Random Group Recommendation ModeI Based on Fuzzy CIustering

Zhe Ding | Zhen Qin | Qi-Xu Wang | Zhi-Guang Qin

Abstract—The group recommendation system is a viral requirement for the Internet service provider to provide recommendation services for all the users in a group.Due to the shared or different interests among users in the group,it is difficult for traditional personal recommendation algorithms to predict items that can meet the requirements of all the users in the group.In this paper,a random group recommendation model is proposed to recommend the top K most appealing items for all the users in a random group.By analyzing item ratings of all the users in the group,the recommendation model can abstract the group as a virtual user.Then a personal recommendation algorithm is applied to suggest the top K most appealing items for the virtual user.And the preference score and fuzzy clustering algorithm based on multiclass are applied to optimize the recommendation result of the group recommendation model.Finally,the MovieLens-100K dataset is applied to verify the efficiency of the recommendation model.The experimental results show that the items recommended by the proposed group recommendation model are more popular for all the users in the group than the items recommended by traditional group recommendation algorithms.

1.Introduction

With the development of Internet technologies,online services have become indispensable parts in our lives.It is very difficult for human perception to obtain the information that users really need by analyzing a huge amount of information on the Internet.As a consequence,the information overload problem has become more and more serious.The recommendation system is a successful technology for overcoming the information overload problem[1].Through analyzing huge amounts of user information,recommendation systems can be applied to model personal preferences in order to suggest suited items to users.Nowadays,there are many studies on the personal recommendation system (PRS) which can produce the recommendation of unrated items to a user based on his or her previous preferences[2].However,in some domains,recommendation systems provide services to all the users in a group rather than an individual user.The preferences of users in a group may be similar or conflicting.As a result,PRS cannot be directly applied to recommend suitable items to all the users in the group.

The group recommendation system (GRS) can be applied to discover the suitable items that satisfy the preferences of all the users in a group[3].There are two categories of studies on GRS.The first category is that all the users in a group have similar preferences.In this category,users in the same group become highly internally correlated,so that group preferences can be centralized over time,and can then be easily found to satisfy every user in the group[4].The second category is that the interests of all the users in a group are random.The preferences of users in the group may be similar or conflicting.As a result,the group may have high confliction group preferences[5].In the paper,we focus on GRS based on the random group.

In this paper,we propose the recommendation model to recommend the topKmost appealing items for all the users in a random group.One successful method for GRS is extending PRS to GRS[6].For our recommendation model,according to the item ratings of all the users in a group,the profile of a virtual user is modeled to represent the preferences of all the users in the group for common items.And then PRS based on collaborative filtering (CF)is applied to recommend the topKappealing items for the virtual user.The recommendation results are also suited for all the users in the group.

CF has been successfully applied in PRS.The underlying assumptions behind recommendation systems based on CF are as follows:1) Users’ preferences are consistent over time[7]and 2) users with similar behaviors on the observed items (e.g.,ratings) have similar taste on the unobserved items.But the second assumption is not always tenable.In reality,two users have a similar preference on one item subset and may have totally different preferences on another set[8].In this paper,we apply the co-clustering model[9],[10],which has an assumption that each user and item can belong to multiple clusters,to improve the efficiency of the proposed group recommendation model.

In this paper,we also apply the preference score[7]to further improve the efficiency of the proposed recommendation model.Through analyzing different rating distributions of users to items,the preference score can identify latent user preferences from user ratings.And the preference score is easy to incorporate PRS based on CF[7].To summarize,our key contributions are the followings.

1) A new group recommendation model based on fuzzy clustering,which is denoted as GRMFC,is proposed to recommend the topKmost appealing items for all the users in a random group.

2) By importing public data to the proposed model,experimental results show that the proposed recommendation model is more effective than the traditional group recommendation models.

The rest of this paper is organized as follows.Section 2 presents an overview of related work on RPS and GRS.In Section 3,we describe the proposed group recommendation model.In Section 4,we utilize public data to evaluate the efficiency of the proposed group recommendation model.Finally,conclusions are given in Section 5.

2.ReIated Work

The CF method makes automatic predictions about the interests of a user by analyzing the preferences or taste information of many users[1].There are two categories of research on PRS based on CF[11].The first category is PRS based on the neighborhood model.Based on the similarity between users or items,PRS based on the neighborhood model applies the aggregation function to generate predictions for the target user[12].The second category is PRS based on the latent factor model.The research on the second category can utilize matrix factorization techniques to discover latent interests of users from the observed ratings[13],[14].Nowadays,there are many studies which introduce the clustering technology to the recommendation model based on CF.In 2005,Xueet al.applied the Pearson correlation-coefficient function to measure the similarity between users in order to generate the cluster for users.And then the clustering result is utilized to optimize the results of recommendation systems[15].In 2010,Gong applied item clustering to fill vacant ratings for users in order to improve the efficiency of recommendation systems[16].In 2005,George and Merugu applied the weighted co-clustering algorithm which involves simultaneous clustering of users and items to improve the efficiency of recommendation systems[17].Most clustering algorithms applied in the recommendation model have an assumption that a user or an item belongs to a single cluster.In reality,users or items maybe fall into several clusters[9].In 2016,Buet al.introduced a multiclass co-clustering model which captures relationships of user-to-item,user-to-user,and item-to-item simultaneously to PRS[8].In 2016,Leeet al.made use of the preference score to optimize the recommendation result of PRS[7].

GRS has been commonly adopted in many fields such as tourism[18]and entertainment[19].There are two major strategies for GRS[3].The first strategy is the aggregation of individual recommendation lists.In the first strategy,PRS is applied to recommend the suited item lists for all the members in a group.And then all the recommended lists are merged into a single list recommended to all the members in the group[19].Based on the recommendation items for all members in a group,Baltrunaset al.proposed a rank aggregation method to generate the joint ranking of the items recommended to the group[20].The second strategy is the aggregation of the individual rating.In the second strategy,according to the rating of all the members in a group,the preferences of a virtual user are created by different aggregation functions.And then PRS is applied to recommend the suited items to the virtual user.The recommended items for the virtual user are also suited for the whole group.In 2016,based on the separable nonnegative matrix factorization technique on a group rating matrix,Wanget al.proposed the member contribution score model[6].Based on the aggregation of the individual rating,Ortegaet al.proposed group recommendations using matrix factorization based on CF[21].By comparing the experimental results of these two strategies,Berkovsky and Freyne found that the second strategy is better than the first strategy[5].

3.Proposed ModeI

In this paper,we propose a group recommendation model to suggest the topKmost appealing items for all the users in a random group.Our model has three phases.For a random group,in the first phase,according to the item ratings of all the users in the group,the average strategy is applied to create the item ratings of a virtual user.The rating of the virtual user to an item represents the preferences of all the users in the group to the item.In the second phase,the multiclass co-clustering model[6]is applied to obtain clusters which contain the virtual user.For each cluster,PRS based on CF is applied to recommend the suited items for the virtual user.And the preference score[7]is applied to optimize the recommendation results.In the third phase,according to the recommendation results for the virtual user in all the clusters containing the virtual user,the function of the weighted sum is applied to obtain the final recommendation results for the group.

3.1.Preferences of AII the Users in a Group

In this section,based on the item ratings of all the users in a group,the average strategy is applied to create the ratings of the virtual user to all the items.LetG={g1,g2,…,gm} be the set ofmusers that belong to the groupG.And letI={i1,i2,…,in} be the set ofnitems.The rating of the virtual userutoin(1≤n≤i) is denoted asru,inand can be obtained by

whererg,inis the rating of the usergtoinandU={g∣g∈G,rg,in≠0}.Ru,I={ru,i1,ru,i2,…,ru,in} is a set of the ratings of the virtual useruto all the items inI.

3.2.MuIticIass Co-CIustering

The multiclass co-clustering was proposed in [8].In this section,the multiclass co-clustering model is applied in GRMFC to find all the clusters containing the virtual useru.For the multiclass co-clustering model,the fuzzyc-means is applied to cluster all the items and the users tocclasses.Those users include the virtual user and the users not contained in the groupG.

Suppose that there are the ratings ofs-1 users,who are not contained in the groupG,to all the items inI.The user-to-item matrix R is shown in (2):

wherer1,j(1≤j≤n) is the rating of the virtual useruto the itemijandrk,j(1＜k≤s,1≤j≤n) is the rating of the userk,who is not contained in the groupG,to the itemij.The steps for multiclass clustering in GRMFC are shown as follows.

Step 1:Based on the user-to-item matrix R,the Pearson correlation is applied to measure the similarities between users and between items,respectively.The similarity between the userpand userq,denoted as sim(p,q),can be obtained by

whereIp,q={k∣rp,k≠0,rq,k≠0}, which is the set of users whose rating for the itemkis not equal to 0 and ¯rpis the average rating of the userp.The similarity between items is computed in a similar way.As a consequence,the user-to-item matrix R is applied to represent the relationship of user-to-item.The matrix H∈Rs×sis applied to represent the relationship of user-to-user where each elementHm,nis the Pearson correlation between the useruand userv.The matrix L∈Rn×nis applied to the relationship of item-to-item where each elementLi,jis the Pearson correlation between the itemiand itemj.

Step 2:The matrix F shown as (4) is applied to represent the relationship of user-to-item,user-to-user,and item-to-item[6]:

where Esis an identity matrix in the size ofs×s.andare two diagonal degree matrices.Andwhereis an element inandwhereis an element in.THis a diagonal degree matrix whose diagonal elementsatisfies.TLis a diagonal degree matrix whose diagonal element.The detail of the matrix loss has been shown in [8].

Step 3:Thersmallest eigenvalues of the matrix F are obtained and x1,x2,…,xrare eigenvectors corresponding to those eigenvalues and are sorted by their corresponding eigenvalues.The first row in the matrix X=[x1,x2,…,xr]is the information of the virtual user.The other rows in X are the information of all the items and users who are not contained in the groupG.

Step 4:The fuzzyc-means[22]is applied to cluster all the users and items tocclasses.Thec-means minimizes the loss function shown in (8) to cluster all the items and users tocclasses,where P is a membership matrix,V is a center matrix,Pi,jis the membership of entry xi(a user or an item) in classj,and vjis the center of classj.The functiondis the Euclidean distance andlis 2.Thec-means applies (9) and (10) to updatePi,jand the center of class.

3.3.Recommendation

In subsection 3.2,GRMFC can obtain all the clusters which contain the virtual useru.In this section,PRS is applied to recommend the items for the virtual useru.And the preference score,proposed by Leeet al.[7]to optimize the personal recommendation result,is applied to optimize the group recommendation results in this paper.

Suppose thatQ={q1,q2,…,qz} (1≤z≤c) is the set of classes containing the virtual useruand is provided by the multiclass co-clustering algorithm.The rating matrix of Pqi(1≤i≤z) is a submatrix of R and shown as

wheret1,j(1≤j≤bi) is the rating of the virtual useruto the itemjcontained in the cluster qi.Andtk,j(1＜k≤ai,1≤j≤bi)is the rating of the userk,who is not contained in the groupGwhile is contained in the cluster qi,to the itemj.

For Pqi,={tk,i∣tk,i≠0,1≤i≤bi} is a set of the items.And the ratings of the userkto all the items belonging toare not equal to 0.The preference score of the usermto the itemjis shown in (11):

where pref＞(tm,j)=∣{tm,k∣1≤k≤mqi,tm,j＞tm,k}∣,pref=(tm,j)=∣{tm,k∣1 ≤k≤mqi,tm,j=tm,k}∣,α=1, andβ=0.5.

For qi,based on the preference score,the personal recommendation algorithm based on singular value decomposition (SVD) is applied in GRMFC to predict the interesting level of unknown items for the virtual user as(12):

where piis the factor of the useriand qjis the factor of the itemj.Finally,for Pqi,the interesting level of the virtual useruto the unknown itemiis obtained as

where puis the factor of the virtual useruand piin (13) is the factor of the unknown itemiin qi.

For all the classes containing the virtual useru,supposeuu,iis the relative weight of the virtual userubelonging to class qj.As a consequence,the interesting level of the virtual useruto the unknown itemiis obtained as

4.Performances EvaIuation

In this paper,the MovieLens-100K dataset is applied to verify the efficiency of GRMFC.This dataset contains 100000 anonymous ratings of 1682 movies provided by 962 users.For each specific group size,i.e.,3,6,9,12,15,and 18,1500 groups are randomly generated.And 40% group ratings are selected as the test ratings and these ratings are not used during the learning phase.

4.1.EvaIuation Metric

GRMFC suggests the topKappealing items for all the users in a group.In this paper,averageF1 and average nDCG are applied to verify the quality of experimental results.For the groupG,F={i∣u∈G,ru,i≥4} is the set of the items and the ratings of all the users in the group to these items are greater than 4.AndF^ is a set of the items provided by the recommendation model.F1 of the group is shown as

In this paper,averageF1 for 1500 groups is applied to verify the quality of the experimental results.

For the useruin the groupG,suppose the sequence ofI1,I2,…,IKis the recommendation list provided by the group recommendation model.nDCG for the userucan be obtained by

whereru,Iiis the rating of the useruto the itemIiin the test data set.IDCGu,Kis the optimal possible gain value foru.In the groupG,(20) is applied to obtain nDCG for a user.nDCG for the group is the average of nDCG for all the users.In this paper,we make use of average nDCG for 1500 groups to verify the quality of the recommendation model.

4.2.Adjusting Parameters

There are 3 parameters in GRMFC.The first parameterris the number of eigenvectors for the matrix F in Step 3 of the multiclass clustering process.The second parametercis the number of classes forc-means in Step 4 of the multiclass clustering process.The third parameterkis the dimension of SVD in (13).In this section,5-fold cross validation is applied to obtain these parameters.And we make use of GRMFC to suggest top 20 items for the group which has 6 users.According to the recommendation results,we can obtain those parameters.

To estimate the first parameterr,we set other parameters as fixed values (e.g.,c=20 andk=20).Then we trained the model with differentrfrom 1 to 10.The experimental results show that when the value ofris greater than or equal to 6,the stable recommendation performance can be obtained.The values of averageF1 and nDCG are equal to 0.12 and 0.28,respectively.So we setras 6 in the following experiments.

To estimate the second parameterc,we set other parameters as fixed values (e.g.,r=6 andk=20).Then we trained the model with differentcfrom 5 to 30.The experimental results show that when the value ofcis greater than or equal to 25,the stable recommendation performance can be obtained.The values of averageF1 and nDCG are equal to 0.17 and 0.21,respectively.So we setcas 25 in the following experiments.

To estimate the first parameterk,we set other parameters as fixed values (e.g.,c=25 andr=6).Then we trained the model with differentkfrom 5 to 35.The experimental results show that when the value ofkis greater than or equal to 30,the stable recommendation performance can be obtained.The values of averageF1 and nDCG are equal to 0.21 and 0.42,respectively.So we setkas 30 in the following experiments.

4.3.Contrast Experiments

In this section,there are 3 contrast experiments in this paper.Letru,ibe the rating of the useruin the groupGto the itemi.These contrast experiments are shown as follows.

1) Group recommendation based on the least misery strategy[3],denoted as GRLM.

The least misery strategy is applied to create the profile of the groupG.The rating of the groupGto the itemiin the group profile can be obtained as

where min(ru,i) means the minimum nonzero-rating of all users in the groupGto the itemi.And then basic userbased CF is applied to suggest the topKmost popular items to the groupG.

2) Group recommendation based on the average strategy[19],denoted as GRAS.

The average strategy is applied to create the group profile of the groupG.And then basic user-based CF is applied to suggest the topKmost popular items to the groupG.

3) Group recommendation based on SVD[21],denoted as GRSVD.

The average strategy is applied to create the group profile of the groupG.And SVD is applied to recommend items for the groupG.

4.4.AnaIysis of Experiment ResuIts

GRMFC can recommend the topKmost popular items to all the users in a group.We carried out two experiments to verify the efficiency of the recommendation model.

In the first experiment,we set the size of a group as 6.With the increase ofK,the tendencies of averageF1 and average nDCG are showed in Fig.1.AverageF1 and average nDCG of all the recommendation algorithms are improved by increasingK.When the value ofKis greater than or equal to 12,GRMFC performs better and averageF1 is larger than 0.24.And when the value ofKis greater than or equal to 12,average nDCG of GRMFC is larger than 0.3.

AverageF1 and average nDCG of GRMFC are better than those of other recommendation algorithms.Because the preference model can obtain the distribution of the ratings for all the users including the virtual user and the users not contained in the groupG.For multiclass co-clustering,in the cluster containing the virtual user,the interests of the users not contained in the groupGare more similar with those of the users contained in the cluster while not containing the virtual user.As a consequence,GRMFC can be more accurate in terms of the interesting level of the unknown items for the groupG.

In the second experiment,we set the value ofKas 30.With the increase of group size,the tendencies of averageF1 and average nDCG are showed in Fig.2.AverageF1 and average nDCG of all the recommendation algorithms are increasing with the increase of group size.When the value of group size is larger than or equal to 12,averageF1 of GRMFC is less than 0.21.And when group size is larger than or equal to 12,average nDCG of GRMFC is less than 0.27.AverageF1 and average nDCG of GRMFC are better than those of other recommendation algorithms.It means that the recommendation results of GRMFC are more popular than those of other recommendation algorithms for each user in the groupG.

5.ConcIusions

In this paper,the random group recommendation model based on fuzzy clustering was proposed to recommend topKmost popular items to all the users in a group.The model was based on the personal recommendation algorithm and applied the preference model and multiclass co-clustering to optimize the recommendation results.The experimental results on the MovieLens-100K dataset showed that with the increase ofKand the group size,the precision of GRMFC is better than that of the traditional group recommender algorithms.