is used Alphabetical NCS is represented.Wherein, Random algorithms are to enter row stochastic classification to not labeled summit；ICA algorithm is using local The information of neighbor node carry out structural classification device, node is classified；GReg algorithms are the methods by random walk, according to The class belonging to node being labeled draws the class belonging to not labeled summit.The results show this method can be effective Improve the accuracy of the result of link prediction in ground.

The comparison of the algorithms of different of table 1. node-classification performance on data set Slashdot and Epinions

The rate of convergence of this method is very fast simultaneously, and Fig. 2 shows the vertex classification of tape symbol network proposed by the present invention The transition matrix of mapping method and the rate of convergence of user preference matrix and grader matrix, the every adjacent iteration twice of definition The value of mean difference error between transition matrix and user preference matrix and grader matrix

What wherein t was represented is the t times iteration；Test result indicates that this method is in 15 times or so rear convergences of iteration, algorithmic statement speed Rate is fast.

Claims (10)

1. a kind of mapping method of the vertex classification of tape symbol network, it is characterised in that comprise the following steps：

Step 1, label matrix Y is drawn according to labeled summit；

Step 2, final preference matrix P, the transition matrix Q for needing to optimize, and the matrix w needed for grader are obtained；

Step 3, Q is fixed respectively^p,Qⁿ, P, three therein of w obtain Q^p,Qⁿ, P, w Optimized Iterative formula；

Step 4, according to obtained Optimized Iterative formula to Q^p,Qⁿ, P, w is iterated renewal simultaneously；

Step 5, according to the Q after iteration^p,Qⁿ, P, w optimal value, to the classification belonging to summit not labeled in tape symbol network Make prediction.

2. the mapping method of the vertex classification of tape symbol network as claimed in claim 1, it is characterised in that described in step 1 Label matrix Y is obtained, specific method is as follows：

According to the adjacency matrix A of tape symbol, each summit may carry class-mark, if C={ c₁,c₂,...,c_mIt is m class Tag set, c₁..., c_mFor m label of class；If u^L={ u₁,u₂,...,u_n' it is the individual vertex sets of n ' being labeled Close；n’<N, n are the number on the summit in network, u^nL=u u^LBy the individual not labeled vertex sets of n-n ', i.e., to be pushed up at n The labeled individual summits of n ' are removed in point；With Y ∈ R^n×mRepresent to set u^LLabel matrix,

Y_ik=1 represents summit u_iIt has been marked as class c_k, otherwise Y_ik=0, Y_ikIt is the element of the i-th row kth row in label matrix Y.

3. the mapping method of the vertex classification of tape symbol network as claimed in claim 1, it is characterised in that described in step 2 The final preference matrix P for needing to optimize is obtained, the A mapping matrix Qs corresponding with preference matrix P and classification are abutted on positive side Matrix w needed for device, is comprised the following steps that：

2.1st, network is divided into sub-network：Positive line set G^pWith negative side set Gⁿ；

2.2nd, two sub-networks are obtained and distinguish corresponding adjacency matrix A^pAnd Aⁿ；

2.3rd, user preference matrix P, positive edge adjacency matrix A are defined^pTransition matrix Q between user preference matrix P^p, and it is negative Edge adjacency matrix AⁿTransition matrix Q between user preference matrix Pⁿ；

2.4th, defining classification device Pw, and draw the function F (Q to be optimized^p,Qⁿ,P,w)。

4. the mapping method of the vertex classification of tape symbol network as claimed in claim 3, it is characterised in that asked in step 2.2 Go out the adjacency matrix A of two sub-networks^pAnd AⁿSpecific method is：

A^pFor positive line set G^pAdjacency matrix；

AⁿFor negative side set GⁿAdjacency matrix；

Wherein, A=A^p-Aⁿ, wherein | A | it is A absolute value matrix.

5. the mapping method of the vertex classification of tape symbol network as claimed in claim 3, it is characterised in that in step 2.3 just Beginningization user preference matrix P is specially：

If P_i=(p_i1,p_i2,...,p_im) it is summit u_iClassification preference matrix, P_iIt is the element composition of the i-th row of preference matrix Vector；Wherein p_ij(1≤j≤m) represents summit u_iBelong to class c_jPreference probability；

If positive line set G^pAdjacency matrix A^pThere is transition matrix Q between user preference matrix P^p,

If negative side set GⁿAdjacency matrix AⁿThere is transition matrix Q between user preference matrix Pⁿ；

So that A^pAnd PQ^pAs close possible to AⁿAnd PQⁿAs close possible to, P is n*m rank matrixes,

Wherein, Q^pAnd QⁿIt is m*n rank matrixes.

6. the mapping method of the vertex classification of tape symbol network as claimed in claim 3, it is characterised in that step 2.4 is defined Grader Pw, and draw the function F (Q to be optimized^p,Qⁿ, P, w), specially：

If grader is Pw, wherein w is m*m rank matrixes, for u^LIn summit u_i, P_iW=y_i, i.e., to uⁿIn summit, y_i= P_iW is summit u_iClass label vector, take y_iLargest component is y_ik, then u_iBelong to kth class c_k；Wherein y_iFor class label matrix Y's The vector of i-th row element composition；

According to user preference matrix P, the transition matrix Q and matrix w of adjacency matrix and user preference matrix draw what is optimized Function F (Q^p,Qⁿ, P, w), i.e.,

$F(Q^p,Q^n,P,w)=\underset{P\&GreaterEqual;0,w}{\underset{Q^p\&GreaterEqual;0,Q^p\&GreaterEqual;0,}{\min }}\left(\begin{array}{c}\left|\right|A^p-{\mathrm{PQ}}^p|{|}_F^2+\mathrm{\&beta;}\&CenterDot;||A^n-{\mathrm{PQ}}^n|{|}_F^2+\mathrm{\&alpha;}\&CenterDot;\underset{u_i\&Element;u^L}{\mathrm{\&Sigma;}}\left|\right|P_{i}w-y_i|{|}_F^2\\ +\mathrm{\&lambda;}\&CenterDot;\left(\right|\left|Q^p\right|{|}_F^2+\left|\right|Q^n|{|}_F^2+|\left|P\right|{|}_F^2+\left|\right|w\left|{|}_F^2\right)\end{array}\right)---\left(1\right)$

Wherein,It is in order to prevent the regular terms of overfitting phenomenon, for side The iterative optimization procedure in face, remembers n*n rank diagonal matrix D=diag (d after an action of the bowels₁,d₂,...,d_n), d_iDefinition be：

$d_i=\left\{\begin{array}{c}1;u_i\&Element;u^L\\ 0;otherwise\end{array}\right.$

Then (1) formula can be rewritten as：

$F(Q^p,Q^n,P,w)=\underset{P\&GreaterEqual;0,w}{\underset{Q^p\&GreaterEqual;0,Q^p\&GreaterEqual;0,}{\min }}\left(\begin{array}{c}\left|\right|A^p-{\mathrm{PQ}}^p|{|}_F^2+\mathrm{\&beta;}\&CenterDot;||A^n-{\mathrm{PQ}}^n|{|}_F^2+\mathrm{\&alpha;}\&CenterDot;\left|\right|D(Pw-Y)|{|}_F^2\\ +\mathrm{\&lambda;}\&CenterDot;\left(\right|\left|Q^p\right|{|}_F^2+\left|\right|Q^n|{|}_F^2+|\left|P\right|{|}_F^2+\left|\right|w\left|{|}_F^2\right)\end{array}\right)---\left(2\right)$

Wherein, β, λ and α are parameters.

7. the mapping method of the vertex classification of tape symbol network as claimed in claim 1, it is characterised in that obtained in step 3 Q^p,Qⁿ, P, w Optimized Iterative formula, detailed process is：

3.1st, fixed Qⁿ, P, w, draw Q^pOptimized Iterative formula：

$Q_{ij}^p\&LeftArrow;Q_{ij}^p\frac{{\left(P^T{A}^p\right)}_{ij}}{{\left(P^T{\mathrm{PQ}}^p\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(Q^p\right)}_{ij}}---\left(8\right)$

3.2nd, fixed Q^p, P, w, draw QⁿOptimized Iterative formula：

$Q_{ij}^n\&LeftArrow;Q_{ij}^n\frac{\mathrm{\&beta;}\&CenterDot;{\left(P^T{A}^n\right)}_{ij}}{\mathrm{\&beta;}\&CenterDot;{\left(P^T{\mathrm{PQ}}^n\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(Q^n\right)}_{ij}}---\left(9\right)$

3.3rd, fixed Q^p、Qⁿ, w, show that P Optimized Iterative is public：

$P_{ij}\&LeftArrow;P_{ij}\frac{{\left(A^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&beta;}\&CenterDot;{\left(A^n{Q}^{n^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DYw}}^T\right)}_{ij}}{(1+\mathrm{\&beta;})\&CenterDot;{\left({\mathrm{PQ}}^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DPww}}^T\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(P\right)}_{ij}}---\left(10\right)$

3.4th, fixed Q^p、Qⁿ, P, draw w Optimized Iterative formula：

$P_{ij}\&LeftArrow;P_{ij}\frac{{\left(A^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&beta;}\&CenterDot;{\left(A^n{Q}^{n^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DYw}}^T\right)}_{ij}}{(1+\mathrm{\&beta;})\&CenterDot;{\left({\mathrm{PQ}}^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DPww}}^T\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(P\right)}_{ij}}---\left(11\right).$

8. the mapping method of the vertex classification of tape symbol network as claimed in claim 7, it is characterised in that in step 3.1 Go out Q^pOptimized Iterative formula specific method be：

Due to Qⁿ, P, w value fix, constant can be regarded as, to object function F (Q^p,Qⁿ, P, it is following that optimization w) is equivalent to optimization Function：

$\begin{array}{c}L(Q^p,Q^n,P,w)=\left|\right|A^p-{\mathrm{PQ}}^p|{|}_F^2+\mathrm{\&beta;}\&CenterDot;||A^n-{\mathrm{PQ}}^n|{|}_F^2+\mathrm{\&alpha;}\&CenterDot;\left|\right|D(Pw-Y)|{|}_F^2\\ +\mathrm{\&lambda;}\&CenterDot;\left(\right|\left|P\right|{|}_F^2+\left|\right|Q^p|{|}_F^2+|\left|Q^n\right|{|}_F^2+\left|\right|w\left|{|}_F^2\right)\end{array}---\left(3\right)$

Using gradient descent method to Q^pOptimization is iterated, Qⁿ, P, w regard constant as, to Q^pLocal derviation is asked to obtain

$\frac{\&part;L}{\&part;Q^p}=\frac{\&part;}{\&part;Q^p}\left(\right||A^p-{\mathrm{PQ}}^p|{|}_F^2+\mathrm{\&lambda;}\left|\right|Q^p\left|{|}_F^2\right)---\left(4\right)$

According to the definition of Frobenius norms, for matrix B=[b of a m*n rank_ij]_m*n, matrix B^TIt is the transposition of matrix B；For B Frobenius functions；

Then known by definitionWherein tr (B^TB) it is square formation B^TThe sum of B diagonal entry, is referred to as side Battle array B^TB trace (mark)；

So being changed as follows

$\frac{\&part;L}{\&part;Q^p}=\frac{\&part;}{\&part;Q^p}tr\left({\left(A^p-{\mathrm{PQ}}^p\right)}^T\right(A^p-{\mathrm{PQ}}^p\left)\right)+\mathrm{\&lambda;}\&CenterDot;\frac{\&part;}{\&part;Q^p}tr\left(Q^{p^T}{Q}^p\right)---\left(5\right)$

Expansion, is obtained according to the property of mark

$\frac{\&part;L}{\&part;Q^p}=\frac{\&part;}{\&part;Q^p}tr(-2\&CenterDot;Q^{p^T}{P}^T{A}^p+Q^{p^T}{P}^T{\mathrm{PQ}}^p)+\frac{\&part;}{\&part;Q^p}tr\left(Q^{p^T}{Q}^p\right)---\left(6\right)$

According to the Rule for derivation of mark, it can obtain

$\frac{\&part;L}{\&part;Q^p}=-2\&CenterDot;P^T{A}^p+2\&CenterDot;P^T{\mathrm{PQ}}^p+2\mathrm{\&lambda;}\&CenterDot;Q^p---\left(7\right)$

OrderFollowing renewal rule is derived by KKT conditions

$Q_{ij}^p\&LeftArrow;Q_{ij}^p\frac{{\left(P^T{A}^p\right)}_{ij}}{{\left(P^T{\mathrm{PQ}}^p\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(Q^p\right)}_{ij}}---\left(8\right).$

9. the mapping method of the vertex classification of tape symbol network as claimed in claim 1, it is characterised in that changing in step 4 In generation, updates, and detailed process is as follows：

First, to Q^p,Qⁿ, P, w tax initial values, initial value can be random number；According to formula

$Q_{ij}^p\&LeftArrow;Q_{ij}^p\frac{{\left(P^T{A}^p\right)}_{ij}}{{\left(P^T{\mathrm{PQ}}^p\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(Q^p\right)}_{ij}}---\left(8\right)$

$Q_{ij}^n\&LeftArrow;Q_{ij}^n\frac{\mathrm{\&beta;}\&CenterDot;{\left(P^T{A}^n\right)}_{ij}}{\mathrm{\&beta;}\&CenterDot;{\left(P^T{\mathrm{PQ}}^n\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(Q^n\right)}_{ij}}---\left(9\right)$

$P_{ij}\&LeftArrow;P_{ij}\frac{{\left(A^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&beta;}\&CenterDot;{\left(A^n{Q}^{n^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DYw}}^T\right)}_{ij}}{(1+\mathrm{\&beta;})\&CenterDot;{\left({\mathrm{PQ}}^p{Q}^{p^T}\right)}_{ij}+\mathrm{\&alpha;}\&CenterDot;{\left({\mathrm{DPww}}^T\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(P\right)}_{ij}}---\left(10\right)$

$w_{ij}\&LeftArrow;w_{ij}\frac{{\left(P^{T}DY\right)}_{ij}}{\mathrm{\&alpha;}\&CenterDot;{\left(P^{T}DP\right)}_{ij}+\mathrm{\&lambda;}\&CenterDot;{\left(w\right)}_{ij}}---\left(11\right)$

Four iterative formulas, to Q^p,Qⁿ, P, the iteration that w value is synchronized updates, until convergence；Wherein formula (8)-(11) are distinguished For Q^p,Qⁿ, P, w Optimized Iterative formula.

10. the mapping method of the vertex classification of tape symbol network as claimed in claim 1, it is characterised in that step 5 pair not by Classification belonging to the summit of mark is made prediction, and is specially：

According to the Q after iteration^p,Qⁿ, P, w it is optimal be worth to i-th in last label matrix Y, wherein label matrix Y (1≤i≤ N) the row number j (1≤j≤m) where the maximum score value of row is summit u_iAffiliated classification c_j, i.e., just can be to band according to label matrix Y Classification in symbolic network not belonging to labeled summit is made prediction.