CN106777123A - A kind of group based on two-way tensor resolution model recommends method - Google Patents

Abstract

Recommend method the invention discloses a kind of group based on two-way tensor resolution model, including：1) an interactive relation D for representing colony G, user U and product I is defined_S；2) tensor resolution model is built；3) conversion solution is carried out to tensor resolution model using Bayes's personalized ordering method, obtains the parameters value in tensor resolution model；4) g-th colony is obtained to i-th colony's preference of productAnd travel through colony preference of all commodity g-th colonies of acquisition to all products；5) g-th colony is carried out into descending sort to colony's preference of all products, and selects top n product to be pushed to g-th colony as recommended products list.Individual preference is modeled as two-way process by the present invention, can effectively reflect the true forming process of individual preference, improves the precision of group's recommendation, and with preferable robustness.

Description

A kind of group based on two-way tensor resolution model recommends method

Technical field

Recommend field the invention belongs to group, specifically a kind of group based on two-way tensor resolution model recommends (BTF- GR) method

Background technology

Social networks turns into a key activities part in social media environment already, and user can be certainly in social network-i i-platform Hair composition colony, and the preference for catching each colony is beneficial to us and deep behavioural analysis is carried out to user group, enters And be that target product and service are recommended by colony.But colony recommends to be different from individual recommendation, because colony is typically by with various Change user's composition of preference, so colony recommends to be difficult to realize.The core missions that group recommends seek to be polymerized individual preference with Colony's recommendation results are produced, existing aggregation strategy is all that the formation of colony's preference is modeled as into an one-way process, though Ran Ji colonies preference is the result of individual preference polymerization, but colony and individuality have reciprocation in real social environment, And existing aggregation strategy can not catch the influence that colony produces to individual preference, group is caused to recommend accuracy not high；User's The group property of individual character and colony is presented variation, so influence having differences property of the colony to individual preference, but it is existing Polymerization can not portray the difference of this influence so that group's recommendation results are unsatisfactory；And when existing group recommends method to be applied to During sparse data set, performance is recommended to be decreased obviously, so existing group recommendation method can not be solved under big data environment well Sparse Problem, do not possess preferable robustness.

In recent years, be decomposed into most popular recommended technology, by decompose user and product can be described interact work With, although tensor resolution is applied to be achieved in the recommendation problems such as label recommendations, ad click prediction and preferably recommends performance, But the time complexity of tensor resolution is high, is limited to data scale, so being not ideally suited under big data environment Group recommends problem.

The content of the invention

The weak point that the present invention exists for existing group's Generalization bounds, proposes a kind of based on two-way tensor resolution model Group recommends method, and to embody the reciprocation of colony and individuality in the modeling of individual preference, and it is inclined to individuality to portray colony The otherness of good influence, by polymerization, accurately individuality preference forms accurate colony's preference, so that lifting group recommends precision, and Recommend suitable for the group under extensive, sparse data environment precisely, stable.

To reach above-mentioned purpose, the technical solution adopted by the present invention is：

The present invention is to carry out in accordance with the following steps the characteristics of a kind of group based on two-way tensor resolution model recommends method：

Step one, one interactive relation for representing colony G, user U and product I of definition：The interaction Relation D_SIn, G={ G₁,...,G_g,...,G_|G|Represent colony's set, G_gRepresent any g-th colony, 1≤g≤| G |；U= {U₁,...,U_u,...,U_|U|Represent user's set, U_uRepresent u-th user；I={ I₁,...,I_i,..., I_|I|Represent product set, I_iI-th product is represented,

Step 2, using formula (1) build g-th colony in u-th user to i-th tensor resolution model of product

In formula (1),U-th user is to i-th individual preference of product in representing g-th colony； Represent individual preference of u-th user to itselfInfluence,Represent g-th belonging to u-th user Colony is to u-th individual preference of userInfluence, b_iRepresent i-th deviation of product；Represent u-th user Bulk properties is to u-th weight of user；U_u,lRepresent u-th l-th hidden variable of user, k_uRepresent u-th hidden variable of user Number；Represent l-th hidden variable of i-th product interacted with u-th user's generation；Represent belonging to u-th user G-th group property of colony is to u-th weight of user；G_g,mRepresent g-th m-th hidden variable of colony, k_gRepresent g The hidden variable number of individual colony；Represent m-th hidden variable of i-th product interacted with g-th colony's generation；

Step 3, using Bayes's personalized ordering method to the tensor resolution modelSolution is optimized, is obtained To the tensor resolution modelIn parameters value；

Step 4, g-th colony is obtained using formula (2) to i-th colony's preference of productSo as to obtain g-th group Colony preference of the body to all products：

In formula (2), Δ () is average polymerization function；

Step 4, g-th colony is carried out descending sort to colony's preference of all products, and select top n group Product corresponding to body preference is pushed to g-th colony as recommended products list.

The characteristics of group of the present invention recommends method lies also in, and the step 3 is to carry out as follows：

Step 3.1, obtain the tensor resolution model using formula (3)Object function

In formula (3),U-th user is to i-th in representing g-th colony_aThe individual preference of individual product with to i-th_bIt is individual The difference of the individual preference of product；Represent i-th_aIndividual product belongs to u-th positive feedback set of user in g-th colony, The positive feedback collection is combined into all product set crossed with u-th user mutual in g-th colony；Represent i-th_bIt is individual Product belongs to u-th negative-feedback of user and missing value set in g-th colony, and negative-feedback and missing value set are and g-th All product set that u-th user did not interact in colony；Represent logistic functions；Θ represents described Amount decomposition modelIn parameter sets, and haveλ_ΘRepresent regularization parameter；

Step 3.2, initiation parameter set Θ and regularization parameter λ_Θ；

All products in step 3.3, traversal g-th colony in u-th positive feedback set of user, and in traversal During each product one is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set Product；

Step 3.4, parameter in the parameter sets Θ is tried to achieve using stochastic gradient descent method's Gradient；In parameterWithDuring for definite value, to the parameterRenewal is iterated respectively, until convergence Untill, so as to obtain parameterOptimal value；

All products in step 3.5, traversal g-th colony in u-th positive feedback set of user, and in traversal During each product a product is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set；

Step 3.6, parameter in the parameter sets Θ is tried to achieve using stochastic gradient descent methodWithGradient； ParameterDuring for optimal value, to the parameterWithRenewal is iterated respectively, until converging to Only, so as to obtain parameterWithOptimal value.

Compared with the prior art, beneficial effects of the present invention are embodied in：

1st, the formation of colony's preference is modeled as being polymerized individual preference by the present invention first and colony produces shadow to individual preference Loud two-way process, recommends method to be modeled as being polymerized by colony's preference the one-way process of individual preference, this hair compared to existing group Bright idea about modeling more meets the real scene that colony's preference is formed, and the present invention can not only catch the friendship between colony and individuality Interaction, but also the otherness that colony produces influence on the individual preference of different user can be portrayed, so as to effectively increase Group recommends precision, obtains satisfied group's recommendation results.

2nd, the present invention is modeled as paired interactive tensor resolution by by user, colony, product three, solves tensor point The time complexity problem high that solution model is present, while tensor resolution model proposed by the present invention is due to being integrated with colony's preference, The negative effect of Sparse can be effectively reduced, so can apply to big data environment the invention enables tensor resolution model Under group recommend problem, the present invention in pairs interaction tensor resolution model can obtain higher in linear time complexity Forecast quality.

3rd, there are a large amount of sparse hidden feedback data under big data environment, directly by predicting preference score value solving model There is relatively large deviation in the individual preference of method prediction, so as to cause to recommend precision and satisfaction to decline, and the present invention seeks model Solution is converted into sequencing problem, and sort method has good adaptability for sparse hidden feedback data, can obtain accurately partially Good sequence.The present invention can obtain accurately individuality ordering of optimization preference, Jin Erju using Bayes's personalized ordering method solving model Accurate colony's ordering of optimization preference is combined into, so effectively improving the accuracy and satisfaction of group's recommendation.

4th, it is of the invention for user is provided with personalized weight, it is used to catch individual preference and group influence to different user Differentiation is acted on, and the setting of personalized weight causes that model more presses close to the real situation that individual preference is formed, and helps to obtain More preferable group recommends precision.

5th, during true group recommends environment, the strategy being usually taken is to provide a recommendation list as long as possible to realize to the greatest extent May more cover the preference of all users in colony.When recommendation list is more long, group proposed by the invention recommends method not only With preferable robustness, and performance is more excellent, so the present invention is applied to group and recommends environment.

6th, large-scale groups are because preference diversity increases so that the recommendation for large-scale groups is very difficult and not smart Really, group proposed by the present invention recommends method for the colony of different scales with preferable robustness.

7th, the present invention can be used for the digital products such as the entity products such as household electrical appliances and food, music and film, tourism route and degree Group's commending system of the service products such as vacation arrangement, can use in platforms such as the webpages and APP of computer and mobile phone, have a wide range of application It is general.

Brief description of the drawings

Fig. 1 is schematic flow sheet of the invention；

Fig. 2 is the comparison diagram of institute's extracting method of the present invention and conventional method；

Fig. 3 is represented and solution scheme for data of the invention；

Fig. 4 a are the Average Accuracy average comparison diagram of the present invention and benchmark algorithm；

Fig. 4 b are the present invention and the recall rate comparison diagram that the recommendation list length of benchmark algorithm is 5；

Fig. 4 c are the average sequence inverse comparison diagram of the present invention and benchmark algorithm；

Fig. 5 a are the Average Accuracy average comparison diagram of personalized weight and fixed weight；

Fig. 5 b are personalized weight and the recall rate comparison diagram that the recommendation list length of fixed weight is 5；

Fig. 5 c are the average sequence inverse comparison diagram of personalized weight and fixed weight.

Specific embodiment

Tensor resolution model proposed by the present invention is a kind of two-way paired interactive tensor resolution model, i.e. colony's preference Be formed as two-way process, and user, colony, product three are modeled as paired interactive relation.Group proposed by the present invention pushes away Method is recommended to set up on the basis of following 2 points hypothesis：

1st, each user in a colony has a kind of inherent preference for product.Each user is for product Inherent preference may be influenceed by affiliated colony；

2. colony is between users dramatically different for the influence of individual preference.The final preference of user is inherent inclined The comprehensive function result of good and group influence.

In the present embodiment, as shown in figure 1, a kind of group based on two-way tensor resolution model recommends method, according to following step Suddenly carry out：

Step one, one interactive relation for representing colony G, user U and product I of definition：Interactive relation D_SIn, G={ G₁,...,G_g,...,G_|G|Represent colony's set, G_gRepresent any g-th colony, 1≤g≤| G |；U= {U₁,...,U_u,...,U_|U|Represent user's set, U_uRepresent u-th user；I={ I₁,...,I_i,..., I_|I|Represent product set, I_iI-th product is represented,The modeling of traditional colony's preference only considers user U and product I Interaction, and the present invention not only allows for the interaction of user U and product I, while the interaction between colony G and user U is have also contemplated that, And had differences for this interactive intensity of different user, colony's preference idea about modeling proposed by the present invention with tradition Colony's preference idea about modeling difference it is as shown in Figure 2.

Step 2, by the interactive relation of colony G, user U and product I carry out it is interactive in pairs decompose, colony G, user U and The data of product I are represented with paired interactive tensor resolution model proposed by the present invention as shown in figure 3, Fig. 3 also show this hair The difference of the tensor resolution model of bright proposition and traditional tensor resolution model, in recycling formula (1) just can build g-th colony U-th user is to i-th tensor resolution model of product

In formula (1),U-th user is to i-th individual preference of product in representing g-th colony； Represent individual preference of u-th user to itselfInfluence,Represent g-th belonging to u-th user Colony is to u-th individual preference of userInfluence, b_iRepresent i-th deviation of product；Represent u-th user's Individual character is to u-th weight of user；U_u,lRepresent u-th l-th hidden variable of user, k_uRepresent u-th hidden change of user Amount number；Represent l-th hidden variable of i-th product interacted with u-th user's generation；Represent belonging to u-th user G-th colony group property to u-th weight of user；G_g,mRepresent g-th m-th hidden variable of colony, k_gRepresent the The g hidden variable number of colony；Represent m-th hidden variable of i-th product interacted with g-th colony's generation；

Step 3, using Bayes's personalized ordering method to tensor resolution modelSolution is optimized, is opened Amount decomposition modelIn parameters value, will the direct solution of individual preference be converted into the sequence of individual preference；

Step 3.1, solution tensor resolution modelU-th user in g-th colony is given, u-th use is tried to achieve The optimized parameter at family, so showing that the learning objective of tensor resolution model is exactly to maximize according to Bayes's personalized ordering method Posterior probability in formula (2)

In formula (2), Θ represents tensor resolution modelIn parameter sets, and have Represent ordering of optimization preference of u-th user in g-th colony to all products；Expression is obtained by sample set G-th colony in u-th user to the individual preference likelihood function of all products；Represent the priori of parameter. Wherein likelihood functionFormula (3) can be expressed as：

In formula (3),U-th user in g-th colony is represented in the ordering of optimization preference of all products, productCome productAbove, and each pair product sequence independently of other products pair sequence；Represent g-th U-th user of colony is compared to product i_bFor productIndividual preference probability, while formula (4) can be expressed as：

In formula (4),U-th user is to i-th in representing g-th colony_aThe individual preference of individual product with to i-th_bIt is individual The difference of the individual preference of product；Represent logistic functions.According to this transform mode, and assume the elder generation of parameter Test knowledgeIt is 0 to obey average, and covariance matrix is ∑_ΘGaussian Profile, then in formula (2) posterior probability logarithmic form Formula (5) can be reduced to:

Tensor resolution modelLearning objective be just converted into minimize formula (6) object function

In formula (6),Represent i-th_aIndividual product belongs to u-th positive feedback set of user in g-th colony, positive and negative Feedback collection is combined into all product set crossed with u-th user mutual in g-th colony；Represent i-th_bIndividual product belongs to U-th negative-feedback of user and missing value set in g-th colony, negative-feedback and missing value set are and u in g-th colony All product set that individual user did not interact；λ_ΘRepresent regularization parameter；

Step 3.2, initiation parameter set Θ and regularization parameter λ_Θ；

All products in step 3.3, g-th colony of traversal in u-th positive feedback set of user, and traveling through each During product a product is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set；

Step 3.4, parameter in parameter sets Θ is tried to achieve using stochastic gradient descent methodLadder Degree；In parameterWithDuring for definite value, to parameterRenewal is iterated respectively, untill convergence, So as to obtain parameterOptimal value；

All products in step 3.5, g-th colony of traversal in u-th positive feedback set of user, and traveling through each During product a product is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set；

Step 3.6, parameter in parameter sets Θ is tried to achieve using stochastic gradient descent methodWithGradient；In parameterDuring for optimal value, to parameterWithRenewal is iterated respectively, untill convergence, so as to obtain ParameterWithOptimal value.

Step 4, g-th colony is obtained using formula (7) to i-th colony's preference of productSo as to obtain g-th group Colony preference of the body to all products：

In formula (7), Δ () is average polymerization function；

Step 4, g-th colony is carried out into descending sort to colony's preference of all products, and select top n colony inclined Good corresponding product is pushed to g-th colony as recommended products list.

Experimental demonstration is carried out for the inventive method, is specifically included：

1) standard data set is prepared

The present invention uses CiteULike and Last.fm, and the two are recommending the widely used data set in field as standard Data set verifies that group proposed by the present invention recommends the performance of method.First data set CiteULike is a scientific researcher On-line communities website.On CiteULike, scholar can use label for labelling academic article, while can also create and add Group shares the article of reference.The CiteULike data sets that experiment is used include 130321 " colony-user-product " ternarys Group, 11168 articles therein are formed by from 584 the 1310 of colony user annotations, and average population size is 5.4, from Preceding 10 articles are selected in each colony as test set, remaining data are used as training set；Second data set Last.fm be The individual on-line communities website towards musomania.On Last.fm, musomanias can mark musician or song, create or Person with have the humanoid into colony of similar grade.The Last.fm data sets that experiment is used contain 317907 " colonies-user-product Product " triple, 1992 musicians therein are formed by from 2716 the 3605 of colony user annotations, and equal group size is 21.2, preceding 10 musicians in each colony are selected as test set, remaining data are used for training set.

2) evaluation index

It is the recall rate (Rec N) of N to use length of recommended, and Average Accuracy average (MAP) and average sequence are (MRR) reciprocal The evaluation index tested as this.Recall rate assessment group commending system returns to the ability of all Related products, and Average Accuracy is equal Value and average sequence inverse are disclosed in the accuracy of Related product in recommendation list.Recommendation list length is the recall rate Rec@N of N Computing formula is：

In formula (8), N_relatedIt is the product number occurred simultaneously in sorted lists and test set；N is phase in test set Close the number of product.

Average Accuracy mean value computation formula is：

In formula (9), wherein | G | is the number of colony in test set,It is an indicator variable, if colonyRecommendation During the product of ranking n-th also appears in test set in list, then value is 1, and remaining situation is all 0.The recommendation of expression The accuracy rate of result, formula is：

In formula (10), whereinIt is the product number occurred simultaneously in sorted lists and test set,It is to recommend row The number of Related product in table.

Average sequence inverse is that the inverse company of first correct product of sequence multiplies, and computing formula is：

3) tested on standard data set

In order to verify that the present invention puies forward the validity of model, we are by the two-way tensor for group's recommendation proposed by the present invention Decompose (BTF-GR) model and 4 kinds of pedestal methods are compared, 4 kinds of pedestal methods are：Collaborative filtering based on user (UserCF) method-arest neighbors (UserKNN) algorithm based on user, collaborative filtering (ItemCF) method based on product- Arest neighbors (ItemKNN) algorithm based on product, matrix decomposition (IMF) method based on hidden feedback, the shellfish based on matrix decomposition Leaf this personalized ordering (BPRMF) method.It is modeled with 5 kinds of methods on CiteULike data sets and Last.fm data sets And recommendation, and recommendation results are compared.Experimental result is as shown in Fig. 4 a, Fig. 4 b, Fig. 4 c.Compared with 4 kinds of pedestal methods, this Inventing the group for proposing recommends method all to obtain more excellent recommendation precision on Last.fm and CiteULike data sets, and for Sparse hidden feedback data, performance advantage of the invention is more obvious.

In order to detect that personalized weight proposes the influence of model for the present invention, we unify by for all individual settings Fixed weight construct a receptor model, as control experiment.Solid line represents the present invention in Fig. 5 a, Fig. 5 b, Fig. 5 c Two-way tensor resolution (BTF-GR) model result, dotted line is the result of receptor model.Result is displayed in CiteULike data On collection and Last.fm data sets, two-way tensor resolution (BTF-GR) model is always better than the receptor model with fixed weight.This The explanation of individual result, user preference and group influence play different effects in the forming process of personal preference, and two-way tensor Decomposing (BTF-GR) model can capture this species diversity, so as to obtain preferably recommend precision.

The robustness of model is put forward for the checking present invention, and understands the robustness contrast situation with 4 kinds of pedestal methods, I By changing recommendation list length and population size, separately designed 2 experimental groups and verified.Experimental result shows this hair Bright two-way tensor resolution (BTF-GR) model all has preferable robustness in recommendation list length and population size, And recommend precision to be better than 4 kinds of pedestal methods all the time, while when recommendation list is more long, two-way tensor resolution (BTF-GR) of the invention Model performance is more excellent, i.e., the present invention is applied to group and recommends environment.

Claims (2)

1. a kind of group based on two-way tensor resolution model recommends method, it is characterized in that carrying out in accordance with the following steps：

Step one, one interactive relation for representing colony G, user U and product I of definition：The interactive relation In DS, G={ G₁,...,G_g,...,G_|G|Represent colony's set, G_gRepresent any g-th colony, 1≤g≤| G |；U= {U₁,...,U_u,...,U_|U|Represent user's set, U_uRepresent u-th user；1≤u≤|U|；I={ I₁,...,I_i,..., I_|I|Represent product set, I_iRepresent i-th product, 1≤i≤| I |；

Step 2, using formula (1) build g-th colony in u-th user to i-th tensor resolution model of product

${\hat{z}}_{g,u,i}={\mathrm{\ω}}_u^U\·\underset{l=1}{\overset{k_u}{\Σ}}{U}_{u,l}\·I_{i,l}^U+{\mathrm{\ω}}_u^G\·\underset{m}{\overset{k_g}{\Σ}}{G}_{g,m}\·I_{i,m}^G+b_i---\left(1\right)$

In formula (1),U-th user is to i-th individual preference of product in representing g-th colony；Table Show individual preference of u-th user to itselfInfluence,Represent g-th group belonging to u-th user Body is to u-th individual preference of userInfluence, b_iRepresent i-th deviation of product；Represent u-th individuality of user Characteristic is to u-th weight of user；U_u,lRepresent u-th l-th hidden variable of user, k_uRepresent u-th hidden variable of user Number；Represent l-th hidden variable of i-th product interacted with u-th user's generation；Represent belonging to u-th user The g group property of colony is to u-th weight of user；G_g,mRepresent g-th m-th hidden variable of colony, k_gRepresent g-th The hidden variable number of colony；Represent m-th hidden variable of i-th product interacted with g-th colony's generation；

Step 3, using Bayes's personalized ordering method to the tensor resolution modelSolution is optimized, institute is obtained State tensor resolution modelIn parameters value；

Step 4, g-th colony is obtained using formula (2) to i-th colony's preference of productSo as to obtain g-th colony pair Colony's preference of all products：

${\hat{r}}_{g,i}=\mathrm{\Δ}\left({\hat{z}}_{g,u,i}\right)---\left(2\right)$

In formula (2), Δ () is average polymerization function；

Step 4, g-th colony is carried out into descending sort to colony's preference of all products, and select top n colony inclined Good corresponding product is pushed to g-th colony as recommended products list.

2. group according to claim 1 recommends method, it is characterized in that, the step 3 is to carry out as follows：

Step 3.1, obtain the tensor resolution model using formula (3)Object function

$f_{g,u,i_a,i_b}=\arg \underset{G,U,I}{min}\underset{g\∈G}{\Σ}\underset{u\∈U}{\Σ}\underset{i_a\∈I_{gu}}{\Σ}\underset{i_b\∈I\backslash I_{gu}}{\Σ}(-ln\mathrm{\σ}(\widehat{z_g},u,i_a,i_b)+{\mathrm{\λ}}_{\mathrm{\Θ}}|\left|\mathrm{\Θ}\right|{|}^2)---\left(3\right)$

In formula (3),U-th user is to i-th in representing g-th colony_aThe individual preference of individual product with to i-th_bIndividual product Individual preference difference；i_a∈I_guRepresent i-th_aIndividual product belongs to u-th positive feedback set of user, institute in g-th colony State positive feedback collection and be combined into all product set crossed with u-th user mutual in g-th colony；ib∈I\I_guRepresent i-th_bIndividual product Product belong to u-th negative-feedback of user and missing value set in g-th colony, and negative-feedback and missing value set are and g-th group All product set that u-th user did not interact in body；Represent logistic functions；Θ represents the tensor Decomposition modelIn parameter sets, and haveλ_ΘRepresent regularization parameter；

Step 3.2, initiation parameter set Θ and regularization parameter λ_Θ；

All products in step 3.3, traversal g-th colony in u-th positive feedback set of user, and traveling through each During product a product is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set；

Step 3.4, parameter U in the parameter sets Θ is tried to achieve using stochastic gradient descent method_u,l,G_g,m,b_iLadder Degree；In parameterWithDuring for definite value, to the parameter U_u,l,G_g,m,b_iRenewal is iterated respectively, until convergence Untill, so as to obtain parameter U_u,l,G_g,m,b_iOptimal value；

All products in step 3.5, traversal g-th colony in u-th positive feedback set of user, and traveling through each During product a product is arbitrarily selected from g-th colony in u-th negative-feedback of user and missing value set；

Step 3.6, parameter in the parameter sets Θ is tried to achieve using stochastic gradient descent methodWithGradient；In parameter U_u,l,G_g,m,b_iDuring for optimal value, to the parameterWithRenewal is iterated respectively, untill convergence, from And obtain parameterWithOptimal value.