CN108681913A - A kind of digraph recommendation method based on AUC optimizations - Google Patents

A kind of digraph recommendation method based on AUC optimizations Download PDF

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CN108681913A
CN108681913A CN201810294394.4A CN201810294394A CN108681913A CN 108681913 A CN108681913 A CN 108681913A CN 201810294394 A CN201810294394 A CN 201810294394A CN 108681913 A CN108681913 A CN 108681913A
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陈伯伦
花勇
袁燕
李芬芬
张永军
于永涛
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Huaiyin Institute of Technology
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Abstract

A kind of digraph based on AUC optimizations of disclosure of the invention recommends method, is suitable for the analysis field of recommendation method, the specific steps are：The rating matrix of user is set to object function to be optimized first；Then object function is converted to approximate convex majorized function；It reuses gradient descent method and carries out function optimization；Further according to the weight matrix retrieved after function optimization, the interest-degree matrix of user is calculated；Finally the highest N number of projects of top are scored for recommending to the user predicted.The present invention has the characteristics that save time and more accurate real-time.

Description

A kind of digraph recommendation method based on AUC optimizations
Technical field
The invention belongs to applied to the recommendation method analysis technical field in commending system, more particularly to one kind being based on AUC The digraph of (area underthe receiveroperatingcharacteristiccurve) optimization recommends method.
Background technology
With the continuous growth of information content in social networks, the speed that information is propagated also constantly is being accelerated, and people obtain The approach of information also becomes increasingly wider.People are made to propagate and obtain information based on the poly- dissipating bind structure of information that social networks is propagated Ability has obtained unprecedented raising, accelerates interpersonal communication and information flow.In a sense, social network information It propagates on the basis of merging mass media and interpersonal communication, constructs a kind of completely new netted mechanism of transmission of distribution.And In this mechanism of transmission, the diffusion of information between users is often influenced by user force.As can be seen that current Under historical background, carrying out the research of social networks seems particularly significant.
And commending system closely causes the extensive concern of scholar as one of the research hotspot in social networks.Such as It is counted according to VentureBeat, the commending system of Amazon is provided for 35% sales volume of goods.At present in numerous recommendation sides In method, collaborative filtering is to apply most methods.Although collaborative filtering recommending method achieves huge success, it is still deposited In problems, wherein it is important that traditional collaborative filtering method often ignores the structure between user's (product) More nexus natures and user between relationship, such as user select the timing of commodity.It efficiently uses between user's (product) Contact can enrich the information of single user's (product), to more accurately identify the personal interest of user.In addition, in reality Due to different user to information propagate beneficiary importance have difference, for example, enterprise in social networks to big customer into When row Products Show, they often more focused on to user it is whether credible and how the degree of belief degree of progress between user Amount.Therefore, we it is necessary to reasonably recommend method for commending system design in.
An application as social networks, method is recommended to be broadly divided into：Recommendation method based on collaborative filtering, is based on The recommendation method of content, the recommendation method of recommendation method and resource allocation based on correlation rule.At present in numerous recommendation methods In, collaborative filtering is to apply most methods.Basic thought based on collaborative filtering recommending method is：If user has in the past Identical interest, then they can also have identical hobby in future.Collaborative filtering recommending method can be recommended not disposable Complex data, do not influenced by data format while excavating user's new point of interest, but still there is problems, Wherein most typical is exactly network Sparse Problems and cold start-up problem, and especially in more relational networks, this phenomenon is more Obviously.
Many scholars propose the collaborative filtering method based on user relationship mining on this basis, and achieve good Effect.Wherein, some scholars obtain the contact between user using proposition by explicit social network relationships, original Increase user social contact relational matrix on the basis of rating matrix, greatly improves the effect of method.Wu et al. utilizes label information Neighbour is calculated, and assumes that neighbour will have a direct impact on the feature vector of user, is that the feature vector of user increases based on neighbour pass The priori of system.Then by gradient descent method learning characteristic vector, the further perfect matrix decomposition based on neighbor relationships Model.However in actual data, it is relatively difficult to obtain enough social relationships or label information all.In addition, above-mentioned In method, generally all faintly assume that the relationship of influencing each other between user is changeless and symmetrical, however in reality In life, this hypothesis is simultaneously unreasonable.For example, A is the bean vermicelli of B, the behavior of B A is influenced it is very big, influences of the A to B then it is micro- its It is micro-, and the influence power between A and B can gradually change with the time.
Recently many scholars are by timing information in view of in commending system.Wherein Jiang et al. is based on fluid dynamic Theory discloses the behavior of the mankind with the rule of time change, proposes that a kind of fluid that is based on scores (Fluid Rating) Recommendation method.Guo et al. adds the concept of time window in the model of heat transfer, gradually changes the size of time window, It was found that more superior to the effect performance integrally predicted according to the local data that the time extracts.Sun Guang good fortune et al. propose based on when The collaborative filtering recommending method of sequence behavior, this method first model the sequential behavior of user and commodity, find theirs Then these information are dissolved into the collaborative filtering method based on matrix decomposition by nearest-neighbors set, to improvement method Predictablity rate.Ren et al. is according to the dynamic effect of preference pattern (the preference pattern) and preference of user The preference pattern rule of user is turned to a sparse matrix by (preference dynamic effect), and then empty using son Between gradually model personalized and global preference pattern.Although timing information is taken into account method by above-mentioned recommendation method Design process in, but they all ignore different user to information propagate beneficiary importance have difference, user's is credible It spends and how the degree of belief between user is measured.In addition it is important that conventional recommendation method often ignores use Structural relation between family.And the information of user can be enriched by efficiently using the contact between user, to more accurately identify The personal interest of user.So having important theoretical valence during the thought of user's topology information to be applied to the design of commending system Value and actual application prospect.
Therefore, realized in mass data and recommend to need to expend more times how to design a kind of accurate real-time Recommendation method be presently, there are main problem.
Invention content
Goal of the invention：For problems of the prior art, the present invention proposes a kind of saving time and more accurate reality When based on AUC optimization digraph recommend method.
Technical solution：In order to solve the above technical problems, the present invention provides a kind of digraph recommendation side optimized based on AUC Method is as follows：
(1) rating matrix of user is set to object function to be optimized；
(2) object function is converted to approximate convex majorized function；
(3) gradient descent method is used to carry out function optimization；
(4) according to the weight matrix retrieved after function optimization, the interest-degree matrix of user is calculated；
(5) the highest top-N project of user's scoring predicted is recommended.
Further, function optimization is carried out using gradient descent method in the step (3) to be as follows：
(3.1) weight matrix is initialized；
(3.2) update is iterated for the weight vectors on each vertex in network；
(3.3) error analysis is carried out, the condition of convergence is judged, and the weight matrix after final output optimization.
Further, setting object function to be optimized is as follows in the step (1)：
If calculative similarity score is：S=WA, wherein W are n*n rank weight matrix, remember that the row k vector of W is wk, wherein A is n*m rank network topology matrixes, remembers that the jth of A is classified as aj, then skj=wkaj, skjIt is evaluation score matrix S row ks the The element of j row；The AUC value then to score can be used following expression formula to indicate：
Wherein：P=N (N-1)/2 all even number of edges that may be present between node；M is to connect number of edges present in network；k For the row k of weight matrix W；Γ(vk) be node set V in vkThere is neighbours' point set of connection, i.e.,：Γ(vk)={ v | (vk, v) and ∈ E }, E is the set on side in network；Wherein：
Further, object function approximate convex majorized function is converted in the step (2) to be as follows：
The AUC value expression formula to be scored in approximating step (1) with an approximate convex optimization problem, it is below to use optimization instead Object function makes the great W of AUC to obtain：
Wherein, here it is a loss function, λ is regular coefficient.WhereinxkiIt is the spy of node pair Sign vector；
Two are taken to multiply loss function：(x)=(1-x)2, therefore loss function is：
Above formula loss function is rewritten into：
Wherein：
Wherein, Γ (uk) be node set V in ukThere is neighbours' point set of connection, i.e.,：Γ(uk)={ u | (uk,v)∈ E }, target call wk(k=1 ..., n) so that Lk(wk) minimize；
Further, function optimization is carried out using gradient descent method in the step (3) to be as follows：
Then to wkTake appropriate mean value：
Wherein, sum (A, 2) is summed respectively to the often row of matrix A, and repmat (sum (A, 2), n) is meant will be vectorial Sum (A, 2) replicates n times and constitutes completely new matrix.
Update is iterated for the weight vectors on each vertex in network again：
Finally the condition of convergence is judged to be as follows：
The error function E rror that the construction adjacent time moment decomposes matrix W(t)For:
WhereinFor 2 norms of matrix X.
Further, the interest-degree matrix that user is calculated in the step (4) is as follows：
The w of calculatingkThe element of the i-th row jth row of user interest degree the matrix S=WA, S of t moment is calculated with eigenmatrix It indicates to score to the prediction of project j in t moment user i.
Further, it scores the tool that highest top-N project recommended to the user predicted in the step (5) Steps are as follows for body：The target user that the predicts highest top-N project that score is recommended, it is predicted that user's scoring instead User has been answered, to the interest level of project, interest level to be sorted by sequence from high in the end, and the one before project is pushed away constantly It recommends to target user.
Compared with prior art, advantages of the present invention and effect are, using the recommendation method optimized based on AUC, to solve high Dimension, redundant network recommend difficult problem, show as：
(1) dimensionality reduction is carried out to original rating matrix to realize to recommend, can obtain more preferable using the method for AUC optimizations Recommendation results.
(2) it since the dimension of rating matrix is very big, is realized and is recommended using the method for AUC optimizations, utilize gradient descent method The function of pairing approximation optimizes, and each moment all the recommendation process of front need not all be made a new start according to iteration, in this way It not only can greatly shorten the stand-by period of recommendation, but also the recommendation results of high quality can be obtained.
(3) the method blends the topological attribute of network, depends not only upon the selection information of user, and contains use The attribute information at family, this method implements relatively simply, and not additional parameter, because the recommendation effect of the method is more smart Really, robust performance higher.
The recommendation method that the present invention proposes to optimize based on AUC for recommendation problem, weight matrix is decomposed by rating matrix With user's topological characteristic matrix, target problem is converted to approximate convex optimization problem, it is asked using gradient descent method Solution.By decomposite come matrix calculate the new weight matrix of subsequent time, new user interest degree matrix is then calculated, to pre- The highest top-N project of target user's scoring measured is recommended.This method can greatly reduce computing cost and deposit Expense is stored up, the time that user waits for recommendation results is shortened, meets user well to the high-accuracy in commending system It is required that.
Description of the drawings
Fig. 1 is the overview flow chart of the present invention.
Specific implementation mode
With reference to the accompanying drawings and detailed description, the present invention is furture elucidated.
The present invention uses the method optimized based on AUC to realize recommendation, overcomes other insurmountable data of recommendation method The problems such as higher-dimension, sparse, redundancy.Recommendation problem is converted to optimization problem by the present invention, extracts effective network topology characteristic, is led to The method for crossing optimization object function overcomes the problems such as other recommendation methods are of low quality when being recommended, and has higher Robust performance.The computing cost and storage overhead of the present invention is all fewer than traditional recommendation method, but can obtain more high-quality The recommendation results of amount.
The step of the present invention is as follows：
One, object function to be optimized is set
If calculative similarity score is：S=WA, wherein W are n*n rank weight matrix, remember that the row k vector of W is wk, wherein A is n*m rank network topology matrixes, remembers that the jth of A is classified as aj, then skj=wkaj, skjIt is evaluation score matrix S row ks the The element of j row.The AUC value then to score can be used following expression formula to indicate：
Wherein：P=N (N-1)/2 all even number of edges that may be present between node.M is to connect number of edges present in network.k For the row k of weight matrix W.Γ(vk) be node set V in vkThere is neighbours' point set of connection, i.e.,：Γ(vk)={ v | (vk, v) and ∈ E }, E is the set on side in network.Wherein：
Two, object function is converted to approximate convex optimization problem
With an approximate convex optimization problem come approximate expression (1), use optimization object function below instead makes to obtain The great W of AUC：
Wherein, here it is a loss function, λ is regular coefficient.WhereinxkiIt is the spy of node pair Sign vector.
In our method, we take two to multiply loss function：(x)=(1-x)2, in this way, loss function is：
(4) formula is rewritten into：
Wherein：
Wherein, Γ (uk) be node set V in ukThere is neighbours' point set of connection, i.e.,：Γ(uk)={ u | (uk,v)∈ E}.Our target call wk(k=1 ..., n) so that Lk(wk) minimize.
We optimize (6) using gradient descent method, it can be deduced that：
To wkTake mean value appropriateWith following iterative formula, optimal w can be obtainedk：
Three, user interest degree matrix is calculated according to basic matrix and weight matrix
The w calculated according to step 2kThe i-th row the of user interest degree the matrix S=WA, S of t moment are calculated with eigenmatrix The element representation of j row scores to the prediction of project j in t moment user i.
Four, the highest top-N project of user's scoring predicted is recommended
To the user interest degree matrix S that step 3 is calculated, the interest level of target user is carried out from high to low Sequence, the project recommendation of N is to user before coming.
Five, convergence is carried out to the recommendation method optimized based on AUC
The present invention has carried out convergence error analysis estimation to the dynamic updating method of matrix, constructs the adjacent time moment pair The error function E rror that matrix W is decomposed(t)For:
WhereinFor 2 norms of matrix X.
Specifically as shown in Figure 1, AUC indexs are dissolved into link prediction, directly carried out as optimization aim Link prediction.It is following steps：
(1) object function AUC to be optimized is set；
(2) object function is converted to approximate convex optimization problem L (W)；
(3) it is optimized using gradient descent method；
(3-1) initializes weight matrix W (0)；
(3-2) is iterated update weight vectors w (t) for each vertex in network；
(3-3) carries out error analysis, and the condition of convergence judges；
(4) according to W (t) matrixes are obtained, the rating matrix S=WA of user is exported；
(5) the highest top-N project of user's scoring predicted is recommended；
We set calculative similarity score S=WA to the step (1), and wherein W is n*n rank weight matrix, remembers W's Row k vector is wk, wherein A is n*m rank network topology matrixes, remembers that the jth of A is classified as aj, then skj=wkaj, skjIt is evaluation score The element of matrix S row k jth row.The AUC value of scoring is then subjected to majorized function of the rewriting of formula about W.
The step (2) we with an approximate convex optimization problem come approximate AUC expression formulas, use optimization object function instead L (W) makes the great W of AUC to obtain.
In our method, during optimization being utilized two multiplies loss function：(x)=(1-x)2, pass through minimum Change error square come find data optimal function matching.
Our target call w of step (3)k(k=1 ..., n) so that Lk(wk) minimize.We are using under gradient Drop method optimizes function, it can be deduced that in t moment wkIteration function.
The step (4) calculates user interest degree matrix S, i.e., according to the weight matrix W and topological characteristic matrix A of t moment S=WA.
The step (5) recommends the target user that the predicts highest top-N project that score, it is predicted that use Interest level of the user in t moment to project has been reacted in family scoring, interest level is sorted by sequence from high in the end, and before N number of project recommendation is to target user.
Example the above is only the implementation of the present invention is not intended to restrict the invention.All principles in the present invention Within, made by equivalent replacement, should all be included in the protection scope of the present invention.The content category that the present invention is not elaborated The prior art well known to this professional domain technical staff.

Claims (7)

1. a kind of digraph based on AUC optimizations recommends method, which is characterized in that be as follows：
(1) rating matrix of user is set to object function to be optimized；
(2) object function is converted to approximate convex majorized function；
(3) gradient descent method is used to carry out function optimization；
(4) according to the weight matrix retrieved after function optimization, the interest-degree matrix of user is calculated；
(5) highest top-N project is scored for recommending to user.
2. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (3) function optimization is carried out using gradient descent method in be as follows：
(3.1) weight matrix is initialized；
(3.2) update is iterated for the weight vectors on each vertex in network；
(3.3) error analysis is carried out, the condition of convergence is judged, and the weight matrix after final output optimization.
3. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (1) setting object function to be optimized is as follows in：
If calculative similarity score is：S=WA, wherein W are n*n rank weight matrix, remember that the row k vector of W is wk, Middle A is n*m rank network topology matrixes, remembers that the jth of A is classified as aj, then skj=wkaj, skjIt is evaluation score matrix S row k jth row Element；The AUC value then to score can be used following expression formula to indicate：
Wherein：P=N (N-1)/2 all even number of edges that may be present between node；M is to connect number of edges present in network；K is power The row k of weight matrix W；Γ(vk) be node set V in vkThere is neighbours' point set of connection, i.e.,：Γ(vk)={ v | (vk,v) ∈ E }, E is the set on side in network；Wherein：
4. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (2) object function approximate convex majorized function is converted in be as follows：
The AUC value expression formula to be scored in approximating step (1) with an approximate convex optimization problem uses optimization target below instead Function makes the great W of AUC to obtain：
Wherein, here it is a loss function, λ is regular coefficient.WhereinxkiBe node pair feature to Amount；
Two are taken to multiply loss function：(x)=(1-x)2, therefore loss function is：
Above formula loss function is rewritten into：
Wherein：
Wherein, Γ (uk) be node set V in ukThere is neighbours' point set of connection, i.e.,：Γ(uk)={ u | (uk, v) and ∈ E }, mesh Mark requires wk(k=1 ..., n) so that Lk(wk) minimize.
5. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (3) function optimization is carried out using gradient descent method in be as follows：
Then to wkTake appropriate mean value：
Wherein, sum (A, 2) is summed respectively to the often row of matrix A, and repmat (sum (A, 2), n) is meant vectorial sum (A, 2) replicates n times and constitutes completely new matrix.
Update is iterated for the weight vectors on each vertex in network again：
Finally the condition of convergence is judged to be as follows：
The error function E rror that the construction adjacent time moment decomposes matrix W(t)For:
WhereinFor 2 norms of matrix X.
6. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (4) the interest-degree matrix that user is calculated in is as follows：
The w of calculatingkThe element representation that the i-th row jth row of user interest degree the matrix S=WA, S of t moment are calculated with eigenmatrix exists T moment user i scores to the prediction of project j.
7. a kind of digraph based on AUC optimizations according to claim 1 recommends method, which is characterized in that the step (5) user's highest top-N project that score is as follows for recommendation in：The user's scoring predicted is reacted User, to the interest level of project, sorts interest level by sequence from high in the end, and top n project recommendation in t moment To target user.
CN201810294394.4A 2018-04-04 2018-04-04 A kind of digraph recommendation method based on AUC optimizations Pending CN108681913A (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105740430A (en) * 2016-01-29 2016-07-06 大连理工大学 Personalized recommendation method with socialization information fused
CN105913296A (en) * 2016-04-01 2016-08-31 北京理工大学 Customized recommendation method based on graphs
CN106296337A (en) * 2016-07-13 2017-01-04 扬州大学 Dynamic recommendation method based on Non-negative Matrix Factorization
CN107451855A (en) * 2017-07-13 2017-12-08 南京师范大学 A kind of figure structure decomposes the recommendation method of combination learning with L1 regular matrixes

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105740430A (en) * 2016-01-29 2016-07-06 大连理工大学 Personalized recommendation method with socialization information fused
CN105913296A (en) * 2016-04-01 2016-08-31 北京理工大学 Customized recommendation method based on graphs
CN106296337A (en) * 2016-07-13 2017-01-04 扬州大学 Dynamic recommendation method based on Non-negative Matrix Factorization
CN107451855A (en) * 2017-07-13 2017-12-08 南京师范大学 A kind of figure structure decomposes the recommendation method of combination learning with L1 regular matrixes

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Application publication date: 20181019