SAR: A Sentiment-Aspect-Region Model for User Preference Analysis in Geo-tagged Reviews

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1 : A Sentiment-Aspect-Region Model fo Use Pefeence Analysis in Geo-tagged Reviews Kaiqi Zhao, Gao Cong, Quan Yuan School of Compute Engineeing Nanyang Technological Univesity, Singapoe {kzhao2@e., gaocong@, qyuan1@e.}ntu.edu.sg Kenny Q. Zhu Depatment of Compute Science & Engineeing Shanghai Jiao Tong Univesity, Shanghai, China kzhu@cs.sjtu.edu.cn Abstact Many location based sevices, such as FouSquae, Yelp, TipAdviso, Google Places, etc., allow uses to compose eviews o tips on points of inteest (POIs), each having a geogaphical coodinates. These sevices have accumulated a lage amount of such geo-tagged eview data, which allows deep analysis of use pefeences in POIs. This pape studies two types of use pefeences to POIs: topical-egion pefeence and categoy awae topical-aspect pefeence. We popose a unified pobabilistic model to captue these two pefeences simultaneously. In addition, ou model is capable of captuing the inteaction of diffeent factos, including topical aspect, sentiment, and spatial infomation. The model can be used in a numbe of applications, such as POI ecommendation and use ecommendation, among othes. In addition, the model enables us to investigate whethe people like an aspect of a POI o whethe people like a topical aspect of some type of POIs (e.g., bas) in a egion, which offe explanation fo ecommendations. Expeiments on eal wold datasets show that the model achieves significant impovement in POI ecommendation and use ecommendation in compaison to the state-of-the-at methods. We also popose an efficient online ecommendation algoithm based on ou model, which saves up to 9% computation time. I. INTRODUCTION Nowadays, uses can easily convey thei opinions on points of inteest (POIs) by tapping on thei smat mobile devices in location based sevices (LBS) like Yelp, TipAdviso, etc. These LBS systems contain thee kinds of useful infomation fo use pefeence modeling. Fist, they povide a lage amount of use eviews on POIs. Diffeent fom tips in FouSquae o geo-tagged tweets in Twitte, the use eviews contain moe details about why the uses like/dislike the POI, which aspects of the POI satisfy them while which aspects dissatisfy them. The availability of such eviews makes it possible to model use pefeences on the aspect level. Second, the geogaphical coodinates of the POIs in these systems eveal the uses activity aeas and thei spatial pefeences. Fo example, some uses may like to visit a shopping steet while some often visit a egion famous with bas. Thid, the categoy of POIs may help analyze the aspects of the POIs and the aspect pefeences of uses on cetain categoy of POIs, because POIs in the same categoy shae some common aspects (e.g., oom cleanliness/comfot of hotels, taste of estauants, etc.). Recently, seveal studies on geogaphical topic modeling [5], [27] model use pefeences on geo-tagged tweets. Use pefeences ae modeled as a distibution ove topical-egions (called Topical-Region Pefeence). A topical-egion epesents a geogaphical aea in which uses do simila things (such as dining). It compises two components: geo-location and semantics. Fo example, POIs in Cental Pak and those on Wall Steet, Manhattan may fom two diffeent topical-egions. The ones in Cental Pak may have tweets that contain wods like concet, ticket, bid, unning, etc., while the ones on Wall Steet may have tweets about stocks o finance. Howeve, geo-tagged tweets ae too shot fo aspect extaction and the afoementioned studies do not model the use pefeences on aspect level, i.e., they ae not able to captue the Topical- Aspect Pefeences. Topical-aspects ae the aspects of POIs that ae commented by uses, such as envionment, taste, pice, etc. An example fo the topical-aspect pefeences is that a use may like the envionment in westen estauants, but the good taste in Chinese estauants. Moeove, these topical aspect pefeences ae often categoy-awae as illustated in the pevious example. To the best of ou knowledge, no existing wok on modeling geo-tagged textual data models uses topical-aspect pefeences. On the othe hand, seveal poposals [13], [18], [19], [7] on opinion mining aim at identifying latent topical-aspects and pedicting atings/sentiments on identified aspects in poduct eviews. Most of these studies aim at mining item aspects and sentiments but not use pefeences, and thus they do not incopoate use infomation in thei models. Zhang et al. [29] conside aspect, sentiment and use infomation fo ecommendation. Howeve, thei wok and all of the afoementioned poposals fo opinion mining do not conside the geo-tags in the eviews, which ae impotant signals fo modeling use pefeences on spatial data. In summay, neithe existing geogaphical models no opinion mining models conside aspects, sentiment, egions and categoy at the same time. In this pape we popose a novel, unified model to lean use pefeences based on eviews, categoies and geolocations of POIs. Ou model is able to captue the intedependency of thee latent factos including topical-egion, topical-aspect, and sentiment simultaneously fo identifying the topical-egion and topical-aspect pefeences fo each use. Thee ae thee benefits to model the intedependencies. Fist, the leaning of topical-egion pefeence benefits fom topical-aspects and sentiment. Because a use may not like the place she visited befoe, mining topical-egions based on visit histoy without consideing the use s sentiment would lead to incoect use pefeence on some egions. We solve this poblem by in-

2 copoating aspect and sentiment in the leaning of topicalegion. Second, the topical-aspect extaction benefits fom the topical-egions. Some wods in the text ae elated to functional and spatial infomation of the egion, e.g., estauant, New Yok, etc. The topical-egions help ecognize these wods and make the topical-aspects moe accuate, i.e., estauant and New Yok would not appea as epesentative wods in topical-aspects. Thid, we can apply the model to many applications, such as POI ecommendation, use ecommendation and aspect satisfaction analysis in egions, etc., and answe questions like: Which aspect of a location is favoed by people and which is not? Which POI would a use like to visit? Who would be inteested in a given POI? What is the oveall positive aspect of POIs in the same categoy in each egion? Building such a unified model is a challenging task. Fist, the inteaction among the thee types of latent vaiables (fo topical-aspect, sentiment, topical-egion, espectively) and the categoy of POIs is unknown. Second, aspect and sentiment ae usually modeled at sentence level [7] while egion is modeled at the eview o document level [5], [25], which makes it difficult to estimate the paametes of a unified model. To ovecome the fist challenge, we model both the categoyawae topical-aspect pefeences and the topical-egion pefeences as conditional multinomial distibutions. In addition, we popose a geneative pocess of the eview wods, which geneates both topical-aspect wods and topical-egion wods, to captue the implicit inteaction between topical-aspects and topical-egions. To ovecome the second challenge, we popose a two-step expectation-maximization infeence algoithm. We estimate the document-level paametes (elated to topicalegions) in the fist step and the sentence-level paametes (elated to topical-aspects and sentiments) in the second step. We demonstate the effectiveness of ou model on vaious applications such as POI ecommendation, use ecommendation, and aspect satisfaction analysis in egions. We also develop an efficient algoithm to speed up online ecommendation based on ou model. In summay, this pape makes the following contibutions: 1) We popose a novel unified pobabilistic model to captue the inteaction of aspect, sentiment, categoy as well as spatial infomation; 2) We popose an infeence algoithm fo the model and an efficient algoithm fo online top-n POI ecommendation; 3) We apply ou poposed model to ecommend POIs and uses and compae egions, and popose an efficient online ecommendation algoithm. Ou expeimental esults show that the model outpefoms the state-of-the-at methods in POI ecommendation and use ecommendation; We also demonstate that ou model is able to offe explanation fo ecommendations while the baseline methods [22] fail to offe. The est of the pape is oganized as follows: Section II intoduces elated wok; Section III pesents ou unified model and coesponding infeence algoithm; Section IV applies ou model to seveal applications; Section V demonstates the model selection and tuning and then evaluates the model on thee ecommendation tasks. Section VI concludes this pape. II. A. Geogaphical Topic Modeling RELATED WORK Based on the taditional topic modeling techniques such as Latent Diichlet Allocation (LDA) [1] and Pobabilistic Latent Semantic Analysis (PLSA), some ecent studies [3], [17], [5], [27] incopoate geogaphical infomation in topic models. Benefit fom the geogaphic infomation, these models can discove egional topics, which ae shown to be useful in POI ecommendation. Some of these studies [14], [3], [17], [16], [25] focus on analyzing the elation between locations and wods/topics without consideing uses. Mei et al. [14] sample each wod in thei model conditioned on the time, location (id only) and backgound wods. Eisenstein et al. [3] conside the coodinates of locations and use the Gaussian distibution to geneate coodinates fo locations fom latent egions. GeoFolk [17] geneates latitude and longitude of a location fom two Gaussian distibutions detemined by the topic of the location s document. Yin et al. [25] popose a PLSA model with two latent vaiables, egion and topic, in two levels. Regions ae geneated out of the document level, which is shaed by all of the documents. Topics ae geneated in the document level. Each latent egion is modeled as a Gaussian distibution in thei model. Diffeent fom these poposals, ou wok focuses on modeling use pefeences and takes uses and uses sentiment into account. Thee also exist poposals [5], [27], [24] that model use pefeences to geogaphical topics based on geo-tagged tweets. Hong et al. [5] popose a model to analyze the geogaphical topics in geotagged tweets. In this model, latent egions ae modeled as Gaussian distibutions and each egion contains a topic distibution. Yuan et al. [27] exploe the tempoal infomation togethe with the location, topic, and use infomation to model the time-awae pesonalized topic egion. Yin et al. [23] conside that the use behavios depend on both the use s topic pefeences and tempoal topic distibutions. They incopoate categoy and locality pefeence into consideation to make futhe impovement on modelling use pofiles [24]. Ou wok is diffeent fom these poposals in that we focus on use eviews athe than tweets, and we not only exploe the topic-egions but also analyze the topical-aspects and coesponding sentiments in the eviews. B. Sentiment Analysis Ou wok is also elated to the wok on sentiment aspect joint modeling. Accoding to diffeent ganulaities of sentiment, we divide the existing studies into two types: sentence level, and phase level. Sentence level sentiment analysis supposes each sentence expesses one aspect of the poduct. Titov and McDonald [18] pesent a sentence level model, namely MG-LDA, to extact aspects fom eviews. Based on MG-LDA, Titov and McDonald futhe popose a method [19] based on MG-LDA

3 which jointly models the aspect and ating. The model is then used to pedict aspect atings fom a eview. This model can extact aspect level sentiment/ating, but needs aspect ating as obsevable vaiable, which is often not available. Jo and Oh [7] model aspect and sentiment jointly in an LDA-based famewok. Both aspect and sentiment ae modeled as latent vaiables in the model, and each wod has a joint distibution ove topics and sentiment polaities. To identify the polaities, they keep a list of seed wods fo each sentiment polaity, and give highe pobability to geneate a seed wod fom its coesponding polaity. Studies on phase level sentiment [13], [2], [12], [15], [3] use NLP tools to analyze the dependency between the wods in a sentence and extact aspect-opinion phase pais, e.g., < sceen, bight >, with some pedefined pattens. The aspect-opinion phase pais ae then used fo futhe analysis on the sentiment polaities on the aspects. Mei et al. [13] build a PLSA model in which a topic is modeled as a linea mixtue of multinomials fom neutal topics and two sentiments (positive and negative). Wang et al. [2] build a egession model to captue the aspect atings fom the oveall atings. The oveall atings ae modeled as the weighted sum of the sentiments fom all aspects. Howeve, aspects ae fixed and extacted using a list of seed wods and a bootstapping algoithm. Moghaddam and Este [15] popose an intedependent LDA model in which the aspects of a poduct is modeled and the coesponding atings to each aspect is dawn depending on the aspect. Howeve, the atings ae teated as 5 clustes and the model cannot tell which cluste has the ating of 1 and which has the ating of 5. Ou model diffes fom these models in that we jointly conside egion, aspect and sentiment in a unified model. C. POI ecommendation We divide the existing appoaches into thee categoies: memoy-based collaboative filteing, matix factoization and topic models. Since topic models ae mentioned in Section II-A, we focus on memoy-based collaboative filteing and matix factoization in this section. Seveal poposals ecommend POIs based on collaboative filteing () [22], [9], [26]. Ye et al. [22] popose a fusion famewok to combine use-based, fiend-based and geo-based collaboative filteing. In the geogaphic model, the pobability of tanspoting fom one POI to anothe is dawn fom a powe law distibution ove the distances between the two POIs. Levandoski et al. [9] use an item-based fo POI ecommendation, but they mainly focus on how to make the memoy based method efficient on a lage dataset. Yuan et al. [26] popose the poblem of ecommending POIs fo a use specified time, and incopoate the tempoal facto into the use-based model fo ecommendation. Yuan et al. [28] also popose a gaph-based appoach fo time-awae POI ecommendation which integates geogaphical and tempoal influences. In the poposals based on matix factoization, Liu et al. [1] and Cheng et al. [2] popose latent facto models by incopoating the geogaphical infomation using Gaussian distibution. Yang et al. [21] popose a sentiment-enhanced pesonalized location ecommendation system using pobabilistic matix factoization. Vey ecently, Zhang et al. [29] popose an explicit facto model which takes aspect and sentiment into account. Howeve, these poposals do not conside the geogaphical infomation. In summay, no existing wok models aspect, sentiment, spatial infomation and categoy at the same time. And no existing wok is able to discove the latent elation between these vaiables. III. SENTIMENT-ASPECT-REGION MODEL We fist pesent ou objectives to build the unified sentiment-aspect-egion model. To achieve the objectives, we pesent seveal intuitions based on which we build ou model. We then descibe the details of the model, and popose a paamete estimation method. A. Intuitions In this pape, we aim at building a model that is able to 1) extact latent vaiables, i.e., topical-aspect, sentiment, and topical-egion fom the eview data; 2) captue the intedependencies among categoy, POI, use, wods and the thee latent vaiables; and 3) discove use s topical-egion and topicalaspect pefeences. To achieve these objectives, we exploit the following intuitions in designing ou model: Intuition 1: A use visits POIs in a topical-egion because the egion is geogaphically convenient to the use (e.g., close to he activity aeas) and its topics (e.g., shopping steet, education aea, etc.) satisfy the use s inteest. Each use has he own pefeences on the topical-egions. Intuition 2: A use ates highly of a POI because she likes some aspects of the POI. Such pefeences might be indicated in he eview. Some uses like to check the pice ange of a estauant fist while othes might be moe concened with the envionment. Moeove, POIs in diffeent categoies may have diffeent aspects of inteest. Intuition 3: A use decides to visit a POI in a egion by consideing the categoy, categoy-awae topical-aspects of the POI and the distance to it. Fo example, uses may visit POIs of the estauant categoy with good envionment, but she may fist conside the estauants neaby. Intuition 4: When a use wites a eview on a POI, she will use wods fo both the aspects of the POI and he sentiments about the aspects. The use may also use wods fo the topical-egion of the POI. Fo example, a eview on a shop in Times Squae may say: This shop offes best pices in Times Squae. The eviewe uses pice fo aspect, best fo sentiment and Times Squae fo egion. B. Model Desciption We fist define the notations to be used in the poposed model. Let D be the set of use eviews, and U be the set of uses. Fo each eview, we denote the numbe of its sentences by M and numbe of wods in each sentence by N. In ou model, a location has two attibutes: identifie and coodinates. We use l to epesent a location identifie and cd l to denote its coesponding coodinates. Hee cd l is a latitude and longitude pai. We denote the topical-aspect, sentiment and topical-egion

4 bya,s, and, espectively. The notations used in this pape ae listed in Table I. Following the intuitions discussed in Section III-A, we poceed to pesent ou model. TABLE I: Desciption of Symbols c l D Symbol Desciption u, U individual use and the set of uses l, L individual POI and the set of POIs c categoy topical-egion a, s topical-aspect and sentiment d, D single eview and the set of eviews M the numbe of sentences in a eview w, N single wod and the numbe of wods in a sentence Based on Intuitions 1&2, we model the use topical-egion pefeences and topical-aspect pefeences as multinomial distibutions p( u) and p(a u, c), espectively. Based on Intuition 3, a use chooses a POI to visit by consideing both the categoy and the distance. We define the pobability of visiting a POI l given categoy c and egion popotional to p(l c) p(l ). Hee p(l c) is the pobability of selecting POI l fom the categoy c; p(l ) is a the pobability of selecting POI l in egion by consideing the distance fom l to. Afte nomalization, we have the definition p(l c)p(l ) p(l c,) = l p(l c)p(l ). To model the spatial distance, we use a Gaussian mixtue model, i.e., p(l ) N(µ,Σ ), whee µ is the cente of egion and Σ is the covaiance matix which depicts the aea of egion. To model the membeship of a POI to a categoy, we use a unifom distibution fo p(l c). Based on Intuition 4, we model the elationships among wods, topical-aspects, sentiments and topical-egions by p(w a,s,) = λp(w a,s) + (1 λ)p(w ), whee a, s, ae topical-aspect, sentiment and topical-egion, espectively. Hee p(w a, s) is the pobability that the uses wite wod w when they have sentiment s on aspect a; p(w ) is the pobability that the uses use wod w to descibe egion ; paameteλis used to balance the potion of wods dawn fom topical-aspect, sentiment o topical-egion. We model p(w a, s) instead of p(w a) and p(w s) because aspects and sentiments ae closely coupled, and modeling by p(w a) and p(w s) needs an additional tuning paamete. Simila to poposals of sentence level sentiment analysis [18], [19], [7], we assume each sentence expesses opinions on exactly one topical-aspect and each topical-aspect is associated to a positive, negative o neutal sentiment. In summay, the gaphical epesentation of ou model is shown in Figue 1 and the geneative pocess of the eviews witten by use u is descibed as follows: Fo each eview d D u, whee D u is the set of eviews witten by use u. Daw topical egion p( u) Daw categoy c p(c u) Daw location l p(l c,) = p(l )p(l c) l p(l c)p(l ), whee p(l ) N(µ,Σ ) Fo each sentence in eview d Daw aspect a p(a u,c) Daw sentiment s p(s a,l) U Fig. 1: Sentiment-Aspect-Region Model () s w N Fo each wod position in the sentence Daw wod w p(w a,s,) = λp(w a,s)+(1 λ)p(w ) In the model, p(l c) and p(c u) can be estimated diectly fom a given copus. The othe distibution paametes need to be infeed. We fist pesent how to estimate p(l c) and p(c u), and then show the infeence algoithm fo the emaining distibutions in Section III-C. As descibed in Intuition 3, a POI l is geneated fom both categoy and egion. Since POI l and categoy c ae obsevable vaiables, we simply compute p(l c) by Equation (1). p(l c) = I(l,c) = M I(l, c) # of POIs in c { 1 l c othewise Similaly, we compute the categoy pefeences of each use, i.e., p(c u), diectly fom the copus. To handle the ovefitting poblem, we apply the additive smoothing technique. Afte smoothing, even though a use did not a visit some categoy of POIs, the pobability of visiting that categoy still has a small value. The computation of p(c u) is shown in Equation (3). p(c u) = n c +α N +αc, (3) whee n c is the numbe of eviews of POIs in categoy c that use u wites; N is the total numbe of eviews on POIs in c; C is the total numbe of categoies; α is the smoothing paamete which is usually set to a value smalle than 1. In this pape, we set α =.1. C. Infeence Algoithm To infe the paametes of the model, we use the expectation-maximization (EM) appoach. In this section, we pesent the computation of the copus likelihood, the two-step EM algoithm used to infe ou paametes, and initialization of the EM algoithm. (1) (2)

5 1) Likelihood Computation: Ou model has seveal levels, i.e., wod level, sentence level, and document level. The latent vaiables ae on two levels. Region is at document level while aspect a and sentiment s ae at sentence level. This multi-level stuctue poses challenges to the estimation of the log-likelihood. Accoding to the geneative pocess, we have the likelihood of the copus D: D R p(d;φ) = p(u d ) p( u d )p(l d,w d,u d ) (4) d M p(l d,w d,u d ) = p(c ld u d )p(l d,c ld ) p(w d,i c ld,,u d,l d ) p(w d,i c ld,,u d,l d ) = a,s p(a c ld,u d )p(s a,l d ) i N p(w d,i,j a,s,) In Equation (4), Φ is the set of paametes in the model, i.e., p( u), p(a c,u),p(l ),p(s a,l),p(w a,s), p(w ),µ and Σ. Vaiables u d,l d,w d ae the use, location and wods of eview d, espectively. Vaiable w d,i epesents the set of wods in sentenceiof eviewdwhilew d,i,j is thej th wod in sentencei of eview d. Taking logaithm of p(d;φ) leads to a summation inside the logaithm: L = d logp(u d )+log j (5) (6) p( u d )p(l d,w d,u d ) (7) Since this likelihood cannot be estimated diectly, we adopt Jessen s inequality to the log-likelihood, and estimate the lowe bound of the likelihood and the paametes in an iteative manne. 2) Expectation-Maximization: Due to the afoementioned difficulty of computing log-likelihood diectly, we apply Expectation-Maximization (EM) algoithm to estimate the model paametes. In E-step, we compute the expectation of latent vaiables given the obseved data. By applying Jessen s inequality to Equation (7), we get the lowe bound of the likelihood as: L LB = d + d, logp(u d ) p( d)(logp( u d )+logp(l d,w d,u d )) As shown in Equation (8), we need to estimate p( d) to compute the full likelihood. We apply Bayes ule, and obtain the update function of the posteio distibution as (8) p( d) = p(,d) p(,d) (9) p(,d) = p(u d )p( u d )p(l d,w d,u d ) (1) In Equation (1), p(l d,w d,u d ) is computed by Equation (5), and p(u d ) appeas both in the numeato and the denominato, and thus is not necessay to estimate. In M-step, by maximizing the lowe bound of likelihood, we can obtain the update function of paametes at document level that ae elated to topical egion as below. p( u) = d D u p( d) d D u p( d) (11) Howeve, we cannot obtain a close fom solution fo µ and Σ due to the nomalization tem. We adopt a gadient method to obtain the update value of µ and Σ in M-step. Specifically, we use the BFGS quasi-newton method [8], [11]. In the gadient method, we compute the gadient of µ and Σ as follows: L LB µ = d L LB Σ = d p( d)σ 1 ( l q(l )(cd l µ ) l q(l ) l p( d)( q(l )g(l,) l q(l ) ) (cd ld µ ) (12) g(l d,)), (13) whee q(l ) = p(l c l )p(l ) and cd l denotes the coodinates of POI l. The function g(l,) in Equation (13) is the gadient of the Gaussian distibution fo egion w..t. Σ at point l. Since sentiment and aspect ae at the sentence level, we cannot compute logp(l d,w d,u d ) in Equation (8) using p( d). Thus, we popose a second level of EM iteations. Specifically, we intoduce a new latent vaiable to estimate paametes elated to aspect and sentiment. Specifically, we use φ a,s,,di to identify the pobability that the i th sentence in a eview d fom egion is assigned with aspect a and sentiment s. we use φ a,s,,di and p( d) to compute the update function of p(a c, u), p(s l, a), p(w a, s), and p(w ). Denote by n(w,d i ) the numbe of occuences of wod w in sentence i of eview d. We estimate φ a,s,,di as: φ a,s,,di = p(a,s,,d i ) a,s p(a,s,,d i) p(a,s,,d i ) = p(u d )p( u d )p(c ld u d,)p(l d,c ld ) p(a c ld,u d )p(s a,l d ) w p(w a,s,) (14) n(w,di) (15) By maximizing the lowe bound of the likelihood, we obtain the update function of the est paametes: d D p(a u,c) = u p( d) i s φ a,s,,d i a d D u p( d) i s φ (16) a,s,,d i d D p(s l,a) = l p( d) i s φ a,s,,d i s d D l p( d) i s φ (17) a,s,,d i d p(w s,a) = p( d) i φ a,s,,d i n(w,d i ) w d p( d) i φ a,s,,d i n(w (18),d i ) d p(w ) = p( d) i a s φ a,s,,d i n(w,d i ) w d p( d) i a s φ a,s,,d i n(w,d i ), (19) whee D u is the set of eviews witten by use u and D l is the set of eviews fo POI l.

6 3) Initialization of EM Algoithm: EM algoithm can only guaantee to find a local optima. Diffeent initializations may lead to diffeent esults. In this section, we pesent ou methods fo initializing the assignment of aspect, sentiment and egion. Aspect is extacted fom sentence level in ou model. We initialize the aspect by a clusteing pocess on sentences. Each sentence is epesented as a vecto of wods. Given the numbe of aspects, we use K-means clusteing algoithm to assign each sentence an aspect. We then initializep(w a) by the pobability that wod w appeas in sentences caying aspect a. Sentiment has 3 possible values in this pape: positive, negative and neutal. In ode to know the polaity of each sentiment, we need some pio knowledge. We use the same pedefined set of sentiment seed wods as in Jo s poposal [7]. Moeove, we apply a syntactic pase to extact negation of the sentiment wods such as not good and use a special wod not good to epesent the phase not good in ou vocabulay. Fo each wod in the seed wod set, we assign a pobability (p(w s)) of 1 to its polaity and to the othe two polaities. Fo wods not in the seed wod set, we assign an equal pobability fo each polaity. We then use p(w a)p(w s) to appoximate p(w a, s). Region is initialized by a K-means clusteing algoithm based on the coodinates (latitude and longitude). The clusteing algoithm patitions POIs to diffeent egions. Then fo each egion, we compute µ and Σ using a egession ove the POIs in the egion. We compute p(w ) by the distibution of wods in the eviews fo POIs in egion and p( u) by the potion of eviews that use u wites in egion. Fo othe paametes: p(a c, u) and p(s a, l), we initialize them by using the assignment of aspect and sentiment to a sentence (We assign sentiment to a sentence by voting fom sentiment seed wods extacted fom the sentence). Specifically, p(a c, u) is popotional to the numbe of sentences that ae assigned to a and that belong to a eview witten by u fom categoy c; p(s a, l) is popotional to the numbe of sentences that belong to location l and ae assigned to sentiment s and aspect a at the same time. 4) Efficiency Analysis: Let the numbe of sentiment be 3 and we teat it as constant. In E-step, the computation of the expectation of latent vaiables in Equation (9) and the vaiables φ a,s,,di in Equation (19) needs O( D MNRA) = O(WRA), whee W is the numbe of wods in the eviews of all uses in taining set, R is the numbe of egions and A is the numbe of aspects. In M-step, the cost fo updating Equation (16) to (19) is O(UA + LA + VA + VR), whee U,L,V ae the numbe of uses, POIs and unique wods, espectively. To update µ and Σ, we pefom a quasi-newton method. Since each µ and Σ ae two dimensional vecto and 2 2 matix, espectively. The computation cost of matix opeation can be teated as constant. Let D be the numbe of eviews, the cost of computing gadient in Equation (12) and (13) is D + L. Theefoe, the complexity of quasi-newton is O(I q R(D+L)), whee I q is the numbe of iteations of quasi-newton. In summay, the total complexity of the leaning algoithm with I iteations iso(i(wra+i q R(D+L)+UA+LA+VA+VR)). Since WRA (UA + LA + VA + VR), we simplify the cost as O(I(WRA + I q R(D + L))). We can paallelize the computation of both E-step and M-step. In E-step, since the computation of p( d) on each document is independent to othes, we can compute p( d) of each document in paallel. In M-step, the update of Equation (16) to (19) and the quasi- Newton iteations can also be paallelized in the simila way as p( d). Theefoe, the algoithm can be fully paallelized. IV. APPLICATIONS We pesent thee applications of ou model, namely POI ecommendation, use ecommendation, and aspect satisfaction analysis in egions. In POI ecommendation, we povide a way to explain the eason of ecommending a POI and popose an efficient online ecommendation algoithm. A. POI ecommendation We apply ou model to two POI ecommendation tasks and popose an efficient online ecommendation algoithm. The two ecommendation tasks ae All-Categoy Recommendation and Single-Categoy Recommendation. 1) All-Categoy Recommendation: All-Categoy Recommendation is a task of geneating a ank list of POIs in any categoy given a set of POIs and a use. The afoementioned poposals ae all fo all-categoy ecommendation. We calculate the pobability of p(l,s + u), i.e., the pobability of use u visits POI l with positive sentiment, to scoe l fo u as shown in Equation (2). p(l,s + u) = p( u)p(c l u)p(l,c l ) p(a u,c l )p(s + a,l) a (2) Accoding to Equation (2), we make the ecommendation by consideing the matching between use pefeences (i.e., p( u), p(c l u) and p(a u,c l )) and the attibutes of the POI (i.e., p(s + a,l) and p(l,c l )). This ecommendation model enables us to explain why we ecommend a POI to a use. We conside two factos: aspect and egion. Fist, we ank the aspects by p(s + a,l)p(a u,c l ) to eveal which aspects match the use s pefeences. Second, we ank the egions by p( u)p(l ) to eveal which egions contibute moe to the ecommendation. Finally, we choose top seveal aspects and egions fo explanation. 2) Single-Categoy Recommendation: Single-Categoy Recommendation aims at anking POIs given a use and a specific categoy (e.g., estauants). It is a typical scenaio fo POI ecommendation although it has not been coveed in pevious wok. We compute p(l,s + u,c) as shown in Equation (21). Compaed to all-categoy ecommendation, we fix the categoy i.e., emove p(c u) fom Equation (2). All locations that ae not in c will not be consideed in this scenaio. p(l,s + u,c) = p( u)p(l, c) p(a u,c)p(s + a,l) a (21) We can also offe explanation fo the single-categoy ecommendation by following simila method as we employ fo the all-categoy ecommendation.

7 3) Efficient algoithm fo Top-N Online Recommendation: Time efficiency is an essential pat of online ecommendation. A staightfowad method of making ecommendation is to compute the ecommendation scoe as Equation (2) o Equation (21). This method equies tavesing all the egions which is highly time consuming. Anothe choice is the theshold algoithm [4] that may save the computation fo some POIs. Howeve, in ou applications, the numbe of attibutes (i.e., egions and aspects) is lage, and thus it is expensive to compute the ecommendation scoe even fo a single POI. The theshold algoithm cannot help with this, eithe. We popose an optimized top-n items ecommendation algoithm that significantly educes the time cost. As to be shown in the expeiment, ou algoithm is faste than the theshold algoithm in the top-n POI ecommendation using ou model. Ou algoithm can be applied to all o single-categoy POI ecommendation. We use all-categoy POI ecommendation (Equation (2)) as an example to explain the algoithm. Ou algoithm is based on two obsevations: 1) A use only pefes a small numbe of egions; and 2) POIs in the cente of the egion ae moe likely to be ecommended. These two obsevations indicate that only when a use pefes a egion and the POI is nea the cente of the egion, will the scoe p( u)p(l,c l ) contibute significantly to the ecommendation scoe. Theefoe, afte we have computed the most possible egions fo a POI, it may not be necessay to compute the emaining egions. We design a banch and bound algoithm as shown in Algoithm 1 to pune the seach space of the egions. Ou algoithm contains two steps: initialization and puning. In the initialization step (line 2), we find N candidate POIs that ae potentially good fo ecommendation. Specifically, we pick top K egions which cove most of the use s egional pefeences (i.e., K i=1 p( i u) >.9) with smallest K (line 21). If K is lage than N, we pick at most N egions to ensue that we can select at least one candidate fom each egion. In each of the top K egion, we choose top N K POIs w..t. p(l ) as candidates. In the puning step (line 9-1), we check whethe we can avoid tavesing unnecessay egions fo each POI. We tavese the egions accoding to the descending ode of p(l,c l ) fo POI l. Suppose we have tavesed egions { 1,..., i 1 }. The patial scoe we have computed fo the tavesed egions is i 1 PScoe = p( j u)p(l j,c l ). j=1 When we exploe the i-th egion, we compute the uppe bound of ecommendation scoe fo the POI as: i 1 Bound (i) (l) = PScoe+(1 p( j u))p(l i,c l ). (22) j=1 Because we check the egions in the descending ode of p(l,c l ), the actual value of p(l,c l ) fo the emaining egions should be less than the one fo the cuent egion, i.e., p(l i,c l ). Theefoe, we have a patial ecommendation scoe fo the est of the egions, which is at most i 1 (1 p( j u))p(l i,c l ), j=1 whee 1 i 1 j=1 p( j u) is the potion of use pefeences fo the est egions. The uppe bound of p(l,c)p( u) fo all egions is PScoe + (1 i 1 = 1 p( u))p(l i,c l ). Since a p(a u,c)p(s + a,l) 1, Finally, we obtain the uppe bound of the ecommendation scoe in Equation (2) fo the POI by setting a p(a u,c)p(s + a,l) = 1, which esults in Equation (22). If the uppe bound is smalle than the N th candidate (Line 9), we skip the cuent POI (no need to check the emaining egions). Othewise, we continue to check the emaining egions. If all egions ae examined fo the POI and the POI is not puned by the afoementioned uppe bound, we compute the full scoe of the POI to compae with the N th smallest candidate (line 12). We emove the N th candidate in the list and inset the POI to the list if the full scoe is lage than the N th candidate (line 13-15). To maintain the top-n candidate list, we use a binay min-heap. Algoithm 1 POI Recommendation 1: function REC(u, N) 2: H InitialCandidates(N) 3: fo l L and l H do 4: PatS,PatRPo,Skip false 5: while thee exists not examined fo l do 6: NextRegion() 7: PatS PatS +p( u)p(l,c l ) 8: PatRPo PatRPo+p( u) 9: if PatS + (1 PatRPo) p(l,c l ) < H.T op() then 1: Skip tue, beak 11: if Skip = false then 12: S PatS p(c l u) a p(s + a,l)p(a u,c l ) 13: if S > H.Top() then 14: H.DeleteT op() 15: H.Inset(< l, S >) 16: Result Sot H by Scoe S 17: etun Result 18: function INITIALCANDIDATES(N) 19: H 2: 1,..., R Sot the egions by p( u) 21: Pick top K egions satisfies: K = min({k k i=1 p( i u) >.9},N) 22: Fom 1 to R K, Inset top N K POIs odeed by p(l ) to H until H contains N POIs 23: etun H B. Use Recommendation We can also apply ou model to ecommend uses fo a POI. Pedicting which uses may favo a given POI is useful when the owne of the POI wants to taget at o advetise to some of the uses. Given a POI l, we compute the pobability

8 p(u,s + l) of useufavoing POIlby consideing both topicalegion and topical-aspect pefeences of uses as follows: p(u,s + l) = p(u,s +,l) u,s p(u,s,l) (23) p(u,s,l) =p(u)p(c l u) p( u)p(l,c l ) p(a u,c l )p(s a,l), a (24) whee pio p(u) is calculated using the use s eview histoy: p(u) = # of eviews u wote. # of all eviews Since the last two summations ae the same as those in POI ecommendation, Algoithm 1 can also be used to speed up the use ecommendation. C. Aspect Satisfaction Analysis in Regions Discoveing which aspect is satisfied o not by uses in each egion is useful when 1) someone wants to set up a new business o make stategies to attact moe customes, o 2) policy makes make uban planning. Fo example, most of the estauants in a egion of a city may be complained fo the long waiting time. By knowing the dissatisfaction of this aspect, a estauant may think how to achieve competitive advantage ove othe estauants in the egion. We can infe the aspect satisfaction in each egion based on ou model. Specifically, we compute the aspect distibution of each sentiment s, categoy c and egion as p(a s,c,) = u,l p(u)p( u)p(c u)p(a c,u)p(l,c)p(s a,l) a,u,l p(u)p( u)p(c u)p(a c,u)p(l,c)p(s a,l) (25) This pobability shows which aspect is most pobably liked/disliked in POIs fom categoy c and egion. V. EXPERIMENTAL STUDIES We conduct seveal expeiments to evaluate the pefomance of ou model by compaing with the state-of-the-at techniques. Fist, we pesent the expeimental setup in Section V-A and the model selection stategy in Section V-B; Then, we apply ou model to the thee applications. We show the accuacy and efficiency of ou ecommendation algoithm in POI ecommendation in Section V-C and exploe the eason of making a POI ecommendation in Section V-D. Afte that, we show the accuacy of use ecommendation in Section V-E. Finally, we analyze the aspect satisfaction in egions in Section V-F and discuss the quality of topical egions in Section V-G. A. Expeimental Setup We collect data fom two diffeent cities in Yelp, which hosts hundeds of thousands of use eviews and atings fo POIs. One of ou datasets is fom Yelp s Challenge Dataset 1, which contains 11,537 POIs and 43,873 uses fom Phoenix at the time of data collection. We emove uses who wote fewe than 2 eviews and POIs without any eviews afte filteing the uses. This pepocessing esults in a dataset containing 11, challenge/ POIs and 21,98 uses. We cawl the othe dataset fom Yelp Singapoe, and emove uses and POIs without any eviews. The esulting Singapoe dataset contains 8,846 POIs and 1,654 uses. The statistics of the two datasets is shown in Table II. Fo each dataset, we hold out the ecent 1% eviews of each use fo tuning and 1% fo testing, espectively, and use the emaining 8% data as taining set. In the tuning and test data, we geneate the gound tuth, i.e., whethe a use likes the POI o not, by checking how the use ates to that POI. When the use ates moe than 3.5 stas, we conside that she likes the POI and put the use-poi pai into the set of gound tuth. TABLE II: Statistics of the two datasets Phoenix Singapoe #POIs 11,359 8,846 #Uses 21,98 1,654 #Reviews 215,837 2,248 #Reviews pe use #Reviews pe POI We un all expeiments on a machine with Intel Xeon E5-268 (2.8 Ghz) 1-coes CPU and 64GB memoy. We deploy the taining pogam on 8 coes of the CPU and tain the models on Singapoe and Phoenix datasets with the same settings as in Section V-B. The taining time of Singapoe data is minutes and the Phoenix data is minutes. B. Model Selection In ou model, we have two fee paametes: numbe of aspects A and numbe of topical egions R, and a tunable paamete λ. To find a pope value of A and R, we use Bayesian Infomation Citeion (BIC) which is usually used fo model selection. BIC is defined as: BIC = 2L+Kln(N), whee L is the likelihood of the model, K is the numbe of paametes and N is the scale of the copus. In ou scenaio, K is A R, while N is the numbe of eview sentences. We set the default value of paamete λ to.6, and choose A,R which achieve lowest BIC in the tuning set of each dataset. In the Phoenix data, the lowest BIC appeas when R = 8 and A = 3. In the Singapoe data, smalle numbe of aspects and egions ae pefeed because Singapoe is smalle than Phoenix. We set R = 4 and A = 2 fo Singapoe data. C. POI ecommendation Fist, we intoduce seveal existing methods fo competition and the evaluation metics. Then, we compae with the state-of-the-at baselines fo both all-categoy and singlecategoy ecommendation. Finally, we evaluate the efficiency of ou ecommendation algoithm. 1) Recommendation Methods: We compae ou model to five POI ecommendation techniques. : Use-based collaboative filteing model. : A collaboative filteing model incopoating geogaphical influence [22]. : A topic model with pesonalized egions [27]. : A topic model with global egions [6]. : A matix factoization based explicit facto model which extacts aspects and sentiment fom

9 eviews, and models the elation among use, item, aspect and sentiment fo ecommendation [29]. : We multiply the ating scoe with a geogaphical scoe given by exp{ dist(u, l)}. Function dist(u,l) is the aveage distance fom POI l to POIs that the use has visited. 2) Evaluation Metics: Evaluating a ecommended list has two ways: one of them is how many tue esults ae hit by the list and the othe is how simila the esulting ank and the gound tuth ank ae. Theefoe, we use two kinds of metics to measue the pefomance of ou model and the pees. These metics ae: 1) the pecision and ecall fo the top N items, namely Pecision@N and Recall@N, espectively. We investigate N = 5 and N = 1 because the top few esults ae most impessive to uses. 2) Mean Aveage Pecision (MAP) which is used to show the coectness of a ank list accoding to the position of tue esults in the list. If the tue esults ae anked high in the list, the list is pobably a good ecommendation esult. 3) All-Categoy POI Recommendation: The esult is shown in Figue 2. All esults epoted in this section pass t-test with p-value<.1, which means the impovements ae significant. Ou model outpefoms the best pee by 33%, 34% and 61% in tems of Pecision@1, Recall@1 and MAP, espectively on the Phoenix dataset, while 59%, 9% and 62% in tems of Pecision@1, Recall@1 and MAP, espectively on the Singapoe dataset. Among the baseline methods, and do not conside geogaphical infomation, which limits the pefomance of these two methods. Compaed to, pefoms bette because it exploes the use pefeences on aspect level. pefoms the best among the baselines, but still wose than because it does not model the intedependencies. model consides latent egions. Howeve, it does not conside aspect and sentiment. pefoms wost because it estimates the pobability p(l ) by the pobability density function of Gaussian distibution without any nomalization. The Gaussian distibution in ovewhelms the othe pobabilities (i.e., the pefeences of the use). incopoates the gaphical infomation into the model of. Howeve, without consideing the content of the eviews, cannot eveal use s pefeences on aspect level. Ou model discoves use s latent inteest on seveal factos: aspect, sentiment, categoy, and egion. Benefiting fom the use pefeence analysis on topical-aspects and topical-egions, model outpefoms these methods. 4) Single-Categoy POI ecommendation: The pees ae developed fo all-categoy ecommendation. To apply them to this task, we conside two methods. The fist one is to pick the top N esults that belong to the given categoy fom the allcategoy ecommendation esults. The second one is to divide the visit histoy of each use by categoies and lean the models on data fom each categoy sepaately. The second method suffes fom the poblem of spase data. Theefoe, we adopt the fist method in this expeiment. The esult is epoted in Figue 3. Ou model outpefoms the best pee by 36%, 36% and 42% in tems of Pecision@1, Recall@1 and MAP, espectively on the Phoenix dataset, while 52%, 58% and 8% in tems of Pecision@1, Recall@1 and MAP, espectively on the Singapoe dataset. The eason is that ou model is able to discove the elation between categoy and aspect by modeling the use pefeences to topical-aspects on each categoy, i.e., p(a c, u). 5) Recommendation Efficiency: We evaluate the efficiency of ou optimized POI ecommendation algoithm on both of the datasets by compaing with two algoithms. One of them is the bute-foce algoithm which computes Equation (2) and uses a patial soting method to find the top-n esult. The othe one is the theshold algoithm (TA) [4] that sots p(l,c l ) fo each egion and accesses the POIs on each soted list in paallel. Since the scoing function is a monotonic inceasing function, we follow the theshold algoithm to find the top-n esults. We do not sot by aspects ove POIs because the diffeences among POIs on an aspect (p(s a,l)) is much smalle than those on a egion. Since ap(a u,c)p(s a,l) and p(c u) in Equation (2) ae no lage than 1, we compute the theshold as: T = p( u)max l p(l,c l ). In this expeiment, we etieve top 1 esults fo each use. To investigate the unning time on POIs of diffeent scales, we andomly select subsets with diffeent sizes fom the two datasets. Specifically, we get 1 diffeent subsets with size fom 1 to 1, POIs in Phoenix data while anothe 1 subsets with size fom 8 to 8 POIs in Singapoe data. The time of ecommending top 1 POIs to a single use is computed by aveaging ove all uses. The esult is epoted in Figue 4. Time Cost Pe Use (ms.) B&B Theshold Bute-foce # POIs (in thousands) (a) Phoenix Time Cost Pe Use (ms.) B&B Theshold Bute-foce # POIs (in thousands) (b) Singapoe Fig. 4: All-Categoy POI Recommendation Time Consumption Ou optimized algoithm, namely B&B in Figue 4, always takes the least amount of time on both datasets fo diffeent numbe of POIs. Compaed to TA, we achieve 4 times faste in the Phoenix data and 2 times faste in the Singapoe data. The eason could be that TA needs to update the theshold fo each soted access on any soted list. This exta computation makes TA pefom wose than the butefoce algoithm when the numbe of POIs is small. We give a moe detailed compaison fo the theshold algoithm and ou methods as below. In the theshold algoithm, we still need to access many POIs (aound 4% of the POIs in Phoenix on aveage) in each soted list fo each egion. Howeve, ou algoithm accesses vey few egions fo each POI to compute its patial scoe (less than 1 egions on aveage in Phoenix), and we only compute the full scoe fo POIs that we access all the egions (less than 1% of the POIs in Phoenix). Suppose thee ae

10 Phoenix Singapoe (a) - Phoenix (b) - Singapoe (c) - Phoenix (d) - Singapoe (e) MAP in both datasets Fig. 2: All-categoy POI ecommendation Pecision@1 Pecision@1 Recall@1 Recall@1 Phoenix Singapoe (a) - Phoenix (b) - Singapoe (c) - Phoenix (d) - Singapoe (e) MAP in both datasets Fig. 3: Single-categoy POI ecommendation L POIs, R egions and A aspects and we compute the full scoe fo.4l POIs in theshold algoithm and.1l POIs in ou algoithm 2. In the wost case, the theshold algoithm updates.4lr times of theshold. The total computation cost fo theshold algoithm is.4l(a + 2R). Ou algoithm needs to compute the full scoe fo.1l POIs as well as the patial scoe and the theshold fo the est POIs on 1 egions on aveage. The computation costs is.1l(a+r)+.9l 2 1. When A = 3 and R = 8 in the Phoenix data, the cost of theshold algoithm is 76L while the cost of ou algoithm is 29L. When the numbe of egions inceases, the theshold algoithm has moe soted list to access, which makes it slowe. Wheeas in ou algoithm, we still need to conside only a few egions (nea a POI). Ou algoithm is moe suitable fo the models that have a lage numbe of egions. D. Explanation of Recommendation As discussed in Section V-C, the model can tell why we ecommend o not ecommend a POI. To illustate this, we andomly pick some examples fom the test data. We exploe aspects and egions espectively. To find out which aspects contibute most to the ecommendation, we fist show the top- 5 favoite aspects of the selected use in the categoy of the POI accoding to p(a u,c). Then we epot the top-5 good aspects of the POI accoding to p(s + a,l). We manually give a name to aspect accoding to the wod distibution. Table III shows thee uses and a ecommended POI fo each of them. Use 64 pefes the food and flavo aspects of a estauant and Paadise Dynasty, a estauant of Chinese food, has positive eviews on foods. Use 121 wants a good envionment in a ba, and Wala Wala Cafe Ba has a good envionment. Use 42 pefe a hotel with good facility and sevice and Maina Bay Sands povides good facility although only has neutal eviews on sevice. This table shows that we ecommend to uses the POIs with aspects that match thei pefeences. This 2 We estimate this aveage atio on ou datasets TABLE III: Use Aspect Pefeence & Positive Aspects of Recommended POIs Use Pefeence Positive Aspect POI Aspect Pob Aspect Pob menu.29 geneal.98 flavo.11 taste.96 food.7 Paadise Dynasty food.89 quality.7 (Restauant) flavo.74 sevice.7 menu.69 envionment.36 quality 1 geneal.11 location 1 facility.1 Wala Wala taste 1 taffic.1 Cafe Ba flavo.97 location.9 envionment.87 facility.29 quality 1 sevice.2 facility.84 geneal.9 Maina Bay Sands geneal.8 taffic.7 (Hotel) envionment.7 quality.7 food.56 explains why ou method makes a ecommendation to a use. This is a vey desiable featue fo a ecommendation system, although many existing ecommendation methods cannot offe such explanation. To exploe the influence of egions, we daw the contou of the top 3 egions of Use 64 anked by pobability p( u), and plot the top 5 ecommended POIs to the use. We highlight Paadise Dynasty in blue colo. Figue 5 shows the egions and ecommended POIs. The 5 POIs ae close to the cente of Region 36 o Region 8, two of the use s favoite egions, which is the geogaphical eason fo ecommending those POIs. Ou ecommendation algoithm tends to ecommend POIs that ae close to the cente of the use s favoite egions. E. Use Recommendation 1) Pees and Metics: and, which ae based on topic models, can be easily applied to use ecommendation by multiplying the conditional pobability p(l u) with use popu-

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