CN106227767A - A kind of based on the adaptive collaborative filtering method of field dependency - Google Patents

Abstract

A kind of based on the adaptive collaborative filtering method of field dependency, comprise the steps: that the diversity in auxiliary territory and aiming field is introduced conventional model as regularization term by (1), obtain new model:Wherein: T is the rating matrix having excalation item in target domain, and Z is the filled matrix of aiming field, Z Yu T has identical scoring item；Represent the index set of aiming field,||·||_FRepresent Frobenius norm,||·||_*Represent nuclear norm, | | Z | |_*All singular value sums for matrix Z；γ is regularization parameter, and η ∈ (0,1) represents auxiliary territory and the similarity of aiming field；(2) the canonical optimum solution Z of fixed point iteration algorithm novel model of calculating is then used_*=Z.Present invention can apply to the Internet commending system, by adaptive both estimations dependency, and be introduced into the forecast model of target domain, thus effectively realize knowledge migration, improve the recommendation precision of target domain.

Description

A kind of based on the adaptive collaborative filtering method of field dependency

Technical field

The present invention relates to the field, data mining direction in the information processing technology, particularly one based on field dependency certainly The collaborative filtering method adapted to, can be applicable to the Internet commending system.

Background technology

Growing along with information and technology of Internet of things, the Internet meets user's need in the information age to information Ask, bring and also bring bulk information process problem easily simultaneously.User cannot be therefrom when in the face of magnanimity information Obtain the part information actually useful to oneself so that the service efficiency of big data is reduced on the contrary, occurs in that so-called letter Breath overload problems.Solving one way the most potential of information overload problem is commending system.Commending system should in many Using and play key player, such as, as Amazon, in the e-commerce field such as Taobao, it can help user from a large number Object (such as books, film, music, joke and webpage) in filter out product interested or article.

In recent years, collaborative filtering (CF), as one of a kind of maximally effective proposed algorithm, is paid close attention to widely.When (such as scoring, grade or add up number of clicks) after project is evaluated by user, the scoring square of a user-project can be generated Battle array.Owing to a small amount of project is only evaluated by usual user, therefore rating matrix comprises substantial amounts of unknown-value i.e. missing values. Collaborative filtering (CF) utilizes given data in rating matrix to calculate the similarity between user or project, and utilize similar users or Missing values is predicted by the scoring of project, finally according to predictive value by user may project recommendation interested to user.Pass The collaborative filtering of system includes project-based collaborative filtering, collaborative filtering based on user and based on model Collaborative filtering.In recent years, the efficient proposed algorithm based on collaborative filtering has made further progress.Its In, collaborative filtering based on matrix decomposition is paid close attention to widely.For comprising the rating matrix of missing values, matrix decomposition Technology by becoming the product of two or three low-rank matrix to realize the prediction to missing values by its approximate factorization.

But, when user is only evaluated in very small amount of project, rating matrix can be the most sparse.Now, Common matrix decomposition technology is difficult to be suitable for.Openness problem is also the significant challenge that collaborative filtering faces.Transfer learning It it is a kind of feasible method solving problems.Although the project in current goal field is marked considerably less by user, but user can In other association area (referred to as field of auxiliary), sundry item can be carried out some to evaluate.The purpose of transfer learning is profit By the knowledge of field of auxiliary study, help the scoring of target domain is predicted.Existing transfer learning method is faced with down Some common problems in face:

(1) algorithm typically requires multiple input parameter.Existing transfer learning method is mostly based on matrix decomposition technology and carries Take user or the item characteristic in auxiliary territory, need dimension as input parameter.In addition it is also necessary to auxiliary territory and the phase of aiming field Closing property parameter, and two to three regular terms parameters.The debugging of parameter brings the biggest to algorithm application in practical problem Difficulty.

(2) higher to the data demand of field of auxiliary.Existing transfer learning method requires to assist territory and aiming field mostly There is common user；The project requiring auxiliary territory and aiming field has stronger dependency；Require that user is to auxiliary territory and target The project in territory has similar evaluation method；The user characteristics requiring auxiliary territory and aiming field has identical dimension.These are right The requirement in auxiliary territory reduces the practicality of transfer learning method significantly.

(3) for large-scale data, the amount of calculation required for some transfer learning algorithms is the biggest.In actual applications, logical Often relating to process the mass users scoring to project, amount of calculation required for algorithm is excessive directly limit its practicality.

Summary of the invention

Present invention is primarily targeted at and overcome drawbacks described above of the prior art, propose one based on field dependency certainly The collaborative filtering method adapted to, by adaptive auxiliary territory and the dependency of aiming field of calculating, the most abundant and effective profit Assist the score data in territory with user, thus help the score in predicting precision improving user at target domain.

The present invention adopts the following technical scheme that

A kind of based on the adaptive collaborative filtering method of field dependency, it is characterised in that to comprise the steps:

(1) auxiliary territory and the diversity of aiming field are introduced conventional model as regularization term, obtain new model:

$\underset{Z}{min}\left\{\frac{1}{2}\right|\left|P_{\mathrm{\Ω}}(T-Z)\right|{|}_F^2+\mathrm{\γ}\left|\right|Z|{|}_{*}-\mathrm{\η}\mathrm{\γ}|\left|F_A^{T}Z\right|{|}_{*}\};$

Wherein: T is the rating matrix having excalation item in target domain, and Z is the filled matrix of aiming field, Z with T has phase Same scoring item；Represent the index set of aiming field,| |·||_FRepresent Frobenius norm,||·||_*Represent nuclear norm, | | Z | |_*Owning for matrix Z Singular value sum；γ is regularization parameter, and η ∈ (0,1) represents auxiliary territory and the similarity of aiming field；

(2) the canonical optimum solution Z of fixed point iteration algorithm novel model of calculating is then used_*=Z.

Preferably, in step 1) in by auxiliary domain knowledge is moved in aiming field, construct new objective matrix；A∈ R^p×qIt it is the auxiliary rating matrix that is evaluated q project of field of auxiliary obtaining of p user in target domain；Utilize auxiliary Help the user characteristics U in territory_A, project to aiming field and obtainWith | | Z | |_*-||F_A ^TZ‖_*Represent auxiliary territory and aiming field Diversity, and be incorporated into classical Lagrangian model as regularization termObtain described New model, γ > 0 is regularization parameter, and η ∈ (0,1) represents auxiliary territory and the similarity of aiming field.

Preferably, in step 1) one ratio of middle settingIt is used for describing the phase of field of auxiliary and target domain Guan Xing；Along with in iterative algorithm, Z converges on optimal solution Z_*, η converges on fixed valueWhen auxiliary territory and aiming field are complete Time relevant, the user characteristics of Z and F_AUnanimously, now η=1；When assist territory and aiming field complete uncorrelated time, the user characteristics of Z With F_AOrthogonal, now η=0.

Preferably, in step 2), use fixed point iteration algorithm to non-convex model solution, process is as follows:

2.1) low-rank utilizing classical model to solve companion matrix A approaches matrix Z_A, obtain assisting the user characteristics U in territory_A, And project to aiming field constructsΟ∈0^(m-p)×d, d is F_AOrder；

2.2) calculating Z is initialized_old=S_γ(T), Z_oldRepresent the Z value of last iteration, S_γ() is one and has soft threshold The contraction operator of value；

2.3) at K_maxZ is repeated in secondary iterative computation_old→Y→Z_newIterative operation and η adaptive iteration estimate, Until convergence K_maxRepresent algorithm maximum iteration time；

2.4) Z is made_*=Z_new。

Preferably, described 2.3) in, based on KKT condition and the concept of subgradient, utilize intermediate variable Y to be iterated, repeatedly Generation operation includes:

2.3.1) arrange

2.3.2) make Y=Z_old+P_Ω(T-Z_old)+ηγF_Ag(F_A ^TZ_old), g (F_A ^TZ_old) represent F_A ^TZ_oldSubgradient；

2.3.3) calculate Z_new=S_γ(Y)；

2.3.4) convergence is checked: whenTime, terminating iteration, ε is the control parameter of iteration ends.

From the above-mentioned description of this invention, compared with prior art, there is advantages that

One, the requirement to field of auxiliary score data is low

In existing algorithm, the score data of field of auxiliary there is the highest requirement, as required field of auxiliary and target The on all four user in field；Require that field of auxiliary has consistent dimension with the user characteristics of target domain；Require auxiliary neck The project of territory and target domain has the strongest dependency.In traditional transfer learning method, when field of auxiliary and target are led When the dependency in territory is the most weak, the field of auxiliary knowledge learnt possibly even hinder target domain is marked accurately pre- Survey.In the present invention, field of auxiliary has only to the user that part is identical with target domain, and does not require the feature in two fields There is identical dimension.The more important thing is, the present invention is by field of auxiliary and the ART network of target domain dependency, energy The most abundant and the effective field of auxiliary knowledge learnt that utilizes, help carries out score in predicting to target domain.

Two, only one of which parameter to be adjusted

Traditional transfer learning algorithm at least needs use dimensional parameter, the relevance parameter in field and regularization Multiple parameter such as parameter.In actual applications, these parameters are debugged by needs by repeating experiment, this biggest adding The calculation cost of algorithm.The present invention pertains only to a regularization parameter γ, there is the strongest practicality.

Three, required calculation cost and memory space are little

In the present invention, topmost amount of calculation concentrates on several singular values and singular vectors of maximum of solution matrix Y. In the main flow algorithm such as Lanczos method carrying out singular value decomposition, core calculations amount is to carry out the matrix-vector of shape such as Yb Be multiplied calculating.In view of matrix Y, be there is special structure: Y=Z+P_Ω(T-Z)+ηγF_Ag(F_A ^TZ)=low-rank matrix+sparse Matrix+low-rank matrix.The Practical Calculation cost of matrix Yb is the least.Assuming that r is the order of Z, d is F_AOrder, m and n is target respectively The line number of matrix and columns, then the amount of calculation carrying out matrix-vector multiplication is about Ο (| Ω |)+Ο ((m+n) (r+d)).Use Amount of calculation needed for Lanczos method solves maximum r the singular value of Y is about Ο (r | Ω |+r (m+n) (r+d)).Obviously, whole Individual amount of calculation and the scale of rating matrix and quantity of marking are linear, can apply to large-scale data.

Accompanying drawing explanation

Fig. 1 is the flow chart that the present invention adjusts based on parameter adaptive.

Detailed description of the invention

Below by way of detailed description of the invention, the invention will be further described.

With reference to Fig. 1, the method for the present invention mainly includes two steps: (1) carries on the basis of classical matrix decomposition model The transfer learning model made new advances；(2) use iterative algorithm that new model is solved, and carry out assisting territory and aiming field dependency Adaptive polo placement.

1) new transfer learning model is set up

Conventional model:

Assume that n project of target domain is evaluated by m user, constitute rating matrix T ∈ R^m×n.Note Ω=(i, J) | jth project is evaluated by i-th user }, then the index set evaluated during set omega illustrates T.At present, a kind of Classical optimizing model based on nuclear norm regular terms is

$\underset{Z}{min}\left\{\frac{1}{2}\right|\left|P_{\mathrm{\Ω}}(T-Z)\right|{|}_F^2+\mathrm{\λ}\left|\right|Z\left|{|}_{*}\right\}---\left(1\right)$

Wherein, P_Ω(T) representing matrix T projection in index set, i.e.||·‖_F Represent Frobenius norm,||·‖_*Represent nuclear norm, ‖ Z ‖_*For matrix Z all singular values it With.Here λ > 0 is regularization parameter, for the training error on having markedEnter with the order of matrix Z Row balance.Nuclear norm regularization method such as Soft-Impute optimal solution Z by solving model (1)_*, realize missing number in T According to score in predicting.

The proposition of new model:

When rating matrix T is the most sparse, due to over-fitting problem, the precision of prediction of model (1) may be the lowest.If mesh Q the project of another field (field of auxiliary) is evaluated by certain customers' (being assumed to be front p) in mark field, generates auxiliary The rating matrix A ∈ R in territory^p×q.The present invention will propose new model, utilize the knowledge in auxiliary territory to help aiming field rating matrix T's Missing values is predicted.

First, traditional collaborative filtering is utilized to extract the user characteristics in auxiliary territory.Such as, it is possible to use model (1) Calculate the approximate matrix Z of A_A.NoteFor Z_ASingular value decomposition, then U_AIllustrate the user characteristics in auxiliary territory.

Secondly as the user in auxiliary territory is only the certain customers of aiming field, need the user characteristics projection in auxiliary territory To the dimension consistent with aiming field user.A kind of simple mode is for generatingWherein Ο ∈ R^(m-p)×dZero moment Battle array.

Finally, F is utilized_AStructure auxiliary territory and the diversity of aiming field.Note Z is the filled matrix of aiming field, then assist territory ‖ Z ‖ can be defined as with the diversity of aiming field_*-‖F_A ^TZ‖_*。

Above formula is introduced model (1) as regular terms and can obtain new model

$\underset{Z}{min}\left\{\frac{1}{2}\right|\left|P_{\mathrm{\Ω}}(T-Z)\right|{|}_F^2+\mathrm{\λ}\left|\right|Z|{|}_{*}+\mathrm{\ρ}\left(\right|\left|Z\right|{|}_{*}-\left|\right|{F_A}^{T}Z\left|{|}_{*}\right)\};$

Wherein ρ is regularization parameter.Note γ=λ+ρ, ρ=η γ, then model above can further be expressed as

$\underset{Z}{min}\left\{\frac{1}{2}\right|\left|P_{\mathrm{\Ω}}(T-Z)\right|{|}_F^2+\mathrm{\γ}\left|\right|Z|{|}_{*}-\mathrm{\η}\mathrm{\γ}|\left|{F_A}^{T}Z\right|{|}_{*}\}---\left(2\right)$

Two parameters γ and η is related in model (2).γ is regularization parameter, and η ∈ (0,1) represents auxiliary territory and mesh The similarity in mark territory.When η=0, representing that auxiliary territory and aiming field are the most uncorrelated, model (2) is return as model (1)；When η= When 1, represent that auxiliary territory and aiming field are perfectly correlated.The present invention will provide the ART network algorithm of η, and therefore model (2) is actual Pertain only to parameter γ.

2) iterative algorithm solving model optimal solution is utilized

In model (2), the latter of object functionIt is non-convex, the most traditional convex It cannot be solved by the algorithm of function.Optimal solution Z of model (2)_*KKT condition should be met

$0\∈-P_{\mathrm{\Ω}}(T-Z_{*})+\mathrm{\γ}\∂\left|\right|Z_{*}|{|}_{*}-\mathrm{\η}\mathrm{\γ}\∂|\left|F_A{F_A}^T{Z}_{*}\right|{|}_{*}---\left(3\right)$

Wherein,Represent | | | |_*At Z=Z_*Subgradient.Note Z_*=USV^TFor Z_*Singular value decomposition, the most secondary ladder Degree is defined as follows:

$\∂\left|\right|Z_{*}|{|}_{*}=\{{\mathrm{UV}}^T+E:E_{m\×n},U^{T}E=0,EV=0,\left|\right|E|{|}_2\≤1\}$

NoteThen

KKT condition (3) can of equal value being expressed as

This expression means Z_*Also it is the optimal solution of following optimal problem

$\underset{Z}{min}\frac{1}{2}\left|\right|Z-Y_{*}|{|}_F^2+\mathrm{\γ}|\left|Z\right|{|}_{*}---\left(4\right)$

Here, the optimal solution of model (4) can be expressed as Z_*=S_γ(Y_*)。S_γ() is a contraction with soft-threshold Operator.Note Y_*=U_YΣV_Y ^TFor Y_*Singular value decomposition, Σ=diag (σ₁,…,σ_r), then define S_γ(Y_*)=U_YΣ_γV_Y ^T, Σ_γ =diag ((σ₁-γ)₊,…,(σ_r-γ)₊), (σ_i-γ)₊=max (σ_i-γ,0)。

Thus can derive the basic step of iteration:

$\left\{\begin{array}{c}{Z}_{old}\→Y=Z_{old}+P_{\mathrm{\Ω}}(T-Z_{old}){\mathrm{\η\γF}}_{A}g\left({F_A}^T{Z}_{old}\right)\\ Y\→Z_{new}=S_{\mathrm{\γ}}\left(Y\right)\end{array}\right..$

The algorithm steps of the present invention such as table 1 below:

Table 1

In new iterative algorithm, the present invention has carried out adaptive estimation, i.e. to the dependency in auxiliary territory and aiming fieldAlong with the convergence of iterative solution, relevance parameter η also converges on fixed valueWhen auxiliary territory and target When territory is perfectly correlated, Z_*User characteristics and F_AUnanimously, now η=1；When assist territory and aiming field complete uncorrelated time, Z_*Use Family feature and F_AOrthogonal, now η=0.Therefore, the η estimated in the present invention adaptive can calculate auxiliary territory and aiming field Dependency, to make full use of the user characteristics that auxiliary territory is extracted.

Fig. 1 is the flow chart of the present invention.In FIG, auxiliary territory is consistent with the certain customers of aiming field, auxiliary territory and target Item types and the quantity in territory differ.We extract the user of field of auxiliary first with nuclear norm regularization model (1) Feature, then moves to the feature extracted target domain, thus the low-rank obtaining objective matrix approaches matrix, finally to mesh Disappearance scoring in mark matrix is predicted.

Illustrate:

Data genaration

The data set of the present invention is from the book crossing website douban.com of Largest In China.It comprises 383033 readers 13506215 scorings to 89908 books, score value is the integer of 1～5.This experiment randomly selects 6000 and evaluated No less than the user of 20 books, similarly, randomly select 6000 and be no less than the books that 20 users evaluated.Data The scoring rate of collection is 0.57%.Score data is divided into two parts according to the kind of books by us: half generates auxiliary moment Battle array, second half generates objective matrix.The present invention choose respectively target data concentrate the 70% of every user's score value, 50% and 30% generates different training objective matrix T, and correspondingly, scoring rate is respectively 0.38%, 0.27%, 0.15%.Residue scoring Then it is used for testing precision of prediction.

Comparison algorithm and parameter are arranged

For the prediction accuracy of verification algorithm, test spectrum regularization transfer learning algorithm (TLSR) that the present invention is proposed and Three kinds of non-migratory collaborative filterings: probability matrix decomposition (PMF) [R.R.Salakhutdinov and A.Mnih, “Probabilistic matrix factorization”,Advances in Neural Information Processing Systems,vol.20.Red Hook,NY,USA:Curran Associates,2008,pp.1257- 1264], weighting Non-negative Matrix Factorization (WNMF) [S.Zhang, W.Wang, J.Ford, and F.Makedon, " Learning from incomplete ratings using non-negative matrix factorization,”in Proc.6th SIAM Int.Conf.Data Mining, Bethesda, MD, USA, Apr.2006, pp.549-553] and Soft-Impute enter Row compares, too with transfer learning algorithm: collective's matrix decomposition (CMF) [A.P.Singh and G.J.Gordon, “Relational learning via collective matrix factorization,”in Proc.14th ACM SIGKDD Int.Conf.Knowl.Disc.Data Min., Las Vegas, Nevada, USA, pp.650-658,2008.], Weighting Non-negative Matrix Factorization (GWNMF) [Q.Gu, J.Zhou and C.Dingy, " Collaborative of based on figure Filtering:Weighted Nonnegative Matrix Factorization Incorporating User and Item Graphs,”in Proc.6th SIAM Int.Conf.Data Mining,Columbus,Ohio,USA, Apr.2010, pp.199-210.] and proper subspace migration (FST) [J.Wang and L.W.Ke, " Feature Subspace Transfer for Collaborative Filtering,”Neurocomputing,vol.136,pp.1-6, Jul.2014] compare.

In the algorithm of contrast, PMF needs regularization parameter and characteristic parameter.WNMF characteristics of needs parameter.CMF and FST Capital three parameters of needs: regularization parameter, characteristic parameter and balance parameter.GWNMF need regularization parameter, characteristic parameter and Neighborhood scale parameter.The TLSR of S-IM and the present invention has only to a regularization parameter.Each parameter is chosen two or three by this experiment Individual different value carries out algorithm contrast.The setting of parameter value such as table 2 below in algorithms of different.

Table 2

Algorithm	Regularization parameter	Potential feature	Balance parameter	Neighborhood scale
					PMF	{0.01,0.1,0.5}	{5,10,15}	——	——
WNMF	——	{5,10,15}	——	——
					S-IM	{90,85,...,10}	——	——	——
CMF	{1,2,5,10,15}	{5,10,15}	{0.2,0.5,0.8}	——
					GWNMF	{1,2,5,10,15}	{5,10,15}	——	{10,20,30,}
FST	{1,2,5,10,15}	{5,10,15}	{0.3,0.6,0.9}	——
					TLSR	{90,85,...,10}	——	——	——

Evaluation index

This experiment uses root-mean-square error (RMSE) and absolute average error (MAE) to calculate precision of prediction.

$RMSE=\sqrt{\underset{(i,j)\∈{\mathrm{\Ω}}_{test}}{\Σ}{(z_{ij}-t_{ij})}^2/\left|{\mathrm{\Ω}}_{test}\right|}$

$MAE=\underset{(i,j)\∈{\mathrm{\Ω}}_{test}}{\Σ}|z_{ij}-t_{ij}|/\left|{\mathrm{\Ω}}_{test}\right|$

Wherein, Ω_testRepresent the index set of test event, z_ijRepresent prediction scoring, t_ijRepresent original scoring.

Experimental result

Each algorithm such as table 3 below of the forecast error in Semen Sojae Preparatum data

Table 2

Test result indicate that, the prediction accuracy of transfer learning algorithm is substantially high than the prediction accuracy of non-migratory algorithm. For the objective matrix of different degree of rarefications, the TLSR algorithm of the present invention, compared with other transfer learning algorithm, has the most more preferably Recommendation precision.It is important to note that the algorithm of the present invention pertains only to a regularization parameter, there is the strongest practicality Property.Additionally, due to take full advantage of the knowledge of field of auxiliary, the present invention has preferable robust to the openness of objective matrix Property.

Above are only the detailed description of the invention of the present invention, but the design concept of the present invention is not limited thereto, all utilize this Design carries out the change of unsubstantiality to the present invention, all should belong to the behavior invading scope.

Claims (5)

1. one kind based on the adaptive collaborative filtering method of field dependency, it is characterised in that comprise the steps: that (1) is by auxiliary The diversity helping territory and aiming field introduces conventional model as regularization term, obtains new model:

$\underset{Z}{min}\left\{\frac{1}{2}\right|\left|P_{\mathrm{\Ω}}(T-Z)\right|{|}_F^2+\mathrm{\γ}\left|\right|Z|{|}_{*}-\mathrm{\η}\mathrm{\γ}|\left|{F_A}^{T}Z\right|{|}_{*}\};$

Wherein: T is the rating matrix having excalation item in target domain, and Z is the filled matrix of aiming field, Z Yu T has identical Scoring item；Represent the index set of aiming field,||·||_F Represent Frobenius norm,||·||_*Represent nuclear norm, | | Z | |_*All unusual for matrix Z Value sum；γ is regularization parameter, and η ∈ (0,1) represents auxiliary territory and the similarity of aiming field；

(2) the canonical optimum solution Z of fixed point iteration algorithm novel model of calculating is then used_*=Z.

2. as claimed in claim 1 a kind of based on the adaptive collaborative filtering method of field dependency, it is characterised in that: in step Rapid 1) by moving in aiming field by auxiliary domain knowledge in, new objective matrix is constructed；A∈R^p×qIt it is the p in target domain User is evaluated the auxiliary rating matrix obtained to q project of field of auxiliary；Utilize the user characteristics U in auxiliary territory_A, projection Obtain to aiming fieldWith | | Z | |_*-||F_A ^TZ||_*Represent auxiliary territory and the diversity of aiming field, and as canonical Change item and be incorporated into classical Lagrangian modelObtain described new model, γ > 0 for regularization Parameter, η ∈ (0,1) represents auxiliary territory and the similarity of aiming field.

3. as claimed in claim 2 a kind of based on the adaptive collaborative filtering method of field dependency, it is characterised in that: in step Rapid 1) ratio is set inIt is used for describing the dependency of field of auxiliary and target domain；Along with in iterative algorithm Z converges on optimal solution Z_*, η converges on fixed valueWhen assist territory and aiming field perfectly correlated time, the user characteristics of Z with F_AUnanimously, now η=1；When assist territory and aiming field complete uncorrelated time, the user characteristics of Z and F_AOrthogonal, now η=0.

4. as claimed in claim 3 a kind of based on the adaptive collaborative filtering method of field dependency, it is characterised in that: in step Rapid 2), using fixed point iteration algorithm to non-convex model solution, process is as follows:

2.1) low-rank utilizing classical model to solve companion matrix A approaches matrix Z_A, obtain assisting the user characteristics U in territory_A, and throw Shadow constructs in aiming fieldO∈0^(m-p)×d, d is F_AOrder；

2.2) calculating Z is initialized_old=S_γ(T), Z_oldRepresent the Z value of last iteration, S_γ() is one and has soft-threshold Contraction operator；

2.3) at K_maxZ is repeated in secondary iterative computation_old→Y→Z_newIterative operation and η adaptive iteration estimate, until Convergence, K_maxRepresent algorithm maximum iteration time；

2.4) Z is made_*=Z_new。

5. as claimed in claim 4 a kind of based on the adaptive collaborative filtering method of field dependency, it is characterised in that: described 2.3) in, based on KKT condition and the concept of subgradient, utilizing intermediate variable Y to be iterated, iterative operation includes:

2.3.1) arrange

2.3.2) make Y=Z_old+P_Ω(T-Z_old)+ηγF_Ag(F_A ^TZ_old), g (F_A ^TZ_old) represent F_A ^TZ_oldSubgradient；

2.3.3) calculate Z_new=S_γ(Y)；

2.3.4) convergence is checked: whenTime, terminating iteration, ε is the control parameter of iteration ends.