Item Silk Road: Recommending Items from Information Domains to Social Users

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1 Item Silk Road: Recommending Items from Information Domains to Social Users ∗ Xiang Wang Xiangnan He National University of Singapore National University of Singapore [email protected] [email protected] Liqiang Nie Tat-Seng Chua ShanDong University National University of Singapore [email protected] [email protected] 1 INTRODUCTION ABSTRACT Nowadays online platforms play a pivotal role in our daily life Online platforms can be divided into information-oriented and social-oriented domains. Œe former refers to forums or E- and encourage people to share experiences, exchange thoughts, commerce sites that emphasize user-item interactions, like Trip.com and enjoy online services. Regardless of applications, we can roughly divide the existing platforms into information-oriented and Amazon; whereas the laŠer refers to social networking services and social-oriented domains. Œe former typically refers to forums (SNSs) that have rich user-user connections, such as Facebook or E-Commerce sites that have thorough knowledge on items, such and TwiŠer. Despite their heterogeneity, these two domains bridge can be bridged by a few overlapping users, dubbed as as point-of-interests in Trip.com, movies in IMDb, and products in cross-domain social users Amazon. Œese sites have ample user-item interactions available . In this work, we address the problem of , recommending relevant items of information recommendation , in the form of users’ reviews, ratings, along with various kinds i.e. domains to potential users of social networks. To our knowledge, ]. On the other hand, 1 of implicit feedback like views and clicks [ the social-oriented domains are mainly social network sites, which this is a new problem that has rarely been studied before. emphasize the social connections among users [15]. Existing cross-domain recommender systems are unsuitable When adopting an item, besides consulting the information for this task since they have either focused on homogeneous information domains or assumed that users are fully overlapped. sites, a user usually gathers more detailed information from her , which Neural Social Collaborative Towards this end, we present a novel experienced friends. Œis refers to word-of-mouth marketing Ranking (NSCR) approach, which seamlessly sews up the user-item is widely recognized as the most e‚ective strategy for producing 1 interactions in information domains and user-user connections , more than 45% of recommendation. As reported by Cognizant travelers rely on social networks to seek advice from friends for in SNSs. In the information domain part, the aŠributes of users travel. However, most existing SNSs, like Facebook and TwiŠer, are and items are leveraged to strengthen the embedding learning of designed mainly for users to rebuild their real-world connections, users and items. In the SNS part, the embeddings of bridge users rather than for seeking options regarding items. Œough some item are propagated to learn the embeddings of other non-bridge users. Extensive experiments on two real-world datasets demonstrate the cues implying users’ preference can be found in SNSs, they typically contain item names only with limited details. Œe sparse and weak e‚ectiveness and rationality of our NSCR method. user-item interactions greatly hinder the ability of SNSs to o‚er item recommendation services. CCS CONCEPTS Fortunately, some users may be simultaneously involved in both → Information systems • Social recommendation; Retrieval SNSs and information-domain sites, who can act as a bridge to models and ranking; Recommender systems; propagate user-item interactions across domains. For example, it is not unusual for a user to share her travel experiences in Trip.com; KEYWORDS and if the user also holds a Facebook account, we can recommend arXiv:1706.03205v1 [cs.IR] 10 Jun 2017 Cross-domain Recommendation, Deep Collaborative Filtering, her friends in Facebook with her liked items from Trip.com. In Neural Network, Deep Learning to route silk road social circles, these bridge users are like the relevant items from information domains to (non-bridge) users of social networks. As such, we formulate the task of cross-domain ∗ Xiangnan He is the corresponding author. social recommendation , which aims to recommend relevant items of information domains to the users of social domains. Apparently, Permission to make digital or hard copies of all or part of this work for personal or this task is related to the recently emerging topic — cross-domain classroom use is granted without fee provided that copies are not made or distributed recommendation [ ]. However, we argue that existing e‚orts have 13 for pro€t or commercial advantage and that copies bear this notice and the full citation on the €rst page. Copyrights for components of this work owned by others than ACM multiple sites of the either focused on homogeneous domains ( i.e., must be honored. Abstracting with credit is permiŠed. To copy otherwise, or republish, information domain) [ ], or unrealistically assumed that the users 5 to post on servers or to redistribute to lists, requires prior speci€c permission and/or a ]. Our task to address is particularly are fully overlapped [ 13 , 30 fee. Request permissions from [email protected] SIGIR€17, August 7–11, 2017, Shinjuku, Tokyo, Japan challenging due to the following two practical considerations. 15.00 $ 2017 ACM. 978-1-4503-5022-8/17/08. . . © 1 hŠps://www.cognizant.com. DOI: hŠp://dx.doi.org/10.1145/3077136.3080771

2 • Insucient bridge users. To gain a deep insight, we analyzed the overlapped users between Trip.com and Facebook/TwiŠer, 196 Facebook users and 6 . 9% of €nding that only 10 , . 5% of 8 233 TwiŠer users have public accounts in Trip.com. It is highly , 7 challenging to leverage history of such limited number of bridge users to provide quality recommendation for non-bridge users. • Rich aŠributes. Œe users and items of an information domain are usually associated with rich aŠributes. For instance, Trip.com enables users to indicate their travel preference explicitly, and associates travel spots ( i.e., items) with speci€c travel modes, among other information. However, liŠle aŠention has been Figure 1: Illustration of the cross-domain social paid to leverage these aŠributes to boost the performance of recommendation task. cross-domain recommendation. In this work, we propose a novel solution named Neural Social (NSCR) for the new task of cross-domain Collaborative Ranking 2.1 Problem Formulation social recommendation. It is developed based on the recent Figure 1 illustrates the task of cross-domain social recommendation. advance of neural collaborative €ltering (NCF) [ 11 ], which is further In the information domain, we have the interaction data between M extended to model the cross-domain social relations by combining 1 U } denote a user and the u { = users and items. Let u and 1 t =1 t ]. We entail two key 9 with the graph regularization technique [ whole user set of the information domain, respectively; similarly, technical components of our NSCR as follows. N i and I = { i } we use to denote an item and the whole item t =1 t • For the modelling of information domain, we build an aŠribute- set, respectively. Œe edges between users and items denote their aware recommender based on the NCF framework. To fully , which can be real-valued explicit ratings y { = Y } interactions, ui exploit the interactions among a user, an item, and their or binary 0/1 implicit feedback. Traditional collaborative €ltering aŠributes, we enhance NCF by plugging a pairwise pooling algorithms can then be performed on the user-item interaction data. operation above the embedding vectors of user (item) ID and In addition to the ID that distinguishes a user or an item, most aŠributes. In contrast to the default average pooling used information-domain sites also associate them with abundant side ], our 4 ] and other recent neural recommenders [ 11 by NCF [ information, which can help to capture users’ preferences and use of pairwise pooling beŠer captures feature interactions in item properties beŠer. For example, in Trip.com, the user may the low level [ 10 , 21 ], greatly facilitating the following deep in her pro€le; choose the travel tastes of { luxury travel, art lover } layers to learn higher-order interactions among users, items and is tagged most with travel modes Marina Bay Sands while, the item aŠributes. luxury travel, family travel, nightlife . We term these associated } { For the modelling of social domain, it is natural to guide the • information as , most of which are discrete categorical aˆributes embedding learning of social users by using the embeddings of variables for the web domain [ and g ]. Formally, we denote 10 V bridge users. As the embeddings of bridge users are optimized as an aŠribute and the whole aŠribute set, respectively; g } { = G t t =1 to predict user–item interactions ( ratings and purchases), e.g., u and an item for a user , we can then construct the associated i u i u i propagating their embeddings to social users helps to bridge = , G and } ⊂ G g g g } ⊂ ··· , , ··· g { aŠribute set as G { = , u i 1 1 V V i u the heterogeneity gap between information domain and social G , respectively. domain. To implement such propagation e‚ect, we employ In the social domain, we have social connections between users, the constraint ( i.e., graph Laplacian ) on the social smoothness such as the undirected friendship or directed follower/followee ′ network, which enforces close friends to have similar embedding , all users of the social u relations. We denote a social user as M ′ 2 so as to reƒect their similar preferences. ′ ′′ domain as s , and all social connections as = } S U { = { u . } 2 u u t =1 t We de€ne the bridge users as the overlapping users between the To sum up, the key contributions of this work are three-fold: information domain and social domain. Œese bridge users can be (1) To our knowledge, we are the €rst to introduce the task of cross- U = ∩U U expressed as . In a social network, a user’s behaviours 1 2 domain social recommendation, which recommends relevant and preferences can be propagated along the social connections to items of information domains to target users of social domains. inƒuence her friends. As such, these bridge users play a pivotal role (2) We propose a novel solution that uni€es the strengths of deep in addressing the cross-domain social recommendation problem, neural networks in modelling aŠributed user-item interactions which is formally de€ned as: and graph Laplacian in modelling user-user social relations. } ; a social An information domain with Input: G {U , , I , Y , G (3) We construct two real-world benchmark datasets for exploring u i 1 is nonempty. domain with {U ∩U , S} ; and U the new task of cross-domain social recommendation and 1 2 2 ′ Output: A personalized ranking function for each user u of the extensively evaluate our proposed solution. ′ social domain f : I → R , which maps each item of the u information domain to a real number. 2 PRELIMINARY It is noted that there indeed exist sparse and weak user-item We €rst formulate the task of cross-domain social recommendation, interactions in SNSs as aforementioned. However, we simplify and then shortly recapitulate the matrix factorization model, highlighting its limitations for addressing the task. this scenario of cross-domain social recommendation by only

3 • Œe case can be even worse if we take the aŠributes into account. A typical way to extend MF with side aŠributes is SVDfeature, i.e., by summing aŠribute embedding vectors with user/item embedding vector. As a result, the rich correlations among users, items, and aŠributes are unintentionally ignored. Our proposed NSCR solution addresses the above limitations of MF by 1) using a deep learning scheme to capture the higher-order correlations between user and item latent factors, and 2) devising a pairwise pooling operation to eciently model the pair-wise correlations among users, items, and aŠributes. 3 OUR NSCR SOLUTION Figure 2: MF as a shallow neural network model. Œe goal of cross-domain social recommendation is to select relevant items from the information domain for social users. Under emphasizing the social connections in SNSs and leaving the the paradigm of embedding-based methods ( aka. representation exploration of weak interactions as the future work. learning), the key for addressing the task is on how to project items (of the information domain) and users (of the social domain) into 2.2 Factorization Model the same embedding space. A generic solution is the factorization Collaborative €ltering (CF) is the key technique for personalized 20 , ], which merges the data from the two domains 21 machine (FM) [ recommendation systems. It exploits user-item interactions by by an early fusion; that is, constructing the predictive model by assuming that similar users would have similar preference on items. incorporating social users as the input features. While the solution , Model-based CF approaches [ ] achieve this goal by describing 1 33 sounds reasonable conceptually, the problem is that the training the interaction data with an underlying model, for which the holistic instances which can incorporate social users are only applicable to goal is to build: the bridge users, which can be very few for real-world applications. As such, the generic recommender solution FM can su‚er severely i f = ( u ) , y ̂ (1) , ui Θ from the problem of insucient bridge users. where y ̂ denotes the underlying model with parameters Θ, and f ui To address the challenge of insucient bridge users, we propose denotes the predicted score for a user-item interaction . Matrix y ui a new framework that separates the embedding learning process of factorization (MF) is one of the simplest yet e‚ective models for each domain. By enforcing the two learning processes to share the the recommendation task, which characterizes a user or an item same embeddings for bridge users, we can ensure that items and with a latent vector, modelling a user-item interaction as the inner social users are in the same embedding space. Formally, we devise product of their latent vectors: the optimization framework as: K ∑ > ) + , (3) (Θ = ) (Θ L L L S I S I p p | i u , f , q ( ) = (2) = p q q , u i i M F ik uk u =1 k (or ) denotes the objective function of the information where L L I S K K domain (or social domain) learning with parameters Θ (or Θ ), R ∈ are model parameters denoting the where q and p R ∈ I S u i Θ are nonempty denoting the shared ∩ and most importantly, Θ latent vector ( representation) for user u and item i , respectively. aka. I S embeddings of bridge users. Despite its e‚ectiveness, we note that MF’s expressiveness can By separating the learning process for two domains, we allow be limited by the use of the inner product operation to model the design of each component to be more ƒexible. Specially, we a user-item interaction. To illustrate this, we present a neural to learn from can apply any collaborative €ltering solution for network view of the MF model. As shown in Figure 2, we feed the L I user-item interactions, and utilize any semi-supervised learning one-hot representation of user/item ID into the architecture, and to propagate the embeddings of bridge users to technique for project them with a fully connected embedding layer. By feeding L S non-bridge users. In the remainder of this section, we €rst present the user/item embedding vectors into the element-wise product our novel neural collaborative ranking solution for , followed h . If we directly project = { p } q layer, we obtain a hidden vector L I uk ik by the design of social learning component . Lastly, we discuss into the output score, we can exactly recover the MF model. As h L S how to optimize the joint objective function. such, MF can be deemed as a shallow neural network with one hidden layer only. Based on this connection, we argue that there are two key limitations of MF-based approaches for cross-domain 3.1 Learning of Information Domain social recommendation: To estimate the parameters for a CF model from user-item First, MF only considers the simple two-way interaction between • interaction data, two types of objective functions — point-wise [ 1 , 26 , ] — are most commonly used. Œe point- a user and an item, by assuming that their cross latent factors 21 11 ] and pair-wise [ 2 , i.e., p wise objective functions aim to minimize the loss between the and q ( ) are independent of each other. However, such an i u independence assumption can be insucient to model real-world predicted score and its target value. Here, to tailor our solution for data, which usually have complex and non-linear underlying both implicit feedback and the personalized ranking task, we adopt structures [10, 15]. the pair-wise ranking objective functions.

4 Formally, we denote an observed user-item interaction as y = 1, ui ˆ otherwise to be = 0. Instead of forcing the prediction score y y ui ui close to , ranking-ware objective functions concern the relative y ui order between the pairs of observed and unobserved interactions: ∑ ˆ , ) y = ( (4) , y L L ui j ui j I ( i ) u ∈O , j , ˆ ˆ ˆ and y y = = y where − − y y y ; O denotes the set of ui ui j u j u j ui ui j of training triplets, each of which comprises of a user u , an item i of unobserved = 1), and an item y i.e., observed interactions ( j ui interactions ( j ) item i.e., y , = 0). An ideal model should rank all ( i ui pairs correctly for every user. To implement the ranking hypotheses, we adopt the regression-based loss [26]: ∑ ∑ Figure 3: Illustration of our Attributed-aware Deep CF 2 2 ˆ ˆ ˆ y (5) − . y y ) 1) = = − − y ( ( L u j ui ui j ui j I model for estimating an user-item interaction. u ( ∈O , ∈O ) j , i i , j ( u ) , where denotes the element-wise product of two vectors. We term Note that other pair-wise ranking functions can also be applied, it as pairwise pooling , which is originally inspired from the design 2 ] and , such as the bayesian personalized ranking (BPR) [ 21 10 19 ]. By applying pairwise pooling of factorization machines [ , 23 ]. In this work, we use the contrastive max-margin loss [ on the item counterpart, we can similarly model the pair-wise regression-based ranking loss as a demonstration for our NSCR, correlation between an item and its aŠributes: and leave the exploration of other choices as the future work. V V V i i i ∑ ∑ ∑ i i i i . Having established A‚ribute-aware Deep CF Model 3.1.1 φ { , q i = ( g g ) = } i g + g (7) . ′ i pair wise t t t t ′ the optimization function for learning from information domain, t =1 t =1 +1 t = t we now present our aŠribute-aware deep collaborative €ltering It is worth pointing out that although pairwise pooling models ˆ model to estimate a user-item interaction . Figure 3 illustrates its y ui the correlation between each pair of features, it can be eciently architecture, which is a multi-layered feed-forward neural network. computed in linear time — the same time complexity with We elaborate its design layer by layer. average/max pooling. To show the linear time complexity of u Œe input to the model is a user Input Layer. , and , an item i evaluating pairwise pooling, we reformulate Eqn.(6) as, G G and their associated aŠributes . We transform them into [ ] u i V V V u u u ∑ ∑ ∑ 1 barbarized sparse vectors with one-hot encoding, where only the u u u u p + = g ( u g u ) ( + − ) u g u − (8) g , u t t t t non-zero binary features are recorded. 2 =1 t t =1 =1 t Œe embedding layer maps each non-zero Embedding Layer. KV ) time. Œis is a very appealing O which can be computed in ( u feature into a dense vector representation. As we have four types property, meaning that the bene€t of pairwise pooling in modelling of features here, we di‚erentiate them with di‚erent symbols: u , i , all pair-wise correlations does not involve any additional cost, i u denote the , and K g -dimensional embedding vector for user , u g t t as compared to the average pooling that does not model any u i i , respectively. item , user aŠribute g g , and item aŠribute t t correlation between input features. Œe output of the embedding layer is a set of Pooling Layer. Hidden Layers: Above the pairwise pooling is a stack of , respectively. As embedding vectors to describe user u and item i full connected layers, which enable us to capture the nonlinear di‚erent users (items) may have di‚erent number of aŠributes, the and higher-order correlations among users, items, and aŠributes. size of the embedding vector set may vary for di‚erent inputs. To Inspired by the neural network view of matrix factorization train a neural network of €xed structure, it is essential to convert Figure 2), we €rst merge user representation and item cf. p ( u the the set of variable-length vectors to a €xed-length vector, i.e., representation with an element-wise product, which models q i pooling operation. and u . We then place a multi- the two-way interaction between i Œe most commonly used pooling operations in neural network layer perceptron (MLP) above the element-wise product. Formally, modelling are average pooling and max pooling. However, we the hidden layers are de€ned as: argue that such simple operations are insucient to capture the  interaction between users/items and aŠributes. For example, the ( e ( p q σ ) + b ) = W  i u 1 1 1 1    average pooling assumes a user and her aŠributes are linearly  W e σ = ) b + e ( 2 1 2 2 2 (9) , independent, which fails to encode any correlation between them  ······   in the embedding space. To tackle the problem, we consider to   e W + = e ) ( σ b 1 L L L L L −  model the pairwise correlation between a user and her aŠributes, and all nested correlations among her aŠributes: e W , σ where , b denote the weight matrix, bias vector, , and l l l l -th hidden layers, l activation function, and output vector of the respectively. As for the activation function in each hidden layer, we V V V u u u ∑ ∑ ∑ u u u u opt for Recti€er (ReLU) unit, which is more biologically plausible φ p g + u = , u ( (6) g ) = } , g { g ′ pair wise u t t t t ′ t =1 t =1 +1 t = t and proven to be non-saturated. Regarding the structure of hidden

5 layers, common choices include the tower [ is de€ned as, 11 ], constant, and , 4 diamond, among others. In this work, we simply set all hidden ∑ 2 1 (0) ′ U ( ) = θ p p − (12) , ′ u layers have the same size, leaving the further tuning of the deep u 2 ′ ∈U u structure as the future work. (0) ′ Prediction Layer: At last, the output vector of the last hidden ′ u where for each bridge user ) is her representation of , (or p p ′ u u layer e is transformed to the prediction score: L the SNS (or information domain). As such, the €Šing constraint essentially acts as the bridges connecting the two latent spaces. > ˆ = , y e (10) w ui L Lastly, we combine the smoothness constraint with the €Šing constraint and obtain the objective function of the social domain where represents the weight vector of the prediction layer. w learning as, Note that we have recently proposed a neural factorization U (13) , ) θ ( = U μθ ) + ( L 2 S machine (NFM) model [ 10 ], which similarly uses a pairwise pooling operation to model the interaction among features. We point out μ is a positive parameter to control the tradeo‚ between two where that the main architecture di‚erence is in our separated treatment constraints. of the user and item channel, where each channel can essentially be With the representations 3.2.1 Prediction for Social Users . seen as an application of NFM on the user/item ID and aŠributes. ′ and ) at hand, we can feed them of social users and items ( i.e., p q i u (9) shows and utilize the into the fully connected layers as Eqn. 3.2 Learning of Social Domain (10) prediction layer as Eqn. displays. At last, we can obtain the With the above neural collaborative ranking solution, we obtain an ′ ̂ predicted preference , as follows, y u i q and p aŠribute-aware representation for each user and item, i u  ′ ( = W σ ( p e b ) q ) + respectively. To predict the anity score of a social user to an item  1 1 1 i 1 u    of the information domain, we need to also learn an representation  ······ . (14) for the social user in the same latent space of the information  W e = σ ( e + b )  1 − L L L L L  from bridge users domain. We achieve this goal by propagating p  u  > ′ e = ̂ y w i u L  to representations for non-bridge users of the social domain. Œe intuition for such representation propagation is that, if two users are 3.3 Training e.g., strongly connected ( close friends with frequent interactions), since it (3) We adopt the alternative optimization strategy on Eqn. it is likely that they have the similar preference on items; as such, can emphasize exclusive characteristics within individual domains. they should have similar representations in the latent space. Œis In the information domain, we employ stochastic gradient descent suits well the paradigm of graph regularization [ 7 , 9 , 28 , 29 ] ( aka. SGD) to train the aŠribute-aware NSCR in the mini-batch mode and semi-supervised learning on graph), which has two components: update the corresponding model parameters. In particular, we €rst Smoothness: Œe smoothness constraint implies the structural , i ) and adopt sample a batch of observed user-item interactions ( u consistency — the nearby vertices of a graph should not vary 11 ] to randomly select an unobserved item j negative sampling [ much in their representations. Enforcing smoothness constraint ). Following that, for each ( u , i , j , u ). We then generate a triplet ( i in our context of social domain learning will propagate a user’s . we take a gradient step to optimize the loss function in Eqn. (5) L I representation to her neighbors, such that when a steady state As such, we obtain the enhanced representations of users. In the reaches, all vertices should have been placed in the same latent SNS, we feed the enhanced representations of bridge users into space. Œe objective function for smoothness constraint is de€ned our graph Laplacian to update all representations of social users. as: Towards this end , we can simplify the derivative of regarding L S 2 ∑ ′′ ′ and then obtain the close-form solution as, P user representation p p 1 u u ′′ ′ , (11) − θ ) = U ( s √ √ 2 u u ( ) 2 − 1 ′ ′′ ′′ ′ d d u u u u ∈U , 1 1 μ 1 2 − − (0) 2 2 SD P D (15) , − I = P μ 1 + 1 + μ ′′ ′ where denotes the strength of social connection between s u u ′′ ′ (0) ′ ′′ ′ ′′ is the embedding of social users, which includes the and (or ) denotes the outdegree of u u d u u (or d P , and ) where u u D for normalization purpose. It is worth noting that the use of and S updated representations of bridge users from NSCR part; normalization is the key di‚erence with the social regularization are the similarity matrix and diagonal degree matrix of social users, ′ ′ ′ ′ ′′ ′ ′′ 36 , 16 respectively, whereinto S used by [ ], which does not apply any normalization on the D . Œerea‰er, = s and = d u u u u u u u ], the use et al. 9 smoothness constraint. As pointed out by He we view the newly updated representations of bridge users as the [ of normalization helps to suppress the impact of popular vertices, next initialization for the bridge users in NSCR. We repeat the above procedures to approximate the model parameter set Θ. As for the which can lead to more e‚ective propagation. We empirically verify , we omit it since we utilize this point in Section 4.3. dropout regularization term in Eqn. (3) Fitting: Œe €Šing constraint implies the latent space consistency technique in neural network modeling to avoid over€Šing. Dropout is an e‚ective solution to prevent deep neural Dropout: across two domains — the bridge users’ representations should be networks from over€Šing. Œe idea is to randomly drop part of invariant and act as the anchors across domains. Towards this end, neurons during training. As such, only part of the model parameters, we encourage the two representations of the same bridge users to be close to each other. Œe objective function for €Šing constraint which contribute to the €nal ranking, will be updated. In our neural

6 Table 1: Statistics of the complied datasets. ‡e social user CR model, we propose to adopt dropout on the pairwise pooling set includes the bridge users. of and q , whereinto ρ p layer. In particular, we randomly drop u i ρ is the dropout ratio. Analogous to the pooling layer, we also Interaction# Item# User# Information Domain conduct dropout on each hidden layer. 532 , 6 Trip.com 998 , 93 952 , 2 SNSs Bridge User# Social User# Social Connection# 502 494 TwiŠer , 7 , 233 42 4 EXPERIMENTS 156 , 8 Facebook 858 , 196 49 To comprehensively evaluate our proposed method, we conducted + − experiments to answer the following research questions: i denote the sets of } = 0 y | j where = = I I and } = 1 { y | { u j ui u u and irrelevant (unobserved) item j for i relevant (observed) item • RQ1: Can our NSCR approach outperform the state-of-the- user u , respectively; and δ is the count function returning 1 if art recommendation methods for the new cross-domain social y ̂ > 0 and 0 otherwise. Below we report the averaged AUC ui j recommendation task? for all testing users. • How do di‚erent hyper-parameter seŠings ( the e.g., RQ2: considers the relevant items within the top K [email protected] : K [email protected] • dropout ratio and tradeo‚ parameters) a‚ect NSCR? positions of the ranking list. A higher recall with lower K K Are deeper hidden layers helpful for learning from user- • RQ3: indicates a beŠer recommender system, which can be de€ned as, item interaction data and improving the performance of NSCR? + |I ∩R | u u R @ K = , (17) + 4.1 Data Description |I | u To the best of our knowledge, there is no available public benchmark where ranked items for the given R K denotes the set of the top- u dataset that €ts the task of cross-domain social recommendation. R . Analogous to AUC, we report the average user u @5 for all As such, we constructed the datasets by ourselves. We treated testing users. Trip.com as the information domain, Facebook and TwiŠer as the By learning representations for social users and information- , 532 active social domains. In Trip.com, we initially compiled 6 domain items together, our NSCR is capable of recommending users, who had at least 5 ratings over 2 , 952 items ( e.g., gardens by items for both bridge and non-bridge users. However, due to the in Singapore and ei‚el tower in Pairs). We transformed the bay limitation of our static datasets, it is dicult for us to evaluate the their 93 998 ratings into binary implicit feedback as ground truth, , recommendation quality for non-bridge users, since they have no indicating whether the user has rated the item. Moreover, we interaction on the information-domain items. As such, we rely on collected 19 general categories regarding the travel mode ( e.g., the bridge users for evaluating the performance. Following the , adventure travel business travel , and nightlife ) and used them as ], 21 , 11 common practice in evaluating a recommender algorithm [ the aŠributes of users and items. Subsequently, we parsed the we holdout the latest 20% interactions of a bridge user as the test users’ pro€les to identify their aligned accounts in Facebook and set. To tune hyper-parameters, we further randomly holdout 20% ]. We obtained 858 and TwiŠer, inspired by the methods in [ 17 , 24 interactions from a bridge user’s training data as the validation 502 bridge users for Facebook and TwiŠer, respectively. Œerea‰er, set. We feed the remaining bridge users, all the non-bridge users in we crawled the public friends or followers of each bridge user to SNSs, and the remaining user-item interactions in the information reconstruct the social networks, resulting in 177 , 042 Facebook users domains into our framework for training. 049 TwiŠer users. However, the original social data are , and 106 Baselines: To justify the e‚ectiveness of our proposal, we study highly sparse, where most non-bridge users have only one friend, the performance of the following methods: making it ine‚ective to propagate users’ preferences. To ensure • ItemPop: Œis method ranks items base on their popularity, as the quality of the social data, we performed a modest €ltering on judged by the number of interactions. It is a non-personalized the data, retraining users with at least two friends. Œis results in method that benchmarks the performance of a personalized a subset of the social data that contains 7 233 TwiŠer users with , system [21]. , , 156 42 494 social connections and 8 196 Facebook users with 49 , • Œis is the standard matrix factorization model that MF: social connections. Œe statistics of the datasets are summarized in leverages only user–item interactions of the information domain Table 1. Eqn.(2)). cf. for recommendation ( Factorization machine [ 19 SFM: • ] is a generic factorization model 4.2 Experimental Settings that is designed for recommendation with side information. We Given a social user, each method generates Evaluation Protocols: construct the input feature vector by using one-hot encoding an item ranking list for the user. To assess the ranking list, we on the ID and aŠributes of users and items. To adjust FM for adopted two popular IR metrics, and , to measure the recall AU C modelling social relations, we further plug a (bridge) user’s quality of preference ranking and top- N recommendation. friends into the input feature vector, dubbed this enhanced model Area under the curve (AUC) [ 12 • AUC: , 21 ] measures the as Social-aware FM (SFM). probability that a recommender system ranks a positive user- 16 Œis [ SR: • ] is a state-of-the-art factorization method for social item interaction higher than negative ones: recommendation. It leverages social relations to regularize the latent vectors of friends to be similar. To incorporate aŠributes ∑ ∑ − + ̂ y 0) > ( δ ui j ∈I j i ∈I u u into their method, we adjust the similarity of two users based (16) , AU C = + − ||I |I | u u on their aŠribute sets, which leads to beŠer performance.

7 Table 2: Performance comparison between all the methods, available in Facebook, which can lead to beŠer embedding when the embedding size and signicance test is based = 64 learning in SNSs. It again veri€es the signi€cance of the bridge on AUC. users. E‚ect of Social Modelling: To analyze the e‚ect of social Facebook-Trip Twitter-Trip Datasets modelling, we only consider the variants, SFM-a, SR-a, and NSCR-a. 5 AUC p [email protected] Methods [email protected] -value p -value 5 AUC Figure 4 presents the performance comparison w.r.t. the number of 7439 0 ItemPop 0249 8 e -6 0 . 7193 0 . 0164 3 e -5 0 . . latent factors on two datasets. We have the following observations. 8596 0 . 0821 1 e -4 0 . 8285 0 . 0375 3 e -4 MF . 0 . 0 . 0856 1 e -3 0 -3 e 8908 0492 . 0 8832 . 0 SFM 2 • ItemPop and MF perform worst since neither of them considers 0 . 1433 4 e -2 0 . 9013 0 . SR 9 e -3 0 . 9267 0747 the social connections from SNSs. It highlights the necessity of - NSCR 0 . 9222 0 . 0807 - 0 . 9390 . 1466 0 social modelling in cross-domain social recommendation. • Clearly, NSCR-a signi€cantly outperforms SFM-a and SR-a Note that for all model-based methods, we optimize them with the by a large margin. Formally, in terms of AUC, the relative (5) for a fair comparison on same pair-wise ranking function of Eqn. . 19% and improvement over SFM-a and SR-a, on average, is 3 the model’s expressiveness. To explore the ecacy of aŠributes, we 01% respectively. While SFM-a considers modelling the social . 1 further explore variants that remove aŠribute modelling from SFM, connections, it treats these connections as ordinary features, SR, and NSCR, named as SFM-a, SR-a, and NSCR-a, respectively. overlooking the exclusive characteristics of social networks. Œis We implemented our proposed framework Parameter Settings: leads to the poor expressiveness of the social users’ embedding. 2 , which will be made publicly on the basis of Tensorƒow On the contrary, SR-a and NSCR-a emphasizes the social available, as well as our datasets. For all the neural methods, modelling via the e‚ective social regularization. we randomly initialized model parameters with a Gaussian • Lastly, NSCR-a shows consistent improvements over SR-a, distribution, whereinto the mean and standard deviation is admiŠing the importance of the normalized graph Laplacian. It 0 and 0 Œe mini-batch size and learning 1, respectively. . again veri€es that the normalized graph Laplacian can suppress 512 , 1024] and rate for all methods was searched in [128 , 256 , the popularity of friends and further prevent the social modelling 0005 0 . 05 , 0 . 1], respectively. We selected Adagrad . 0 , . 0 , 0001 . [0 , 001 from being dominated by popular social users. as the optimizer. Moreover, we empirically set the size of hidden As Figure 5 demonstrates, we E‚ect of Attribute Modelling: layer same as the embedding size (the dimension of the latent verify the substantial inƒuence of aŠribute modelling and the factor) and the activation function as ReLU. Without special e‚ectiveness of our pairwise pooling operation. Due to the poor mention, we employed two hidden layers for all the neural performance of ItemPop and MF, they are omiŠed. Jointly analyzing methods, including SFM, SR, and NSCR. We randomly generated the performance of all the methods and their variants, we €nd that, ten di‚erent initializations and feed them into our NSCR. For other • For all methods, modelling user/item aŠributes can achieve competitors, the initialization procedure is analogous to ensure the signi€cant improvements. By leveraging the similarity of users’ fair comparison. Œerea‰er, we performed paired t-test between aŠributes, SR enriches the pairwise similarity of any two users our model and each of baselines over 10-round results. and strengthens their connections; meanwhile, SFM can model the correlations of user-aŠribute, item-aŠribute, and aŠribute- 4.3 Performance Comparison (RQ1) aŠribute, and accordingly enhances the user-item interactions. We €rst compare the recommendation performance of all the Bene€ting from the pairwise pooling operation, NSCR can methods. We then purpose to justify how the social modelling and encode the second-order interactions between user/item and the aŠribute modelling a‚ect the recommendation performance. aŠributes and boost the representation learning. Œe signi€cance Table 2 displays the performance Overall Comparison: of aŠribute is consistent with [34]. comparison w.r.t. AUC and [email protected] among the recommendation Varying the embedding size, we can see that large embedding • methods on TwiŠer-Trip and Facebook-Trip datasets, where the may cause over€Šing and degrade the performance. In particular, embedding size is 64 for all the methods. We have the following the optimal embedding size is 64 and 32 for AUC and [email protected], €ndings: respectively. It indicates that the seŠing of embedding size can • ItemPop achieves the worst performance, indicating the necessity e‚ect the expressiveness of our model. of modelling users’ personalized preferences, rather than just recommending popular items to users. As for MF, its unsatis€ed 4.4 Study of NSCR (RQ2) performance reƒects that the independence assumption is In this subsection, we empirically study the convergence of NSCR insucient to capture the complex and non-linear structure of and then purpose to analyse the inƒuences of several factors, such user-item interactions. as dropout ratio and tradeo‚ parameter, on our framework. • NSCR substantially outperforms the state-of-the-art methods, Convergence: We separately present the training loss and SFM and SR. We further conduct one-sample t-tests, verifying the performance w.r.t. AUC and [email protected] of each iteration in < p that all improvements are statistically signi€cant with -value Figures 6(a), 6(b), and 6(c). Jointly observing these Figures, we . 0 05. It justi€es the e‚ectiveness of our proposed framework. can see that training loss of NSCR gradually decreases with more • Œe performance on TwiŠer-Trip clearly underperforms that iterations, whereas the performance is generally improved. Œis of Facebook-Trip. It is reasonable since more bridge users are indicates the rationality of our learning framework. Moreover, 2 hŠps://www.tensorƒow.org. the most e‚ective updates occurs in the €rst 20 iterations, which

8 (a) AUC on TwiŠer-Trip (b) [email protected] on TwiŠer-Trip (d) [email protected] on Facebook-Trip (c) AUC on Facebook-Trip 5 the embedding size on Twitter-Trip and Facebook-Trip datasets. Figure 4: Performance comparison of AUC and [email protected] w.r.t. (a) AUC on TwiŠer-Trip (b) [email protected] on TwiŠer-Trip (c) AUC on Facebook-Trip (d) [email protected] on Facebook-Trip 5 w.r.t. Figure 5: Performance comparison of AUC and [email protected] the embedding size on Twitter-Trip and Facebook-Trip datasets. (a) Training Loss (b) AUC (c) [email protected] 5 Figure 6: Training loss and recommendation performance regarding AUC and [email protected] 5 w.r.t. the number of iterations. (a) AUC vs. dropout ratio ρ (b) [email protected] 5 vs. dropout ratio ρ (c) AUC vs. tradeo‚ parameter μ (d) [email protected] 5 vs. tradeo‚ parameter μ 5 Figure 7: Performance comparison of AUC and [email protected] the dropout ratio ρ and tradeo‚ parameter μ on Twitter-Trip and w.r.t. Facebook-Trip datasets. indicates that e‚ectiveness of our learning framework. As model parameters. Figures 7(a) and 7(b) present the performance w.r.t. Figure 6(c) shows, the performance regarding [email protected] ƒuctuates AUC and [email protected] of NSCR-0 by varying the dropout ratio on the pairwise pooling layer, respectively. As we can see, markedly over the iteration times, while that regarding AUC is ρ quite stable. It is reasonable since [email protected] only considers the top-5 when dropout ratio equals to 0, NSCR-0 su‚ers severely from 2 leads to . results rather than the relative order as AUC de€ned. over€Šing. Moreover, using a dropout ratio of 0 . 3 and 0 the best performance on TwiŠer-Trip and Facebook-Trip datasets, We employ the dropout technique in NSCR Impact of Dropout: to prevent our model from over€Šing, instead of regularizing respectively. However, when the optimal dropout ratio exceeds

9 Table 3: Recommendation performance of NSCR with large number of the embedding size has powerful representation di‚erent hidden layers. ], but may adversely hurt the generalization of the model 8 ability [ over€Šing the data) [8, 11]. e.g., ( AUC [email protected] Metrics 5 NSCR- NSCR- 2 2 NSCR- 1 NSCR- 0 NSCR- Factors 1 0 NSCR- 5 RELATED WORK Twitter-Trip 0585 0 . 0604 0 . 0628 . 0 . 8630 8 8704 . 0 8598 . 0 0 5.1 Social Recommendation 0738 0 . 0672 0 . 0812 0 . 8883 0 . 8984 0 . 9026 16 . 0 . 0723 0 . 0742 0 . 0843 0 . 9018 0 . 32 0 . 9109 0 9056 Social recommendation aims to leverage users’ social connections 0717 0 . 0697 0 . 0725 9222 . 0 9175 . 0 9138 . 0 64 0 . to enhance a recommender system [ 18 , 32 ]. It works by modelling 0 . 0688 0 . 128 0 . 9034 0 . 9125 0 . 0519 0 . 0653 9003 social inƒuence, which refers to the fact that a user’s decision Facebook-Trip can be a‚ected by her friends’ opinions and behaviours. Ma 0986 . 8 0 . 8978 0 . 8922 0 . 9034 0 . 0860 0 . 0 0872 ] propose a social regularization term to enforce social 16 [ et al. . 1419 0 1388 . 0 1048 . 0 9265 . 0 9197 . 0 9165 . 0 16 9303 0 . 9322 0 . 9335 0 . 1441 0 . 1486 0 . 1465 0 32 . constraints on traditional recommender systems. Based on a 9337 0 . 9376 0 . 9390 0 . 1353 0 . 1359 0 . 1466 64 0 . ] exploits social inƒuence 31 generative inƒuence model, the work [ 9310 0 1304 . . 1373 . 128 0 . 9270 0 0 0 . 9332 0 . 1168 from friends for item recommendation by leveraging information the optimal seŠings, the performance of NSCR-0 greatly decreases, embedded in the user social network. Œe authors in [ 35 ] utilize which su‚ers from insucient information. Œis highlights the social links as complementary data source to mine topic domains signi€cance of using dropout, which can be seen as ensembling and employed domain-speci€c collaborative €ltering to formulate multiple sub-models [25]. 13 ] represents a star-structured users’ interests. More recently, [ Impact of Tradeo‚ Parameter: Œere is one positive hybrid graph centered at a user domain, which connects with other parameter μ in the social modelling, which can capture the tradeo‚ item domains, and transfers knowledge on social networks. between the €Šing regularizer and the normalized graph Laplacian, It is worth noting that the aforementioned studies are all based shows. Figures 7(c) and 7(d) present the performance (15) as Eqn. on social network relations of an information domain. While in w.r.t. of μ . AUC and [email protected], respectively. As we can see, seŠing this work, we focus on how to distill useful signal from an external 7 can lead to the optimal performance on TwiŠer-Trip . 8 and 0 0 . social network ( Facebook and TwiŠer), so as to improve the e.g., and Facebook-Trip datasets, respectively. And the performance of recommendation service of any information domain. NSCR-0 changes within small ranges nearby the optimal seŠings. It justi€es that our model is relatively insensitive to the parameter 5.2 Cross-Domain Recommendation around its optimal con€guration. Distinct from the traditional recommendation methods that focus on data within a single domain, cross-domain recommendation 4.5 Impact of Hidden Layer (RQ3) concerns data from multiple domains. A common seŠing is To capture the complex and non-linear inherent structure of user- leveraging the user-item interaction of a related auxiliary domain item interactions, we employ the a deep neural network for our task. to improve the recommendation of the target domain. However, It is curious whether NSCR can bene€t from the deep architecture. existing cross-domain recommendation work has an underlying Towards this end, we further investigate NSCR with di‚erent assumption that the target and auxiliary domains are homogeneous. number of hidden layers. As it is computationally expensive to , 6 ], they can be divided into two directions. , 5 Depending on [ 13 for each hidden layer, we simply apply the ρ tune the dropout ratio One is assuming that di‚erent domains share overlapped user or same seŠings for all layers. Œe empirical results on two datasets ] augments ratings of movies and books for 22 item sets. Œe work [ are summarized in Table 3 whereinto NSCR-2 indicates the NSCR the shared users and accordingly conducts CF. Based on the shared method with two hidden layers (besides the embedding layer and users’ latent space, the authors in [ 3 ] leveraged cluster-level tensor prediction layer), and similar notations for others. We have the sharing as a social regularization to bridge the domains. One more following observations: 12 step, the authors in [ ] formulated a generalized triadic user-item- domain relation over the common users and accordingly to capture In most cases, stacking more hidden layers is helpful for the • recommendation performance. NSCR-2 and NSCR-1 achieve domain-speci€c user factors and item factors. More recently, the authors [ 5 consistent improvement over NSCR-0, which has no hidden ] proposed a multi-view deep learning recommendation layers and directly projects the embedding to the prediction layer. system by using auxiliary rich features to represent users from We aŠributed the improvement to the high nonlinearity achieved di‚erent domains. Without aligned user or item, the other direction by stacking more hidden layers. Our €nding is consistent with is on homogeneous data with the same rating scale. Codebook Transfer [ ] represents cluster-level rating paŠerns between two 8 ] and again veri€es the deep neural networks have strong [ 14 rating matrices in two related domains. [ generalization ability. However, it is worth mentioning that such ] introduces a topic 27 a deep architecture needs more time to optimize our framework model to recommend authors to collaborate from di‚erent research and easily leads to the over€Šing due to the limited training data €elds. in our datasets. Despite the compelling success achieved by previous work, liŠle Increasing the width of hidden layers ( • i.e., the embedding size) aŠention has been paid to recommendation across heterogeneous from 8 to 64 can improve the performance signi€cantly, as that of domains. In our seŠings, the source domain is a social network increasing their depth. However, with the embedding size of 128, with user-user relations only, while the target domain is an NSCR degrades the performance. It again veri€es that using a information domain with user-item interactions. Hence, the

10 auxiliary information is the social friendship, rather than the [5] A. M. Elkahky, Y. Song, and X. He. A multi-view deep learning approach for cross WWW , pages 278–288, domain user modeling in recommendation systems. In conventional interaction data. As a result, existing approaches 2015. can be hardly applied to this new research problem. A. Farseev, I. Samborskii, A. Filchenkov, and T.-S. Chua. [6] Cross-domain recommendation via clustering on multi-layer graphs. In SIGIR , 2017. F. Feng, L. Nie, X. Wang, R. Hong, and T.-S. Chua. Computational social indicators: [7] 6 CONCLUSION a case study of chinese university ranking. In SIGIR , 2017. [8] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. In this work, we systematically investigated cross-domain social In CVPR , pages 770–778, 2016. recommendation, a practical task that has rarely been studied [9] X. He, T. Chen, M. Kan, and X. Chen. Trirank: Review-aware explainable recommendation by modeling aspects. In , pages 1661–1670, 2015. CIKM previously. Towards this end, we proposed a generic neural social X. He and T.-S. Chua. Neural factorization machines for sparse predictive [10] collaborative ranking (NSCR) solution, which seamlessly integrates analytics. 2017. user-item interactions of the information domain and user-user [11] X. He, L. Liao, H. Zhang, L. Nie, X. Hu, and T.-S. Chua. Neural collaborative , pages 173–182, 2016. WWW €ltering. In social relations of the social domain. To validate our solution, [12] L. Hu, J. Cao, G. Xu, L. Cao, Z. Gu, and C. Zhu. Personalized recommendation we constructed two real-world benchmarks of the travel domain, via cross-domain triadic factorization. In , pages 595–606, 2013. WWW performing extensive experiments to demonstrate the e‚ectiveness M. Jiang, P. Cui, X. Chen, F. Wang, W. Zhu, and S. Yang. Social recommendation [13] with cross-domain transferable knowledge. TKDE , 27(11):3084–3097, 2015. and rationality of our NSCR solution. Œe key €nding of the work B. Li, Q. Yang, and X. Xue. Can movies and books collaborate? cross-domain [14] is that social signals contain useful cues about users’ preference, collaborative €ltering for sparsity reduction. In , pages 2052–2057, 2009. IJCAI [15] L. Liao, X. He, H. Zhang, and T.-S. Chua. AŠributed social network embedding. even if the social signals are from social networks in a di‚erent , 2017. arXiv preprint arXiv:1705.04969 domain. We achieved the goal by leveraging bridge users to unify H. Ma, D. Zhou, C. Liu, M. R. Lyu, and I. King. Recommender systems with social [16] the relevance signals from the two heterogeneous domains. regularization. In WSDM , pages 287–296, 2011. [17] L. Nie, X. Song, and T. Chua. Learning from Multiple Social Networks . Synthesis Due to our restricted resources in collecting cross-domain data, Lectures on Information Concepts, Retrieval, and Services. Morgan & Claypool the result is preliminary. Here we discuss several limitations of Publishers, 2016. the current work, and our plans to address them in future. First, [18] Z. Ren, S. Liang, P. Li, S. Wang, and M. de Rijke. Social collaborative viewpoint WSDM , pages 485–494, 2017. regression with explainable recommendations. In in this work, we studied the recommendation performance of a ICDM , pages 995–1000, 2010. [19] S. Rendle. Factorization machines. In travel-based information domain only, which is mainly for the [20] S. Rendle. Factorization machines with libfm. TIST , 3(3):57:1–57:22, 2012. S. Rendle, C. Freudenthaler, Z. Gantner, and L. Schmidt-Œieme. BPR: bayesian [21] ease of accessing the users’ account on Facebook/TwiŠer. Œis UAI , pages 452–461, 2009. personalized ranking from implicit feedback. In results in a relatively small number of bridge users of our cross- S. Sahebi and P. Brusilovsky. Cross-domain collaborative recommendation [22] domain datasets. As a future work, we will collect a larger-scale in a cold-start context: Œe impact of user pro€le size on the quality of UMAP , pages 289–295, 2013. recommendation. In set of data from the more popular information domains, such [23] R. Socher, D. Chen, C. D. Manning, and A. Y. Ng. Reasoning with neural tensor as E-commence sites, to explore the generalization ability of our networks for knowledge base completion. In , pages 926–934, 2013. NIPS solution to other information domains. Second, due to the small X. Song, L. Nie, L. Zhang, M. Akbari, and T. Chua. Multiple social network [24] SIGIR , pages learning and its application in volunteerism tendency prediction. In number of bridge users, we forwent the study of user cold-start 213–222, 2015. problem, as further holding out bridge users to simulate the cold- [25] N. Srivastava, G. E. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov. 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