Venue Recommendation is a key application for LocationBased Social Networks (LBSNs) such as Yelp and Foursquare. Bayesian Personalised Ranking (BPR) is a popular pairwise recommendation technique that can be used to recommend a ranked list of venues to users. Social information such as friendship plays an important role in venue recommendation since it can alleviate the data sparsity problem induced by cold-start users with few check-ins and rating information. Indeed, introducing social information into BPR is a promising way to further improve the e ectiveness of the underlying venue recommendation system. In this paper, we propose a novel Bayesian Personalised Ranking Social Regularisation (BPRSoReg) approach that uses social information as a regularisation method to enhance the performance of BPR. Experiments are conducted on a large-scale dataset from Yelp. The experimental results show that the BPRSoReg approach can improve over BPR by up to 54.0% in terms of mean reciprocal rank.
Matrix Factorisation (MF), a class of collaborative ltering algorithms, has
developed extensively since it has been used in recommender systems in the Net ix
Prize competition in 2009 [
To address the sparsity problem, various approaches have been proposed
in the literature to incorporate di erent sources of information including social
information [
As mentioned above, in the current literature, there are two main approaches to address the sparsity problem: either to incorporate di erent sources of information into the traditional MF technique or to leverage implicit feedback in BPR. Since BPR is based on matrix factorisation, in this paper we aim to investigate whether it is possible to integrate both approaches in a single recommender system. Our objective in this paper is therefore to propose a ranking recommender system that can incorporate social information in addition to implicit feedback. Hence, we propose the combination of the social regularisation, originally proposed for MF, into the BPR pairwise recommendation approach; Experiments on a large dataset from the Yelp LBSN demonstrate the bene t of our approach.
The remainder of this paper is structured as follows: In Section 2, we rstly describe the BPR rank-based recommender system then details of how Social Regularisation (SoReg) can incorporate social information i.e. friendship information. Since both BPR and SoReg are based on matrix factorisation, in Section 3, we show how to integrate SoReg and BPR to achieve our objective. Experimental Setup and Results are described in Sections 4 & 5. Concluding remarks follow in Section 6. 2
Bayesian Personalised Ranking: While matrix factorisation is designed for
the rating prediction task, it is not directly optimised for the ranking of venues.
In venue recommendation, the core task is to generate a personalised ranking for
users and hence users will not have to scan through all suggested venues. Instead,
they usually focus on the top ranked venues. Therefore, in many real venues
recommendation applications, giving users the best top ranked venues is more
useful than making rating predictions. Building on matrix factorisation, BPR [
OP T := ln p( j >u) = where represents the parameter vector of an arbitrary model class, is the logistic sigmoid, x^uij is an arbitrary real-valued function of the model parameter vector that captures the special relationship between user u, venue i and venue j ; is a model-speci c regularisation parameter; k:k denotes the Frobenius norm; and ln( ) is the natural logarithm. Therefore p( j >u) is the posterior probability that produces the correct personalised ranking for user u, which BPR aims to maximise through stochastic gradient descent.
Social Regularisation: Social regularisation (SoReg) is a recommendation
model proposed by Ma et al. [
MF where is a parameter controlling the amount of regularisation.
Users' decisions may be in uenced by their friends. For example users often recommend venues to their friends. It is also common for users to ask their friends for suggestions especially when they visit unfamiliar places. Based on the assumption that users are likely to be in uenced by their friends, the SoReg model introduces social information i.e. friendship information, as a regularisation term to minimise the distance between the latent representations of target user Ui and his/her friends, Uf , which further modi es Equation (3) as: L(U; V ) = L(U; V ) +
SoReg MF 2 where F (:) is the set of friends of user i and is a parameter that controls social in uences; pcc() estimates the similarity between the ratings of two users using the Pearson Correlation Coe cient (PCC):
i=1 j=1 L(U; V ) = min 1 X X Ii;j (Ri;j
U;V 2 m n
UiT Vj )2 where Ii;j is an indicator variable that is 1 if user i rated venue j, otherwise 0. A regularisation term is added to Equation (2) to avoid over- tting, as follows: pcc(i; f ) = r
P j2Vr(i)\Vr(f)() (Rij
Ri)(Rfj
Rf )
P j2Vr(i)\Vr(f)() (Rij
Ri)2:r
P j2Vr(i)\Vr(f)() (Rfj
Rf )2 where Vr(i) are the venues that user i has rated and Ri is their average rating.
In Equation (4), the loss function of the social regularisation model is the sum of the loss function of MF and the social regularisation term. The Frobenius norm of the di erence between the latent representations of the user and his/her friends is then multiplied by the PCC, which scales according to how similar the user and his/her friends are, based on their rating history.
The functionality of SoReg is to ensure that the user-friend pair who share
similar interests are predicted to rate similarly other venues. The more similar
a user is to his/her friend, the greater the correlation. By applying the SoReg
model, not only a user and his/her friends become closer based on their similarity
level in the latent space, but so do the friends' friends, who become closer at
the same time. This means that not only a user is recommended venues by
his/her friends, but also by his/her friends' friends, although indirectly. The
range of Pearson Correlation Coe cient is [
While BPR is based on matrix factorisation, the objective function is Equation (1) introduced above. It can be noted in Equation (4) that the objective function of SoReg is the objective function of MF augmented by the social regularisation. Therefore, to combine BPR with SoReg, we t Equation (1) into Equation (4) to replace the L(U; V ) part, thereby making the objective function
MF of our proposed BPRSoReg approach as follows:
L(U; V ) = BP RSoReg
X (u;i;j)2Ds (6) Using Equation (6), a pairwise recommender system that takes into account social information can therefore be established. 4
We use the Yelp challenge Round-13 dataset to conduct all our experiments. This dataset has 6,685,900 rating records, 1,637,138 unique users and 192,606 unique venues. Hence, the data sparsity is 0.002120%. Of all these users, there are 122,824 regular users (users with 10 rating records) and 1,514,314 coldstart users (user with < 10 rating records). On average, the regular users have 36.1 friends, while the cold-start users have 6.8 friends. While no ltering is applied on the dataset, we analyse separately the regular users' and cold-start users' results, to determine how di erently our proposed model performs on di erent types of users.
We use Spotlight, a Python recommendation platform that includes an
implementation of a BPR implicit factorisation, to conduct our experiments1.
Following previous work in [
Following the existing literature in recommender systems, to measure the e ectiveness of recommendations, mean reciprocal rank (MRR) is used where the reciprocal rank is the multiplicative inverse of the ranked venues for a speci c user. The average value is taken for all users in the dataset as an estimation of the performance of the system. MRR is computed as follows:
M RR = 1 XjUj
1 U i=1 ranki (7) where ranki is the rank position of the rst relevant venue retrieved for user i.
In our experiments, we vary the social parameter (see Equation (4)), which controls the in uence of the social regularisation, from 10 7 to 1, multiplying by 10 at each step. In the Yelp challenge Round-13 dataset, 45.4% of users have a friend-list through which we can nd their friends' information according to the user-id(s) provided. With this information, the Pearson Correlation Coe cient between users is pre-computed before training commences, to increase training e ciency. We compare the e ectiveness { in terms of MRR { of BPRSoReg with di erent amounts of social regularisation to the BPR baseline. Finally, signi cance tests are conducted using a paired t-test with p < 0:01. 5
Table 1 reports the e ectiveness of BPRSoReg and BPR in terms of MRR for different groups of users. From the left hand group of Table 1, it can been seen that the BPRSoReg model can consistently outperform BPR in terms of MRR across all users - indeed, the best performance occurs when =10 6, signi cantly improving MRR by 54.0%. This demonstrates that social regularisation can greatly improve the e ectiveness of BPR. As increases, the model's e ectiveness starts to saturate, which means that the social regularisation is penalising models that produce results that are too di erent from each given user's friends. Conversely, for a very small , social regularisation gives a very small penalty to models where users di er widely from their friends, and the performance naturally returns to that of the baseline. Such a variance can be observed clearly in Figure 1, which shows how MRR varies with .
Next, the centre and right-hand groups of Table 1 report the obtained results for the regular and cold-start users, respectively. From the table, we observe that introducing social information leads to a consistent improvement for coldstart users but for regular users the ranking performance drops markedly when 10 4. This might be because for regular users, their check-ins are enough for the BPR model to capture their interests so the model does not bene t from receiving additional regularisation for those users' friends. However, the cold-start users have very few check-ins, hence the model will bene t when additional social information is available. As noted in Section 4, regular users have, on average, 6 times as many friends are cold-start users. While the cold-start users and regular users share the same social parameter during training, it is possible that the 0.0024 0.0022 R R M0.0020 0.0018 0.0016
BPR-SoReg BPR large numbers of friends mean that forcing the regular users' latent factors to be similar to all of their friends is too aggressive in penalising models that would otherwise be e ective. Therefore, the best e ectiveness is obtained when is small. 6
In this paper, we explored whether social information can be leveraged to improve Bayesian Personalised Ranking (BPR). We proposed BPRSoReg, which incorporates social information as a regularisation for BPR. Our experiments on a large LBSN dataset demonstrate that we can signi cantly enhance the e ectiveness of BPR. Furthermore, our experiments show that BPRSoReg particularly bene ts cold-start users. In the future, we plan to add more ranking metrics including Hit Ratio and Normalised Discounted Cumulative Gain. In addition, we plan to integrate social information to di erent frameworks of recommender systems such as those based on neural networks to examine the generalisation of social information in recommender systems.
Acknowledgements. We thank ACM SIGIR for providing the rst author with an FDIA 2019 travel grant.