While recent studies have explored the idea of adopting collaborative ranking (CR) for recommendation, there has been no attempt to incorporate contextual similarities between venues. In this study, we explore the e ect of incorporating contextual similarities into the learning strategy of a CR model. By enhancing the latent associations between users with contextual similarities, our experiments show that contextual similarities improve the performance of CR.
Generating venue suggestions plays a crucial role in satisfying the user needs,
for example when exploring a new city [
In this study, we explore the e ect of incorporating contextual similarities of venues into CR. We design the objective function of the CR model to include the contextual similarity measures in the loss function with a focus on ranking relevant venues at the top of the recommendation list. This enables our model to propagate venue contextual proximity to the users, thus addressing the sparsity problem that appears in the check-in data. For example, in the conventional collaborative ltering approaches, the latent associations are captured only if users have visited the same venue, whereas incorporating venue similarities in our CR model can capture the associations even if users have only visited contextually similar venues but not the same ones. 2
Let P = f 1; : : : ; ng and L = fl1; : : : ; lmg be the sets of n users and m venues, respectively. We consider user ratings 1, 2, and 3 on venues as negative feedback, while ratings 4 and 5 as positive one. For each user i, we de ne Li+ as the set of relevant venues, and Li as the set of irrelevant ones. Moreover, let Sz 2 Rm m be the similarity matrix of venues based on a contextual feature z. Contextual Similarities. In our approach we compute a contextual similarity between two venues li and lj based on their content and location. In the following we brie y introduce three similarity measures, de ning Sij = fSz(i; j) : z 2 f1; 2; 3gg as the set of contextual similarity functions.
{ Geographical: rst, we compute the geographical similarity between two venues to incorporate the geographical context while characterizing the user's geographical preferences. The similarity is inversely proportional to the distance between two venues, denoted by S1(i; j). { Review based: for venue li, we train a Support Vector Machine (SVM) classi er with linear kernel to estimate the review-based similarity. We consider positive reviews as positive training samples and negative reviews as negative training samples to train the SVM and call the trained classi er SVMi. Then, for each venue lj : j 2 L we classify the reviews of lj using SVMi. We take the value of the decision function as the similarity measure, denoted by S2(i; j). { Category based: S3(i; j) is the cosine similarity between the category vectors of li and lj.
Collaborative Ranking with Contextual Similarities. Here we present our model, called CRCS, which suggests venues for each user i placing relevant venues at the top of the recommendation list. Our goal is to understand the user's check-in behavior with the contextual similarities of venues explained in Section 2. For example, a user may like all venues that are in the city center and serve pizza. Building ranking functions considering di erent contextual similarities between venues also allows us to model latent associations between users with similar tastes who would not be considered in a traditional CR setting. This happens because CRCS takes into account the venue similarities as it updates the user and item latent matrices. CRCS can build the associations between users as it considers content- and context-based similarities while updating the latent matrices. Notice that our CRCS model does not rely on the type of contextual similarity and is not limited to a certain type of contextual features. Hence, it can be a general framework for incorporating any type of contextual features.
We focus on ranking the venues that a user likes higher than the ones she does not. Formally, we aim at ranking venues that belong to Li+ higher than those that are in Li . Our goal is to rank the venues with emphasis on the top of the list. Let Hi(lj ) be the \height" of an irrelevant venue, that is: Hi(lj ) = X
3
X h k2Li+ z=1 z
i 1[fi(lk+) fi(lj )] =Sz(k; j) ; where z is the weight of contextual similarity Sz and 1[:] is an indicator function. Dividing the indicator function by Sz allows the model to incorporate the contextual similarities into the model while constructing the height for irrelevant items. For example, if an irrelevant item is ranked higher than a relevant item, but they are contextually very similar based on Sz, then the denominator will be higher, which means the height of the irrelevant venue will be reduced accordingly. The objective function should aim at minimizing Hi for all irrelevant venues of user i. A lower value of Hi means that there are fewer irrelevant venues ranked higher than relevant ones, and those that are ranked higher are more similar to relevant items. However, indicator functions are not convex and they are not suitable to our optimization strategy. Therefore, we use the logistic loss of the di erence between the two functions as a convex upper bound surrogate. We de ne the di erence between the kth venue and the jth as follows: 3 i(k; j) = uiT X z(vk vj)= exp(jSz(k; j)j) : Therefore, the surrogate height function Hi0(lj ) becomes:
Hi0(lj ) =
X log 1 + exp
i(k; j) : z=1 k2Li+ Finally, the objective function is de ned as follows:
m R(U; V ) = X 1 X i=1 ni j2Li
Hi0(lj ) 2 : 3
We evaluate our approach on a mixed dataset of two benchmark datasets, made
available by the TREC. The datasets are for the TREC Contextual Suggestion
Track (TREC-CS) 2015 and 2016. We used the publicly available crawls of [
Table 1 reports the performance of all the models on TREC-CS in terms of nDCG@k with k 2 f1; 2; 3; 4; 5g. Our proposed CRCS model signi cantly P-Push RH-Push IRenMF GeoMF Rank-GeoFM CRCS outperforms all state-of-the-art methods in terms of nDCG@k for all values of k (according to pairwise t-test at p < 0:05). Compared to the state-of-the-art method, Rank-GeoFM, the improvements in terms nDCG@1 and nDCG@5 are 21% and 7%, respectively. This indicates that our proposed CRCS can address the data sparsity problem by incorporating di erent types of contextual similarities. While the geographical similarity includes the neighborhood in uences in the model, the category-based similarity takes into account users with similar tastes when they do not share the same check-in records. In addition to that, the review-based similarity models venues similarities in terms of other users' opinions in various contexts. Fusing these similarity measures with a CR-based model enables CRCS to form complicated similarity a nities among venues and propagate it to the users. Hence, our proposed CRCS addresses the data sparsity problem better than other state-of-the-art models, indicated by the high recommendation accuracy.