CN102789499A - Collaborative filtering method on basis of scene implicit relation among articles - Google Patents

Abstract

The invention discloses a collaborative filtering method on the basis of a scene implicit relation among articles. The collaborative filtering method comprises the following steps of: 1, extracting scores of the articles in different scenes from original score data and establishing an article-scene score matrix; 2, decomposing the article-scene score matrix by a matrix decomposition method to obtain an implicit factor matrix of the articles; 3, establishing a scene feature vector for each article by using the obtained implicit factor matrix of the articles so as to calculate the similarity among the articles by utilizing a Pearson correlation coefficient and establish an article implicit relation matrix; and 4, integrating obtained article implicit relation information into a probability matrix decomposition matrix to generate a personalized recommendation. According to the invention, scene information can be sufficiently utilized to mine the implicit relation information among the articles, and the recommendation is generated by utilizing the implicit relation among the articles; the collaborative filtering method has high expandability for the scene information, and a candidate scene set can be regulated according to the application requirements; and the accuracy and the personalization degree of the recommendation can be effectively improved.

Description

Collaborative filtering method based on sight implicit relationship between article

Technical field

The present invention relates to collaborative filtering method, relate in particular to a kind of collaborative filtering method based on sight implicit relationship between article.

Background technology

In recent years, serious day by day along with the internet information overload, a lot of services the support that all presses for personalized recommendation system is provided.Yet traditional recommended technology has only been considered two kinds of entities i.e. " user " and " project ", and has ignored the influence of context information (like time, position, personnel, active state, status of equipment, network condition etc.) to recommending.For this reason, the context aware commending system receives publicity gradually, facts have proved, the introducing of context information can effectively improve the accuracy and the personalized degree of recommendation.

At present; The proposed algorithm of context aware mainly is divided into three major types: the pre-filtering that (1) sight is relevant: from observation data, extract the data relevant with targeted customer's situation of presence, utilize the data that obtain to train the proposed algorithm in conventional two-dimensional space and predict again.(2) the relevant back filtration of sight: the proposed algorithm of at first using on the traditional two-dimensional space is predicted, utilizes context information that recommendation list is revised again.(3) the relevant modeling of sight: directly set up model, context information is incorporated whole recommendation generative process based on the user preference data that comprises sight.

Not enough below above-mentioned context aware proposed algorithm exists: the sparse property of (1) data problem: along with the introducing of context information; Three-dimensional user-article-sight rating matrix is more sparse than traditional user-article rating matrix, and the pre-filtering that sight is relevant and the recommend method of back filtration are difficult to obtain desirable accuracy.(2) scalability problem.Although the modeling method that sight is relevant, the pre-filtering method more relevant than sight more can adapt to sparse data with the back filter method, and often computation complexity is higher for the relevant modeling method of present existing sight, poor expandability.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art, a kind of collaborative filtering method based on sight implicit relationship between article is provided.

Step based on the collaborative filtering method of sight implicit relationship between article is following:

1) from the three-dimensional score data of original user-article-sight, extracts the scoring of article under different sights, set up article-sight rating matrix;

2) through the method for matrix decomposition article-sight rating matrix is decomposed, obtain the latent factor matrix of article with respect to sight;

3) use the latent factor matrix of article to set up the proper vector of sightization, and then utilize Pearson correlation coefficient to calculate the similarity between the article, set up article implicit relationship matrix for each article;

4) article implicit relationship matrix is incorporated the probability matrix decomposition model, for the user generates personalized recommendation.

Described sight is to influence the user and the mutual factor of commending system comprises time, place; The three-dimensional score data of described user-article-sight is by the user of website records and the interaction data of commending system, promptly the user under different situations to the scoring of different article.

Described step 1) is: the active degree of user under each sight: D is calculated in (1) _Ik=N _Ik/ N _i, D wherein _IkThe active degree of expression user i under sight k, N _IkThe scoring number of expression user i under sight k, N _iThe total number of scoring of expression user i; (2) from the three-dimensional rating matrix of user-article-sight

Middle article-sight the matrix that extracts

Here m representes user's number, and n representes the article number, and k representes the sight number, Be real number space, matrix R _IcIn j capable, the element r of k row _JkThe scoring of expression article j under sight k, and have

Wherein

Represent user i scoring to article j under sight k.

Described step 2) be: adopt the method for matrix decomposition to decompose article-sight rating matrix, obtain the latent factor matrix of article:

R wherein _IcBe article-sight matrix, I _{N * f}Be the latent factor matrix of article,

It is the latent factor matrix of sight.Here latent factor matrix I _{N * f}With In element be model parameter, in decomposable process, the method that descends through gradient at random minimizes objective function

Obtain model parameter, wherein r _JkBe the scoring of article j under sight k, || || _FExpression Frobenius norm, I _iAnd C _kDifference representing matrix I _{N * f}The capable and matrix of i

K capable; Article conceal factor matrix I _{N * f}Reflected the implicit features of article, the capable implicit features vector of promptly representing article i with respect to sight of its i with respect to sight.

Described step 3) is: utilize Pearson correlation coefficient to calculate article with respect to the similarity between the implicit features vector of sight, set up article implicit relationship matrix S:

I wherein _iExpression article i is with respect to the implicit features vector of sight, I _IfBe I _iF dimension,

Be I _iIn the mean value of each element.

Described step 4) is: (1) makes the latent factor vector of article receive its neighbours' influence in the implicit relationship information of introducing on the basis of probability matrix decomposition model between article; In common probability matrix decomposition model, the conditional probability of the latent factor matrix of article is

Wherein V representes the latent factor matrix of article, and N representes normal distribution, and its expectation is 0, and variance is σ ²I, I representation unit matrix; And in improved probability matrix decomposition model, the conditional probability of the latent factor matrix of article is

Wherein

Identical with common probability matrix decomposition model, remain just too distribution; And Wherein S representes the implicit relationship matrix between article, S _IjImplicit relationship value between expression article i and the article j, N _iNeighbours' set of expression article i, promptly with the set of the nearest article of article i implicit relationship, V _iThe i that is matrix V is capable, i.e. the latent factor vector of article i; The posterior probability of the maximized latent factor matrix of ultimate demand is:

$p(U,V|R,S,{\mathrm{\σ}}_R^2,{\mathrm{\σ}}_S^2,{\mathrm{\σ}}_U^2,{\mathrm{\σ}}_V^2)\∝p\left(R\right|U,V,{\mathrm{\σ}}_R^2)p\left(U\right|{\mathrm{\σ}}_U^2)p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2),$ Wherein:

$\left\{\begin{array}{c}p\left(R\right|U,V,{\mathrm{\σ}}_R^2)={\mathrm{\Π}}_{u=1}^m{\mathrm{\Π}}_{i=1}^n{\left[N\left(R_{\mathrm{ui}}\right|U_u^T{V}_i,{\mathrm{\σ}}_R^2)\right]}^{I_{\mathrm{ui}}^R}\\ p\left(U\right|{\mathrm{\σ}}_U^2)={\mathrm{\Π}}_{u=1}^{m}N\left(U\right|0,{\mathrm{\σ}}_U^{2}I)\\ p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2)={\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|{\mathrm{\Σ}}_{j\∈N_i}{V}_j{S}_{\mathrm{ij}},{\mathrm{\σ}}_S^{2}I)\×{\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|0,{\mathrm{\σ}}_V^{2}I)\end{array}\right.$

Wherein R is user-article rating matrix; U and V represent the latent factor matrix of user and article respectively;

is the indication function; If the scoring of user u to article i arranged in R; Then

otherwise

(2) adopt

in the method maximization steps (1) that gradient at random descends to obtain latent factor matrix U and V; And prediction the unknown is marked to use , and then be each user-customized recommended top-N article.

The present invention compared with prior art has the following advantages:

1) a kind of method of extracting the article implicit features is proposed.Matrix decomposition is a kind of method that implicit features is extracted that is widely used in, and adopts the mode of gradient decline at random to optimize MAE, thereby solves latent factor matrix parameter.Through decomposing article-sight rating matrix, can access the implicit features of article about sight.More efficient with respect to additive method, more accurate.

2) a kind of similarity calculating method that incorporates context information is proposed.Represent its implicit features with article with respect to the latent factor vector of sight, and based on the similarity between these implicit features tolerance article.Compare based on the similarity calculating method of article scoring with tradition, institute's extracting method does not receive the influence of the sparse property of data, thereby can measure the similarity between the article more accurately.

3) a kind of personalized recommendation generating algorithm that incorporates the article implicit relationship is proposed.Implicit relationship information introducing on the basis of probability matrix decomposition model between article makes the latent factor vector of article receive its neighbours' influence, and then improves the probability matrix decomposition model, and obtains better recommendation effect.Because the implicit relationship between article is based on the context information acquisition, improved model has been introduced context information through indirect mode, but not directly handles higher dimensional matrix, and the modeling method computation complexity that therefore more existing sight is relevant is lower, and extendability is better.The present invention can be applied in cinemusic and recommend, commercial product recommending, and recommend tourist attractions, and the field is recommended in the dining room.

Description of drawings

Fig. 1 is based on the process flow diagram of the collaborative filtering method of sight implicit relationship between article;

Fig. 2 is the scoring vector synoptic diagram of article i about sight;

Fig. 3 (a) is common probability matrix decomposition model figure;

Fig. 3 (b) is improved probability matrix decomposition model figure.

Embodiment

Step based on the collaborative filtering method of sight implicit relationship between article is following:

1) from the three-dimensional score data of original user-article-sight, extracts the scoring of article under different sights, set up article-sight rating matrix;

2) through the method for matrix decomposition article-sight rating matrix is decomposed, obtain the latent factor matrix of article with respect to sight;

3) use the latent factor matrix of article to set up the proper vector of sightization, and then utilize Pearson correlation coefficient to calculate the similarity between the article, set up article implicit relationship matrix for each article;

4) article implicit relationship matrix is incorporated the probability matrix decomposition model, for the user generates personalized recommendation.

Described sight is to influence the user and the mutual factor of commending system comprises time, place; The three-dimensional score data of described user-article-sight is by the user of website records and the interaction data of commending system, promptly the user under different situations to the scoring of different article.

Described step 1) is: the active degree of user under each sight: D is calculated in (1) _Ik=N _Ik/ N _i, D wherein _IkThe active degree of expression user i under sight k, N _IkThe scoring number of expression user i under sight k, N _iThe total number of scoring of expression user i; (2) from the three-dimensional rating matrix of user-article-sight

Middle article-sight the matrix that extracts

Here m representes user's number, and n representes the article number, and k representes the sight number,

Be real number space, matrix R _IcIn j capable, the element r of k row _JkThe scoring of expression article j under sight k, and have

Wherein

Represent user i scoring to article j under sight k.Described step 2) be: adopt the method for matrix decomposition to decompose article-sight rating matrix, obtain the latent factor matrix of article:

R wherein _IcBe article-sight matrix, I _{N * f}Be the latent factor matrix of article,

It is the latent factor matrix of sight.Here latent factor matrix I _{N * f}With

In element be model parameter, in decomposable process, the method that descends through gradient at random minimizes objective function

Obtain model parameter, wherein r _JkBe the scoring of article j under sight k, || || _FExpression Frobenius norm, I _iAnd C _kDifference representing matrix I _{N * f}The capable and matrix of i

K capable; Article conceal factor matrix I _{N * f}Reflected the implicit features of article, the capable implicit features vector of promptly representing article i with respect to sight of its i with respect to sight.

Described step 3) is: utilize Pearson correlation coefficient to calculate article with respect to the similarity between the implicit features vector of sight, set up article implicit relationship matrix S:

I wherein _iExpression article i is with respect to the implicit features vector of sight, I _IfBe I _iF dimension,

Be I _iIn the mean value of each element.

Described step 4) is: (1) makes the latent factor vector of article receive its neighbours' influence in the implicit relationship information of introducing on the basis of probability matrix decomposition model between article; In common probability matrix decomposition model, the conditional probability of the latent factor matrix of article is

Wherein V representes the latent factor matrix of article, and N representes normal distribution, and its expectation is 0, and variance is σ ²I, I representation unit matrix; And in improved probability matrix decomposition model, the conditional probability of the latent factor matrix of article is

Wherein

Identical with common probability matrix decomposition model, remain just too distribution; And

Wherein S representes the implicit relationship matrix between article, S _IjImplicit relationship value between expression article i and the article j, N _iNeighbours' set of expression article i, promptly with the set of the nearest article of article i implicit relationship, V _iThe i that is matrix V is capable, i.e. the latent factor vector of article i; The posterior probability of the maximized latent factor matrix of ultimate demand is:

$p(U,V|R,S,{\mathrm{\σ}}_R^2,{\mathrm{\σ}}_S^2,{\mathrm{\σ}}_U^2,{\mathrm{\σ}}_V^2)\∝p\left(R\right|U,V,{\mathrm{\σ}}_R^2)p\left(U\right|{\mathrm{\σ}}_U^2)p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2),$ Wherein:

$\left\{\begin{array}{c}p\left(R\right|U,V,{\mathrm{\σ}}_R^2)={\mathrm{\Π}}_{u=1}^m{\mathrm{\Π}}_{i=1}^n{\left[N\left(R_{\mathrm{ui}}\right|U_u^T{V}_i,{\mathrm{\σ}}_R^2)\right]}^{I_{\mathrm{ui}}^R}\\ p\left(U\right|{\mathrm{\σ}}_U^2)={\mathrm{\Π}}_{u=1}^{m}N\left(U\right|0,{\mathrm{\σ}}_U^{2}I)\\ p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2)={\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|{\mathrm{\Σ}}_{j\∈N_i}{V}_j{S}_{\mathrm{ij}},{\mathrm{\σ}}_S^{2}I)\×{\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|0,{\mathrm{\σ}}_V^{2}I)\end{array}\right.$

Wherein R is user-article rating matrix; U and V represent the latent factor matrix of user and article respectively;

is the indication function; If the scoring of user u to article i arranged in R; Then

otherwise adopt in the method maximization steps (1) that gradient at random descends to obtain latent factor matrix U and V; And prediction the unknown is marked to use , and then be each user-customized recommended top-N article.

Embodiment 1:

1) film-time rating matrix is set up: from original user-film-time score data, obtain the scoring that each film obtains through average weighted mode under different time, thereby set up film-time rating matrix.At first, calculate the active degree of user under different time: D _Ik=N _Ik/ N _i, D wherein _IkThe active degree of expression user i under time k, N _IkThe scoring number of expression user i under time k, N _iThe total number of scoring of expression user i; From three-dimensional rating matrix of user-film-time

Middle film-the time matrix that extracts

Here matrix R _IcIn j capable, the element r of k row _JkThe scoring of expression film j under time k, and have

Wherein

Represent user i scoring to film j under time k.

2) the film implicit features is extracted: adopt the method for matrix decomposition to decompose film-time rating matrix, obtain the latent factor matrix of film: I wherein _{N * f}It is the latent factor matrix of film.Here latent factor matrix I _{N * f}With

In element be model parameter, in decomposable process, the method that descends through gradient at random minimizes objective function

Obtain model parameter, wherein || || _FExpression Frobenius norm.

3) the latent factor matrix I of film that implicit relationship foundation between film: by step 2) obtains _{N * f}Reflected that film is with respect to the implicit features of time, the capable implicit features vector of film i with respect to the time of promptly representing of its i.Utilize Pearson correlation coefficient to calculate film, set up film implicit relationship matrix S with respect to the similarity between the implicit features vector of time:

I wherein _iExpression film i is vectorial with respect to the implicit features of time,

Be I _iIn the mean value of each element.

4) personalized recommendation generates: the implicit relationship information introducing on the basis of probability matrix decomposition model between film makes the latent factor vector of film receive its neighbours' influence; In common probability matrix decomposition model, the conditional probability of the latent factor matrix of film is

And in improved probability matrix decomposition model, the conditional probability of the latent factor matrix of film is

Wherein

Remain just too distribute and

Method maximization posterior probability through gradient decline at random: $p(U,V|R,S,{\mathrm{\σ}}_R^2,{\mathrm{\σ}}_S^2,{\mathrm{\σ}}_U^2,{\mathrm{\σ}}_V^2)\∝p\left(R\right|U,V,{\mathrm{\σ}}_R^2)p\left(U\right|{\mathrm{\σ}}_U^2)p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2)$ Solve latent factor matrix U and V, and use The unknown scoring of prediction, and then be each user-customized recommended top-N film.

Embodiment 2:

1) dining room-place rating matrix is set up: from original user-dining room-place score data, obtain the scoring that each dining room obtains through average weighted mode under the different location, thereby set up dining room-place rating matrix.At first, calculate the active degree of user under the different location: D _Ik=N _Ik/ N _i, D wherein _IkThe active degree of expression user i under the k of place, N _IkThe scoring number of expression user i under the k of place, N _iThe total number of scoring of expression user i; From user-dining room-the three-dimensional rating matrix in place

Middle dining room-ground the dot matrix that extracts

Here matrix R _IcIn j capable, the element r of k row _JkRepresent the scoring of dining room j, and have with respect to place k Wherein

Expression user i in the place k to the scoring of dining room j; Generally speaking, near more place is marked high more accordingly from the dining room.

2) the dining room implicit features is extracted: adopt the method for matrix decomposition to decompose dining room-place rating matrix, obtain the latent factor matrix in dining room:

I wherein _{N * f}It is the latent factor matrix in dining room.Here latent factor matrix I _{N * f}With

In element be model parameter, in decomposable process, the method that descends through gradient at random minimizes objective function

Obtain model parameter, wherein || || _FExpression Frobenius norm.

3) the latent factor matrix I in dining room that implicit relationship foundation between the dining room: by step 2) obtains _{N * f}Reflected the implicit features of dining room, the capable implicit features vector of promptly representing dining room i with respect to the place of its i with respect to the place.Utilize Pearson correlation coefficient to calculate the dining room, set up dining room implicit relationship matrix S with respect to the similarity between the implicit features vector in place:

I wherein _iExpression dining room i is vectorial with respect to the implicit features in place,

Be I _iIn the mean value of each element.

4) personalized recommendation generates: the implicit relationship information introducing on the basis of probability matrix decomposition model between the dining room makes the latent factor vector in dining room receive its neighbours' influence; In common probability matrix decomposition model; The conditional probability of the latent factor matrix in dining room is

and in improved probability matrix decomposition model, the latent factor matrix in dining room conditional probability is

wherein remain and just too distribute and method maximization posterior probability that descends through gradient at random:

$p(U,V|R,S,{\mathrm{\σ}}_R^2,{\mathrm{\σ}}_S^2,{\mathrm{\σ}}_U^2,{\mathrm{\σ}}_V^2)\∝p\left(R\right|U,V,{\mathrm{\σ}}_R^2)p\left(U\right|{\mathrm{\σ}}_U^2)p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2)$ Solve latent factor matrix U and V, and use

The unknown scoring of prediction, and then be each user-customized recommended top-N dining room.

Claims (6)

1. the collaborative filtering method based on sight implicit relationship between article is characterized in that its step is following:

1) from the three-dimensional score data of original user-article-sight, extracts the scoring of article under different sights, set up article-sight rating matrix;

2) through the method for matrix decomposition article-sight rating matrix is decomposed, obtain the latent factor matrix of article with respect to sight;

3) use the latent factor matrix of article to set up the proper vector of sightization, and then utilize Pearson correlation coefficient to calculate the similarity between the article, set up article implicit relationship matrix for each article;

4) article implicit relationship matrix is incorporated the probability matrix decomposition model, for the user generates personalized recommendation.

2. a kind of collaborative filtering method based on sight implicit relationship between article according to claim 1 is characterized in that described sight is to influence the user and the mutual factor of commending system comprises time, place; The three-dimensional score data of described user-article-sight is by the user of website records and the interaction data of commending system, promptly the user under different situations to the scoring of different article.

3. a kind of collaborative filtering method based on sight implicit relationship between article according to claim 1 is characterized in that described step 1) is: the active degree of user under each sight: D is calculated in (1) _Ik=N _Ik/ N _i, D wherein _IkThe active degree of expression user i under sight k, N _IkThe scoring number of expression user i under sight k, N _iThe total number of scoring of expression user i; (2) from the three-dimensional rating matrix of user-article-sight Middle article-sight the matrix that extracts

Here m representes user's number, and n representes the article number, and k representes the sight number, Be real number space, matrix R _IcIn j capable, the element r of k row _JkThe scoring of expression article j under sight k, and have

Wherein

Represent user i scoring to article j under sight k.

4. a kind of collaborative filtering method based on sight implicit relationship between article according to claim 1 is characterized in that described step 2) be: adopt the method for matrix decomposition to decompose article-sight rating matrix, obtain the latent factor matrix of article:

R wherein _IcBe article-sight matrix, I _{N * f}Be the latent factor matrix of article,

It is the latent factor matrix of sight.Here latent factor matrix I _{N * f}With

In element be model parameter, in decomposable process, the method that descends through gradient at random minimizes objective function

Obtain model parameter, wherein r _JkBe the scoring of article j under sight k, || || _FExpression Frobenius norm, I _iAnd C _kDifference representing matrix I _{N * f}The capable and matrix of i K capable; Article conceal factor matrix I _{N * f}Reflected the implicit features of article, the capable implicit features vector of promptly representing article i with respect to sight of its i with respect to sight.

5. a kind of collaborative filtering method according to claim 1 based on sight implicit relationship between article; It is characterized in that described step 3) is: utilize Pearson correlation coefficient to calculate article, set up article implicit relationship matrix S with respect to the similarity between the implicit features vector of sight: I wherein _iExpression article i is with respect to the implicit features vector of sight, I _IfBe I _iF dimension,

Be I _iIn the mean value of each element.

6. a kind of collaborative filtering method according to claim 1 based on sight implicit relationship between article; It is characterized in that described step 4) is: (1) makes the latent factor vector of article receive its neighbours' influence in the implicit relationship information of introducing on the basis of probability matrix decomposition model between article; In common probability matrix decomposition model, the conditional probability of the latent factor matrix of article is

Wherein V representes the latent factor matrix of article, and N representes normal distribution, and its expectation is 0, and variance is σ ²I, I representation unit matrix; And in improved probability matrix decomposition model, the conditional probability of the latent factor matrix of article is Wherein Identical with common probability matrix decomposition model, remain just too distribution; And

Wherein S representes the implicit relationship matrix between article, S _IjImplicit relationship value between expression article i and the article j, N _iNeighbours' set of expression article i, promptly with the set of the nearest article of article i implicit relationship, V _iThe i that is matrix V is capable, i.e. the latent factor vector of article i; The posterior probability of the maximized latent factor matrix of ultimate demand is:

$p(U,V|R,S,{\mathrm{\σ}}_R^2,{\mathrm{\σ}}_S^2,{\mathrm{\σ}}_U^2,{\mathrm{\σ}}_V^2)\∝p\left(R\right|U,V,{\mathrm{\σ}}_R^2)p\left(U\right|{\mathrm{\σ}}_U^2)p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2),$ Wherein:

$\left\{\begin{array}{c}p\left(R\right|U,V,{\mathrm{\σ}}_R^2)={\mathrm{\Π}}_{u=1}^m{\mathrm{\Π}}_{i=1}^n{\left[N\left(R_{\mathrm{ui}}\right|U_u^T{V}_i,{\mathrm{\σ}}_R^2)\right]}^{I_{\mathrm{ui}}^R}\\ p\left(U\right|{\mathrm{\σ}}_U^2)={\mathrm{\Π}}_{u=1}^{m}N\left(U\right|0,{\mathrm{\σ}}_U^{2}I)\\ p\left(V\right|S,{\mathrm{\σ}}_V^2,{\mathrm{\σ}}_S^2)={\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|{\mathrm{\Σ}}_{j\∈N_i}{V}_j{S}_{\mathrm{ij}},{\mathrm{\σ}}_S^{2}I)\×{\mathrm{\Π}}_{i=1}^{n}N\left(V_i\right|0,{\mathrm{\σ}}_V^{2}I)\end{array}\right.$

Wherein R is user-article rating matrix; U and V represent the latent factor matrix of user and article respectively;

is the indication function; If the scoring of user u to article i arranged in R; Then

otherwise

adopt

in the method maximization steps (1) that gradient at random descends to obtain latent factor matrix U and V; And prediction the unknown is marked to use

, and then be each user-customized recommended top-N article.

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