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Introduction • Chapter 8 • Focus on user, and locations are employed as enhanced information for better understanding them. • Chapter 9 • Aim at understanding locations based upon the collective social knowledge of users (e.g., the knowledge contained in their GPS trajectories) starting with generic travel recommendations and then looking at personalized recommendations. 312年12月26⽇日星期三
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Introduction • Generic Travel Recommender systems • these recommender systems ﬁrst infer the most interesting locations in a region from the given trajectories, and then detect the popular travel sequences among these locations • Personalized Recommender systems • the personalized recommender uses the times that a particular individual has visited a location as her implicit ratings on that location, and estimates an individual’s interests in unvisited places by considering her location history and those of other users • Collaborative ﬁltering(CF) • individually used to infer a user’s ratings of these unvisited locations 412年12月26⽇日星期三
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Mining Interesting Locations and Travel Sequences • Traveling to an unfamiliar city or region, people usually like to know the most interesting locations and the most popular travel sequences. • Hot Region • But, hot region will change caused by many factors • Hot region also changed by time, daytime or evening, coupon in different times • In order to deal with this dilemma, it is necessary to gather travel recommendations automatically and in a timely manner from social media such as the vast amount of GPS trajectories generated by the large number of users traveling in a city. 612年12月26⽇日星期三
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280 Yu Zheng and Xing Xie Mining Interesting Locations and position (denoted as the red star). Additionally, when the user reaches a location, the recommender system will provide her with a further suggestion by presenting Travel Sequences (cont.) the top three most popular sequences starting from this location. GeoLife Fig. 9.1 The user interface of a generic location recommender Fig. 9.1 The user interface of a generic location recommender Fig. 9.2 Location 7 recommendations on a GPS-phone12年12月26⽇日星期三
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Mining Interesting Locations and Travel Sequences (cont.) Some challenges when conducting the generic recommendations : • Interest level of a location - the number of users visiting the location - users’ travel experiences(knowledge) • Individual’s travel experience and interest-level of a location are relative values, and are region-related - An individual who has visited many places in New York might have no idea about Beijing. - the most interesting restaurant in a district of a city might not be the most interesting one in the whole city 812年12月26⽇日星期三
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9.2.1.2 Methodology for Mining Interesting Locations To address the above challenges, the location histories of users are ﬁrst modeled Methodology for Mining Interesting with a tree-based hierarchical graph (TBHG) according to the following two steps demonstrated in Fig. 9.3. Locations c11 l1 c11 G1 {C } Ascendant c21 c22 c22 l2 c21 Descendant G2 c31 c32 c33 c34 c35 l3 c31 c33 c34 Stands for a stay point s c32 c35 G3 Stands for a stay point cluster cij A Tree-Based Hierarchical Graph A Tree-Based Hierarchy (TBHG) Fig. 9.3 Building a tree-based hierarchical graph 912年12月26⽇日星期三
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of pages, authority ranking and hub ranking. For every page in the expanded set, HITS assigns them an authority score and a hub score. As shown in Fig. 9.4, an Methodology for Mining Interesting authority is a Web page with many inlinks, and a hub is a page with many out-links. The key idea of HITS is that a good hub points to many good authorities, and a Locations (cont.) good authority is pointed to by many good hubs. Thus, authorities and hubs have a mutually reinforcing relationship. More speciﬁcally, a page’s authority score is the sum of•theHITS(Hypertext Induced Topic Search)-basedhub score model integration of hub scores of the pages it points to, and its inference is the is pro- authority scores with the TBHG. posed of the pages pointed to by it. Using a power iteration method, the authority and hub scores of eachvalues,can be calculated. The main strength of HITS • This model infers two page the interest level of a location and a user’s is ranking travel experience to the query topic, which may provide more relevant pages according authority and hub pages. However, HITS requires time consuming operations, such as online • 1) the mutually reinforcing relationship between the two values expanding page sets and calculating the hub and authority scores. • 2) the geo-regional conditions. An authority A Hub Authorities Hubs Fig. 9.4 The basic concept of HITS model 1012年12月26⽇日星期三
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have a mutually reinforcing relationship. More speciﬁcally, a user’s travel experi- ence is represented by the sum of the interest values of the locations that the user Methodology for Mining Interesting has been to, and the interest value of a location is denoted by the sum of the experi- ences of users who have visited this location. For simplicity’s sake, in the remainder Locations (cont.) of this chapter, a user with rich travel experience (i.e., relatively high hub score) in a region is called an experienced user of that region and a location that attracts peo- ple’s profound interests (relatively high authority score) is denoted as an interesting location. Mutually reinforcing relationship: u1 u2 u3 u4 Users (Hub) Hub score: users’ travel experiences l3 Locations (Authority) c33 c35 Authority score: c31 c34 interest level of locations c32 G3 Fig. 9.5 The HITS-based inference model a user’s travel experience : the sum of the interest values of the locations that the user hasRegion-related: Intrinsically, a user’s travel experience is region-related, i.e., a been to user who has a great deal of travel knowledge of a city might have no idea about the interest value of Also, an individual, whoof the experiences ofin a particularhaveof another city. a location : the sum has visited many places users who part visited thiscity might know little about another part of the city (especially if the city is very a location. large, like New York). This concept11 aligned with the query-dependent property of is12年12月26⽇日星期三 HITS. Thus, specifying a geospatial region (a topic query) and formulating a dataset
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Methodology for Mining Interesting Locations (cont.) Region-related: Intrinsically, a user’s travel experience is region-related Thus, specifying a geospatial region (a topic query) and formulating a dataset that contains the locations in this region are needed for conducting the HITS-based inference model. Strategy for Data Selection: The interest of every location can be calculated in advance using the regions speciﬁed by their ascendant clusters. -A location might have multiple authority scores based on the different regions it falls in -A user might have multiple hub scores conditioned by the regions of different clusters. 1212年12月26⽇日星期三
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Strategy for Data Selection: Actually, on a TBHG, the shape of a graph node (cluster of stay points) provides an implicit region for its descendent nodes. These Methodology for Mining Interesting regions covered by the clusters on different levels of the hierarchy might stand for various semantic meanings, such as a city, a district, or a community. Therefore, the Locations (cont.) interest of every location can be calculated in advance using the regions speciﬁed by their ascendant clusters. In other words, a location might have multiple authority scores based on the different regions it falls in. Also, a user might have multiple hub scores conditioned by the regions of different clusters. Deﬁnition 9.1 (Location Interest). In this system, the interest of a location (ci j ) is represented by a collection of authority scores Ii j = {Ii1j , Ii2j , . . . , Iil j }. Here, Iil j denotes the authority score of cluster ci j conditioned by its ascendant nodes on level l, where 1 ≤ l < i. Deﬁnition 9.2 (User Travel Experience). In our system, a user’s (e.g., uk ) travel experience is represented by a set of hub scores ek = {ekj | 1 ≤ i < |L|, 1 ≤ j ≤ |Ci |} i (refer to Deﬁnition 8.5), where ekj denotes uk ’s hub score conditioned by region ci j . i Figure 9.6 demonstrates these deﬁnitions. In the region speciﬁed by cluster c11 , 1 1 it is possible to respectively calculate an authority score (I21 and I22 ) for clusters 1 1 1 c21 and c22 . Meanwhile, within this region, the authority scores (I31 , I32 , I33 , I341 1 and I35 ) for clusters c31 , c32 , c33 , c34 and c35 can be inferred. Further, using the 2 region speciﬁed by cluster c21 , we can also calculate authority scores (I31 and I32 ) 2 2 2 2 for c31 and c32 . Likewise, the authority scores (I33 , I34 and I35 ) of c33 , c34 and c35 can be re-inferred within region c22 . Therefore, each cluster on the third level has two authority scores, which can be used 13 various occasions based on user inputs. on For instance, as depicted in Fig. 9.6 A), when a user selects a region only covering12年12月26⽇日星期三
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Methodology for Mining Interesting Locations (cont.) 9 Location-Based Social Networks: Locations 285 c11 c11 {C } {C } Ascendant c21 c22 c21 c22 c31 c32 c33 c34 c35 Descendant c31 c32 c33 c34 c35 A) A region covering locations B) A region covering locations from single parent cluster from multiple parent clusters Stands for a stay point cluster cij A region specified by a user Stands for a cluster that covers the region specified by the user Fig. 9.6 Some cases demonstrating the data selection strategy 1412年12月26⽇日星期三
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ulq = ∑ vi0 ecovers the region× l0j ; 0 by the user 0 1 1 1 j specified i u3 0 1 (9.3) 2 0or a cluster that M= u2 1 ci j ∈clq 2 1 0 0 u4 0 (9.1) 0 0 1 1 Methodology for Mining Interesting u3 0 0 1 2 0 demonstrating u4 Then, the mutually reinforcing relationship of user travel experi the data selection0strategy 1cendant node on0the 0 level,11 ≤ l < i. For instance, as shown lth interest Iil jofLocations (cont.)locationually reinforcing relationship isuser travel experience ek and represented as follows:cendant node on the ﬁrst level of the hierarchy is c11 , and its ijthe second follows:is c21 . Thus, if l = 2, clq stands for c21 andepresented as level Inference: c31 c32 c1133 and34 3135 , . . . , cl35 ) ∈ c11 .k c c co, if l = 1, clq denotes , (c , c32 li j = ∑ elq × vkj ; i u1 l1 = 1 ek 0 vk ; 0 0 286 i l u2 1 uk1 ∑ lq 2denote the matrix form,wej use J to× i j 0 0 column vector(9.2) all the with uk ∈U Y M to denote the ∈U use E = u 0 column lvector 0 all the hub∑ vkj × lil j ; with k (9.1) scores. Con- 3 ek = 0 1 vk1 l ; 2 1 elq = lq = ∑ and× ,in . toI denote authority e2 , . hub 4scores at th (I lq i j 1E j . ), 1 c, (9.3) i. . , e ).n of cluster 4 11use ci 0 31 , I32 . 1 , 351 and E = (e11 i j ∈clq If u c , J Jn∈c 0 we 0 and j 11 11 iterative processes for generating the ﬁnal results are k j reinforcing relationship is ci j ’s ≤ l < i. For instance, and locationy’s ascendant node on theclthof user travel experience ei j as shown level, 1 ≤ l < i. Fo where lq level, 1 ascendant node on the lth T T 1 ’s ascendant node on the ﬁrst c31 ’s of the hierarchy is c11 , J · M · J level of the hier J level ascendant node on the its in Fig. 9.6,esented as follows:J = M · E Jn = M and ﬁrstde on the second level is c21 . Thus, if l = 2, clq stands for c21 and n−1(9.4) ascendant node on the second level is cJ21 . Thus, if l = 2, clq T1 . Also, if l = 1, clq denotesM · J Ec=) c11 cand Also,32 , .l. =c1,)n∈ c11 . · M · En−1 (c , c , . . . , (c31 , c E c denotes c . , 35 = M (9.5) (cwe,use J ∈ denote the column vector with all the11 , and 31 32em in matrix form, 31 32 to 21 .k if lq l ∑ li j = k Writing × vi j ; with all form, we use J to e (9.2)es, and use E to denote u ∈U lqthem in matrix the hub scores. Con- denote the colum the column vectore region ofStarting with Jscores, ,and(1, 1, .=.(e1), 2 , .theecolumn vector with all clusterauthority31 , I32 , E0 I35 ),use E to , 1 , e11 . . , 4 able to calculate the c11 , J = (I 10 = . . . = and . denote are ). we k 1 1 11 11 = ∑ v j × il j ; scoresditioned bykpower iteration method. = (I 1 (9.3) .canI retrieveE ek using the i the lregion of cluster c , J Later, I 1 , . . , 1 ), and th lq , we 11 31 32 35 ci j ∈clq esting locations and the top k most experienced users in a given J J = M ·E 15 (9.4)ascendant node on the = Mlevel, 1 ≤ l < i. For instance, as shown 12年12月26⽇日星期三 E lth · J (9.5) J
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ore of location A(IA ) weighted by the probability of people Methodology for detecting travelequence (OutAC ). Clearly, there are seven (5+2) links pointingom node A, and ﬁve out of seven of these links point directly to sequences C = 5/7 , i.e., only ﬁve sevenths of location A’s authority (IA ) ated to sequence A → C, and thepopular sequences of locations from the graph on a This step detects the top k most rest of IA should be distributed layer of the TBHGore of location C(IC ) weighted by the probability of people’s A popularity score is calculated for each location sequence within a given region basedequence (InAC ). upon two factors:f the users (UAC ) who haveLocation-Based Social Networks: Locations 9 taken this sequence. -the travel experiences of the users taking this sequence -the interests of the locations contained in the sequence A 5 4 E SAC = ∑ (IA · OutAC + IC · InAC + ek ) 4 uk ∈UAC 3 6 2 C 3 = |UAC | · (IA · OutAC + IC · InAC ) + ∑ ek B 2 1 D uk ∈UAC 5 5 = 5 × ( × IA + IC ) + ∑ ek .of mining popularscore of location from a graph IA : Authority travel sequences A 7 8 uk ∈UAC OutAC : The probability of people leaving by this sequence Following this method, the popularity score of sequence C → D InAC : The probability of people entering by this sequence follows: 1 1 16 SCD = 1 × × IC + ID + ∑ ek . 12年12月26⽇日星期三 7 7
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ore of location A(IA ) weighted by the probability of people Methodology for detecting travelequence (OutAC ). Clearly, there are seven (5+2) links pointingom node A, and ﬁve out of seven of these links point directly to sequences C = 5/7 , i.e., only ﬁve sevenths of location A’s authority (IA ) ated to sequence A → C, and thepopular sequences of locations from the graph on a This step detects the top k most rest of IA should be distributed layer of the TBHGore of location C(IC ) weighted by the probability of people’s A popularity score is calculated for each location sequence within a given region basedequence (InAC ). upon two factors:f the users (UAC ) who haveLocation-Based Social Networks: Locations 9 taken this sequence. -the travel experiences of the users taking this sequence -the interests of the locations contained in the sequence A 5 4 E SAC = ∑ (IA · OutAC + IC · InAC + ek ) 4 uk ∈UAC 3 6 2 C 3 = |UAC | · (IA · OutAC + IC · InAC ) + ∑ ek B 2 1 D uk ∈UAC 5 5 = 5 × ( × IA + IC ) + ∑ ek .of mining popularscore of location from a graph IA : Authority travel sequences A 7 8 uk ∈UAC OutAC : The probability of people leaving by this sequence Following this method, the popularity score of sequence C → D Time consuming!! InAC : The probability of people entering by this sequence follows: 1 1 16 SCD = 1 × × IC + ID + ∑ ek . 12年12月26⽇日星期三 7 7
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Itinerary Recommendation while there are many location candidates that can be considered, a traveler usually wants to maximize her travel experience. -To achieve this task, the typical duration that people stay in a location and the average travel time between two locations should be considered. An effective itinerary needs to adapt to a traveler’s present location and available time length as well as her destination. Itinerary Recommendation : -Human intervention [3, 9, 16] -The advantage of such interactive recommender systems is that the more a user knows about traveling in the area, the better the itinerary is. - Automated [8, 18, 37, 38] - See the third paragraph in page 288 for an example 1712年12月26⽇日星期三
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Methodology for Itinerary Recommendation 9 Location-Based Social Networks: Locations 289 Online Offline Query Verification GPS TrajN Trip Candidate Selection Stay Points Extraction and Clustering Top-k Trips Location Graph Trip Candidate Ranking Location Interest and Sequence Mining Itinerary Location-Interest Graph Duration Start/End Collective Locations G Social Intelligence Preference User Fig. 9.8 Framework of the itinerary recommender 1812年12月26⽇日星期三 a location. So, the typical stay duration in each location and general travel duration
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Methodology for Itinerary Recommendation (cont.) Online component: 1) Query Veriﬁcation: This step checks the feasibility of a query according to spatial and temporal constraints. 2) Trip Candidate Selection: This step searches a location-interest graph for candidate itineraries satisfying a user’s query. 3) Trip Candidate Ranking: This step ﬁrst ranks candidate itineraries according to three factors: elapsed time ratio, stay time ratio, and interest density ratio,Then, these itineraries will be re- ranked according to the popularity score of the travel sequences pertaining to an itinerary. 1912年12月26⽇日星期三
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total time needed for an itinerary is much shorter than the available time, the remaining time is wasted. Methodology for Itinerary• Stay Time Ratio (STR): This factor considers how the available time is spent by calculating a ratio between the time that a user could stay in a location and that Recommendation (cont.) for traveling between locations. Intuitively, travelers prefer to spend more time in interesting locations rather than traveling to them. Therefore, an itinerary with Elapsed Time Ratio (ETR): a bigger STR is considered a better choice, i.e., a user can spend Good a longer time visiting actual places. length of a recommended itinerary time• Interest Density Ratio (IDR): IDR is the sum of the interest values of the available time given by user locations contained in an itinerary. The general assumption is that visitors like to visit as Time Ratio (STR): Stay many highly interesting locations as possible on a trip. Therefore, the bigger the IDR value, the better the itinerary. In the implementation, theGood of IDR available stay time given by user an itinerary should be normalized to [0, 1] and divided by the maximum IDR in traveling time between locations the candidate itineraries. As shown in Density Ratio (IDR): Interest Fig. 9.9, a good itinerary candidate is a point located in the upper- Good right corner the this cube, interest values of the locations contained in anSTR, and IDR IDR is of sum of the i.e., simultaneously having larger ETR, itinerary. values. the implementation, the IDR of an itinerary should be normalized to [0, 1] and In To rank candidate itineraries, a Euclidian distance in these three dimensions is divided by the maximum IDR in the candidate itineraries. calculated as Eq. 9.11: To rank candidate itineraries, a Euclidian distance in these three dimensions is calculated ED = α1 · (ET R)2 + α2 · (ST R)2 + α3 · (IDR)2 (9.11) 20• Popular Travel Sequence: This factor represents how popular a recommended12年12月26⽇日星期三
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Methodology for Itinerary Recommendation (cont.) Popular Travel Sequence: This factor represents how popular a recommended itinerary is (according to people’s travel history), by summing up the popularity scores of the travel sequences contained in the itinerary Further differentiate the itineraries returned by the ﬁrst ranking step. As a result, the top k itineraries will be recommended to a user. 2112年12月26⽇日星期三
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Location-Activity Recommendation Besides the need for an itinerary, people usually have two types of questions in mind when traveling. They wonder where to go for sightseeing and food, and they wonder what there is to do at a particular location. This section introduces a location-activity recommender system [40] which answers the above questions by mining a myriad of social media, such as tips-tagged trajectories or check-in sequences. • Data Modeling • Collaborative Inference12年12月26⽇日星期三
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a location. For example, if 5 users had dinner and 7 people watched a movie in this location in a week, the frequency of activity “dining” and “watching movies” is 5 and 7 respectively. This frequency denotes the popularity of an activity in a location and indicates the correlation between an activity, and a location. Data Modeling If this location-activity matrix is completely ﬁlled, the above-mentioned recom- mendations can be easily achieved. Speciﬁcally, when conducting the location rec- Location-activity matrix: ommendation given an activity, we can rank and retrieve the top k locations with In Foursquare a user can leave some tips or a to-do-list in a venue so that her friends are a relatively high frequency from the column that corresponds to that activity. Like- able to view these tips when they arrive at the venue. Sometimes, these tips and to-do- wise, when performing activity recommendation for a location, the top k activities lists clearly specify a user’s activity in a location, enabling us to study the correlation can be retrieved from the row corresponding to the location. between user activities and a location However, the location-activity matrix is incomplete and very sparse. Intuitively, people will not leave tips and to-do-lists in every restaurant and shopping mall. In dining watching movies swimming short, many venues will not have labels of user activities. To address this issue, the information from another two matrices, respectively shown in the left2 right Tainan, Zhong zheng Rd. 7 4 and part of Fig. 9.10, can be leveraged. One is a location-feature matrix; the other is an activity-activity matrix.location-activity matrix is incomplete and very sparse. However, the Features Activities Activities Locations Locations Activities U V Y = UWT X= UVT Z = VVT Fig. 9.10 The collaborative location-activity learning model 2312年12月26⽇日星期三
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a location. For example, if 5 users had dinner and 7 people watched a movie in this location in a week, the frequency of activity “dining” and “watching movies” is 5 and 7 respectively. This frequency denotes the popularity of an activity in a location and indicates the correlation between an activity, and a location. Data Modeling (cont.) If this location-activity matrix is completely ﬁlled, the above-mentioned recom- Location-featurecan be easily achieved. Speciﬁcally, when conducting the location rec- mendations matrix: In ommendation row stands for a location, and a column denotes atop k locations with as this matrix, a given an activity, we can rank and retrieve the category (referred to feature in this high frequency from the column that corresponds to that activity. Like- a relatively section), such as restaurants, cafes, and bars. wise, when performing activity recommendation for a location, the top k activities Usually, a location might include multiple points of interest (POI) pertaining to different can be retrieved from the row corresponding to the location. categories. However, the location-activity matrix is incomplete and very sparse. Intuitively, The motivationnot leave tipsthis location- feature matrix lies in the insight that mall. In people will for building and to-do-lists in every restaurant and shopping people could carry out similar activities in similar locations. activities. To address this issue, short, many venues will not have labels of user the information from another two matrices, respectively shown in the left and right Each item in a location-feature matrix is a TF-IDF value of a category in a location. part of Fig. 9.10, can be leveraged. One is a location-feature matrix; the other is an activity-activity matrix. Features Activities Activities Locations Locations Activities U V Y = UWT X= UVT Z = VVT Fig. 9.10 The collaborative location-activity learning model 2412年12月26⽇日星期三
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a location. For example, if 5 users had dinner and 7 people watched a movie in this location in a week, the frequency of activity “dining” and “watching movies” is 5 and 7 respectively. This frequency denotes the popularity of an activity in a location and indicates the correlation between an activity, and a location. Data Modeling (cont.) If this location-activity matrix is completely ﬁlled, the above-mentioned recom- The activity-activity matrix, achieved. Speciﬁcally, when conducting the location rec- mendations can be easily models the correlation between two different activities, which contributes to thegiven an activity, we can rank and retrieve the topat alocations with ommendation inferences of user activities that can be performed k location. a relatively high frequency from the column that corresponds to that activity. Like- wise, when performing activity recommendation for a location, the top k activities One possible way to calculate this correlation is based upon user-generated tips and to- can be retrieved from the row corresponding to the location. do-lists. In case the user-generated data is not large enough, the results returned by a However, the location-activity matrix is incomplete and very sparse. Intuitively, search engine (like Google and Bing) can be used to compute the correlation as the people will not leave tips and to-do-lists in every restaurant and shopping mall. In correlation between two activities should be generally reﬂected by the World Wide Web. short, many venues will not have labels of user activities. To address this issue, the information from another two matrices, respectively shown in the left and right Counts of the 9.10, can be leveraged. One is a location-feature into [0, 1], representing the part of Fig. results returned by search engine are normalized matrix; the other is an activity-activity matrix. correlation between different pairs of activities. Features Activities Activities Locations Locations Activities U V Y = UWT X= UVT Z = VVT Fig. 9.10 The collaborative location-activity learning model 2512年12月26⽇日星期三
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weighting the contributions of location features, activity correlations,and Xing Xie 294 Yu Zheng and the regu- larization term. These parameters can be learned using a training dataset. In So, this location-activity matrix shares the location T ) measures the the location- loss the objective function, the ﬁrst term (X − UV information with prediction of the feature matrix via Umatrix. The second term knowledgeTwith the activity-activity location-activity m×k , and shares the activity (Y −UW ) measures the prediction Collaborative Inference loss of the location-feature matrix. Minimizing it enforces the information among matrix via Vn×k . In short, the inference model propagates the location latent factor Xm×n , Ym×l and Zn×n by the low-rank matrices Um×k and Vn×k . Finally, an objective U to be good is formulated as Eq. 9.13: the location features. In other words, it helps function as well in representing to propagate theﬁltering (CF) approach based on collective matrix factorization [31] can A collaborative information of location features Y to the prediction of X. The third be employed T train a location-activity recommender, using these matrices as inputs. term (Z − VVto ) measures the prediction loss of the activity-activity correlations. λ Minimizing it enforces the ) = 1 I ◦latent factor2V to1be good as well in representing L(U,V,W activity (X −UV T ) F + Y −UW T 2 + F 2 2 the activity correlations. In other words, it helps to propagate the information of (9.12) λ2 λ3 activity correlations Z to theZ −VV T 2 + X. U 2 + V 2 + W 2 , prediction of F F F F 2 2 Speciﬁcally, to infer the value of each missing entry convex to all the variables, Um×k , In general, this objective function is not jointly an objective function is deﬁned Vn×k , whereto ·|F. denotes the Frobenius norm, and I is an indicatorgradient descent method. and Eq. above, which no closed-form solution for a matrix with its objective accordingWl×kX Also, there is is iteratively minimized using minimizingentry-wise the entry function. Asif result, a numericalotherwise.such operatorgradient descent is employed Ii j = 0 a i j is missing, Ii j =1 method The as the “◦” denotes the ∥·|Fproduct. The Frobenius terms in the objective function control the loss in matrix denotes the ﬁrst three norm to determine the local optimal solutions. Speciﬁcally, the gradient (denoted as ∇) I isfactorization, and the with term controls the regularization overi jthe factorized ma- an indicator matrix last its entry I j = 0 if X is missing, I =1 otherwise. for each variableto prevent over-ﬁtting. λ i ,λ and λi jare three parameters respectively trices so as is represented as follows. Using the gradient descent, a converged The operator “◦” denotes the entry-wise product. 1 2 3 is returned with all the entries ﬁlled: Xm×n weighting the contributions of location features, activity correlations, and the regu- The last term controls the regularization overlearned using a training dataset.to prevent larization term. These parameters can be the factorized matrices so as over-ﬁtting.the objective function, the ﬁrst term (X − UV T ) measures the prediction loss In ∇U L = I ◦ (UV T − X) V + λ1 (UW T −Y ) measures the of the location-activity matrix. The second term (Y −UW T)W + λ3U, prediction (9.13) loss of the location-feature matrix. Minimizing it enforces the location latent factor T U to be good∇V as = I ◦ (UV T − X) the location features. In other3words, it helps L well in representing U + 2λ2 (VV T − Z)V + λ V, (9.14) to propagate the = λ (UW Tof location features Y to the prediction of X. The third ∇W T information −Y )TU + λ3W. L (9.15) 1 term (Z − VV ) measures the prediction loss of the activity-activity correlations. 26 Minimizing it enforces the activity latent factor V to be good as well in representing12年12月26⽇日星期三
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locations regardless of their personal interests, a personalized recommender of- fers locations matching an individual’s preferences, which are learned from the individual’s location history [44, 46]. Speciﬁcally, a personalized recommender us- es a particular individual’s number of visits to a location as their implicit rating of Personalized Travel Recommendations that location, and predicts the user’s interest in an unvisited location in terms of their location history and those of other users. A matrix between users and locations, like the M shown in Eq. 9.16, is formulated, where rows stand for users and columns While a generic travel recommender system can provide users with a variety denote users’ ratings of locations (represented by the times that a user has been to a of locations regardless of their personal interests, a personalized location). One approach for building this matrix with user-generated GPS trajectory recommender offers locations matching an individual’s preferences, which has been introduced in individual’s location history are learned from the Section 8.2.1. c31 c32 c33 c34 c35 u1 1 1 2 0 4 u2 1 M= 1 3 0 2 (9.16) u3 0 0 1 2 0 u4 0 0 0 1 1 Based on user-location matrix M, a collaborative ﬁltering model can be employed to infer a user’s ratings of some unvisited location. Later, by ranking and retrieving • Collaborative Filtering the top k unvisited locations in terms of the inferred values from the row (in M) corresponding to a particular user, we can provide the user with a personalized rec- • Location Recommenders Using User-Based CF ommendation. • following sections, the general idea Item-Based is ﬁrst introduced and In theLocation Recommenders Using of a CF modelCF then two types of CF-based models that have been used in previous literature to • personalized location create a Open Challenges recommender system. One is a user-based location 27 recommender [46]; the other is an item-based one [44].12年12月26⽇日星期三
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Collaborative Filtering Collaborative ﬁltering is a well-known model widely used in recommender systems. The general idea behind collaborative ﬁltering is that similar users make ratings in a similar manner for similar items. Algorithms for collaborative recommendations can be grouped into two general classes: -Memory-based (or heuristic-based) -Model-based Model-based algorithms [10, 12] use the collection of ratings to form a model, which is then used to predict ratings. [4] proposed a probabilistic approach to collaborative ﬁltering. It is assumed that rating values are integers between 0 and n, and the probability expression is the probability that a user will give a particular rating to an item given that user’s ratings of previously rated items. [12] machine learning techniques、Latent Semantic indexing、Bayesian Networks 2812年12月26⽇日星期三
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Memory-based Memory-based algorithms are essentially heuristics that make ratings predictions based on the entire collection of previously rated items by users That is, the value of the unknown rating for a user and an item is usually computed as an aggregate of the ratings of some other (usually, the N most similar) users for the same item. 1) User-based techniques 2) Item-based techniques 2912年12月26⽇日星期三
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User-based techniques User-based techniques are derived from similarity measures between users. when predicting user A’s rating of an item, the more similar user A and B are, the more weight user B’s rating of the item will carry. In most approaches, the similarity between two users is based on their ratings of items that both users have rated, using the Pearson correlation or the Cosine similarity measures. [32] 3012年12月26⽇日星期三
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Item-based techniques Item-based techniques predict the ratings of one item based on the ratings of another item. Amazon’s item-to-item algorithm [22] : Computes the Cosine similarity between binary vectors representing the purchases in a user-item matrix. Slope One [19] : The simplest form of non-trivial item-based collaborative ﬁltering. Its simplicity makes it especially easy to implement it efﬁciently while its accuracy is often on par with more complicated and computationally expensive algorithms. 3112年12月26⽇日星期三
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Location Recommenders Using User- Based CF This section presents a personalized location recommender system [46] using a user- based CF model. Given a user-location matrix like M shown in Eq. 9.16, this location recommender operates according to the following three steps: 1) Infer the similarity between users 2) Location selection 3) Rating inference 3212年12月26⽇日星期三
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Infer the similarity between users 9 Location-Based Social Networks: Locations This personalized location recommender estimates the user Travel Recommendations 9.3 Personalized similarity between two users in terms of their location histories (detailed in Section 8.3), instead of using traditional similarity measures, Socialas the Cosine similaritygeneric travel recommender system can provide users 9 Location-Based such Networks: Locations a or the Pearson correlation. While 297 locations regardless of their personal interests, a personalized Typically, theaPearson correlation between the ratings < two users> based upon the2 297 are ed by 9 Location-Based Social Networks: Locations 297 in user-based CF model, the similarity between 1,an individual’s preferences, which fers locations matching 1, 2, 4 is and < 1, 1, 3, >. individual’s location history [44, 46]. Speciﬁcally, a personalized ratings provided by bothcomputation of the Pearson correlation. Eq. 9.17 details the users. ed by the Pearson correlation between the ratings < 1, number > visits < a location >.thei es a particular individual’s 1, 2, 4 of and to 1, 1, 3, 2 as< 1, 1, 3, 2 >. Eq. 9.17 details the computation ofcorrelation : predicts the user’s interest in an unvisited locati that location, and Pearson the Pearson correlation. location history and those of other users. A matrix between users ∑i∈S(R p )∩S(Rq )shown inREq. ·9.16, is formulated, where rows stand for the M (r pi − p ) (Rqi − Rq ) sim(u p , u p ) = ∑i∈S(R p )∩S(Rq )One approach (Rqi − Rq ) this matrix with (9.17) denote users’ ratings of locations (represented by the times that a (r − R ) · location).p )2pi ∑ p for buildingqi − Rq )2 sim(u p , u p ) =∑i∈S(R p )∩S(Rq ) (r pi − R · i∈S(R p )∩S(Rq ) (R user-genera (9.17) (9.17) has been introduced in Section 8.2.1. − R )2 2 ·∑ ∑i∈S(R p )∩S(Rq ) (r pi − R p ) i∈S(R p )∩S(Rq ) (Rqi q ) 2 Notations: The ratings from a user u p are represented cas an array c34 p c=< 31 c32 c33 R 35 Rp : The ratings from a user p r p0 , r p1 ,Notations: The ratings from implicituratingsrepresented1 as 1 array location . . . , r pn >, where r pi is u p ’s a user p are (the occurrences) in a 0R p =< u1 1 an 2 4 2 M = u2 1 rray R p i. S(Rp0), r p1the. subset of R p , ∀r pi ∈ p ’s implicit = 0, i.e., the set0 of itemsin a 2 0 =< r p is , . . , r pn >, where r pi is u S(R p ), r pi ratings (the u 3 0 occurrences) 1 (locations) location 3 0in a location has been rated (visited)Rby ∀rp . ∈ S(R p ), r pi = 0, i.e.,inuR p 0 of 0items (locations) that i. S(R p ) is of Rsubset of p , u pi The average rating the set denoted as R p 1 In the the has been rated (visited) by u . The average rating in4 R is denoted as R . In 0 1 S(Rp) is that subset p p is s (locations) example, R1 =< 1, 1, 2, 0, 4 >, Rp =< 1, 1, 3, 0, 2 >, S(R1 ) =< 1, 1, 2, 4 >,pand this . 2 Based on user-location matrix M, a collaborative ﬁltering mod ed asRR p=< 1,1,2,0,4 >, R2 2 1 =< 1, 1, 2, 0, 4 >,) infer1,1,2,4 ratings2of some) unvisited location.4Later, by ran . In2 ) =< 1, 1, 3, =< 1,1,3,0,2 >, S(R1 R2 =< 1, 1,>, and S(RS(R1 ) =< 1, 1, 2, >, and 1 S(R this example, R>. to =< a user’s 3, 0, >, 2 =< 1,1,3,2 >1, 2, 4 >, and S(R2 ) =< 1, 1, 3, 2 >. 33 This rating-based similarity measure well represents thein terms of the inferred values fro the top k unvisited locations similarity between two 12年12月26⽇日星期三 This rating-based similarity measure well represents the similarity between two corresponding to a particular user, we can provide the user with
35.
Infer the similarity between users (cont.) Pearson correlation measure well represents the similarity between two users when the items rated by users are relatively independent, such as books, videos, or music. However, dealing with locations (especially, when these locations are derived from user-generated trajectories), this approach loses the information of people’s mobility (e.g., the sequential property) and the hierarchical property of locations. Estimates the user similarity between two users in terms of their location histories Mentioned in Section 8.3 Location selection For a user, this step selects some locations that have not been visited by the user but have been accessed by other users. Note that the inferred rating of a location would not be very accurate if the location has only been accessed by a few users. 3412年12月26⽇日星期三
36.
osine similarity and d ∑ sim(ucorrelation. − Rq ); r pi = R p + the Pearson p , uq ) × (rqi uq ∈U (9.18) ection:+ d ∑ sim(uuq,∈U ) × (rqi −some locations that (9.18) = R p For a user, this step selects Rq ); p uq have not 1 user but= uq ∈U 1∑accessed , uqother users. Note that the inferred have been sim(u p by ); d d= (9.19) 1 would not be |Uq | | u ∈U ∑ sim(u p , location has only been accessed (9.19) |U very accurate if theuq ); = the |U | time,1 same ∑ sim(uupq,the);u ∈U Rating inference using q personalized recommender, a user needs (9.19) Rp R uq ∈U 1 in r system. accumulated∑ thepi .r pi . ion data=p = |S(R theP )| ) ∑ matrix, user p’s interest (r ) in aa(9.20) i can be predicted 1 GivenPuser-location matrix, user p’s interest )| i∈S(R |S(R user-location (9.20) = |S(RP according∑ to the following three Equations : which in alocation ence: Given the r pi . i∈S(R p ) ppredicted )| i∈S(R p ) to the following three Equations, according (9.20) pi is n Eq. Eq. 9.18, the similarity between usersp uthe notations used q uq ), is Zheng and Xing Xie ntation of user-based collaborative ﬁltering. u and uq ,uq , sim(uu , ), is Yu in 9.18, the similarity between users All p and sim(u p , p 298 edistance measure andused 9.17: weight. That, is, is, theumore similarpu p tance measure andbetween as a au p and uThat the pmore similar u 18, the similarity is is used as weight. q sim(u , q ), is meanings with that of Eq. usersmore weight rqiused carryweight.prediction ofmore . Here, sim(uuq uq ) ismeasure and is will as a r in = R That is, thesim(u similar u p p , − Ris);he more weight rqi will carrythethe+ d prediction r pi r pi , u ) × (r p , ) of . Here, sim(u pi in ∑p p q dingrto will the method introduced of ru . Here, sim(u p , uq ) is different the method the prediction Section 8.3.3. However, different ccording to carry in ight qi introduced in in Section 8.3.3. However, pi ∈U qi q (9.18) q t the methodaintroduced in of times 8.3.3. one user might visit a park places a varying number Section (e.g., However, different visit places varying number of times (e.g., one user might visit a park 1 d ∑ ther person may access the= same parksim(utimes, although both of another person may access the one user four p ,visit a park both of a varying number of times (e.g., park four times, q ); same might u although ually interested the park), i.e., |U | uuse thealthough scale differently. rson may accessin the park), i.e., they use the rating bothdifferently. y interested in the same parkthey q ∈U four times, rating scale of (9.19) n adjusted weighted sumuseduse here. justed weighted sum istheyused the rating scale differently. sted in the park), i.e., is here. 1 eadusing sumabsolute values of of using is absolute p R ∑ weighted the the used here. = of ratings, thetherdeviations from the av- values of ratings, deviations from the av- |S(RP rqi − pi . (9.20) g the absolute values user are the )|i.e., rqi)R , q , the R q denotes the the corresponding of ratings,used,deviationsqfromwhere qRdenotes of corresponding user are used, i.e., i∈S(R p − Rwhere av- ng of uq . uq .user arenormalizingrqi − Rq d whereinvolved, calculated in rating of Second, a used, i.e., factor , is involved, calculated in responding Second, a normalizing factor d is Rq denotes q9.19 As: U aU thein Eq. 9.18, theusers who are the most users to toqand uq ,[1, 24] p , uq ), is 9. where normalizing factorfactorof is who are the most similar u p uq . Second, isnormalizing of users involved, between similar u . d shown the collection d similarity calculated in where is collection sim(u e U isUis consideredof ofcalculatingarethe most similar to uq .p )Thatpis, the more similar u p ating scalecollection byusers who are the used similar to (R of ofpuas as scalethe the collection measure and is average rating p ) g essentially considered by calculating themost as a weight. u ʹ′ : is a distance users who the average rating (R isand)u p are, the calculating the average ratingaccessedbyby . ere p represents more collection will carryaccessed by as considered by the collection locations (R p ) of u S(RS(Rq ) represents theweight rof of locations inaccessed p u pu p . of r pi . Here, sim(u p , uq ) is : represents the collection of locations the prediction qi represents theaccordingwell-known method [1,[1,u24], which has8.3.3. However, different collection of well-known methodby p .which has been these equations illustrate a locations accessed 24], in Section been secalculatedillustrate a to the method introduced equations tions illustrate a well-knownsystems. [1, 24], which is not necessary to in many recommendation method Therefore, is not necessary to has been people may visit places a varying number it many recommendation systems. Therefore, 35of times (e.g., one user might visit a park itmecommendation systems. Therefore, it is not necessary to in more detail. 12年12月26⽇日星期三
37.
Location Recommenders Using Item- Based CF [44] User-based CF has a relatively poor scalability as it needs to compute the similarity between each pair of users. Though the approximated method introduced in 8.4.1 can be used to alleviate this problem to some extent, the constantly increasing number of users in a real system leads to a huge computational burden. 1) Mining the correlation between locations 2) Rating inference 3612年12月26⽇日星期三
38.
set up some billboards or advertisements in other places to attract more attention, thereby promoting sales at this mall. Knowing that locations B, C and E have a much Mining the correlation between higher correlation with location A in contrast to locations D and F (according to a large number of users’ location histories), the operator is more likely to maximize locations the promotion effect with minimal investment by putting the billboards or promotion information in locations B, C and E. Another example can be demonstrated using There are a varietyIf aapproaches to determine theare highly correlated locations : in terms Fig. 9.11 B). of museum and a landmark correlations between to a lake of Distance location histories, the museum and landmark can be recommended to - people’s tourists when they travel to the lake. Otherwise, people would miss some fantastic - the category of POIs located in a location places behavior, speciﬁcally, two hundred meters away fromcorrelated in people’s minds - user even if they are only to what extent two locations are these locations. -According to a large number of users’ location histories E Ads!! A Museume F D Billboards!! Promotion!! A A Lake B C A Landmark A) Put promotion information or B) Recommend places to tourists ads. at correlated locations in terms of location correlation Fig. 9.11 Some application scenarios of this location correlation 3712年12月26⽇日星期三
39.
Second, the correlationin which both locations have been B, also 1) This correlation betw sequences between two locations, A and visited. depends on the and B, Cor(A, B), is asymmetric; i.e., Cor(A, B) = Cor(B, A). The semantic msequences in which both locations have been visited. 1) This correlation between A Mining the correlation between of a travel sequence A → B might be quite different from B → A. For exampand B, Cor(A, B), is asymmetric; i.e., Cor(A, B) = Cor(B, A). The semantic meaning a one-way road, people would only go to B from A while never traveling to Aof a travel sequence A → B might be quite different from B → A. For example, on locations (cont.) B. 2) The two locations continuously accessed by a user would be more cora one-way road, people would only go to B from A while never traveling to A from than those being visited discontinuously. Some users would reach B directlyB. 2) The two locations continuously accessed by a user would be more correlated Mining the correlation from people’s location histories another location C two challenges : at B A (A → B) while others would access faces the following before arrivingthan those beingCvisited Intuitively, the Cor(A, B) users wouldthe twoB directly might be dif → B). discontinuously. Some indicated by reach sequences fromA (A → B) whileLikewise, in a sequence A → CdoesB, Cor(A,C) wouldthe number(A →Cor(A others would access another location C before arriving at B of - First, the correlation between two locations → not only depend on be greater thanC → users visitingthe the Cor(A, B)but also liesby the→ users’ travel experiences.different. C. B). Intuitively, user locations indicated in these C, sequences might after visiting the two consecutively accessed A two but traveled to B beLikewise, in a sequence A →accessed by the between twobe greater can be calculatedbe integ The locations sequentiallythe → B, Cor(A,C) would more travel knowledge would as In short, C correlation people with locations than Cor(A, B), bythe user consecutively accessed A → C, but traveled to B little idea aboutC. in a weighted m more correlated than theexperiences of the those having after visitingtrip region. the travel locations visited by users visiting them on a the In short, the correlation between two between location A and B can by calculated as Eq. 9 Formally, the correlation locations can be calculated be integratingthe travel experiences of the userstwo locations, A and B, trip in a weighted sequences - Second, the correlation between visiting them on a also depends on the manner.Formally, the correlation between location ACor(A, can= ∑ α · ek , as Eq. 9.21. in which both locations have been visited. and B B) be calculated uk ∈U Cor(A, B) = ∑ α · ek , (9.21) where U is the collection uk ∈U of users who have visited A and B on a trip; ek travel experience, uk ∈ U , (Section 9.2.1.2 details the method for calculatinwhereʹ′ U the collection of users who have . 0 have ≤ 1 B ondumpingon a trip; ek is uk ’s the i U is is the er’s travel experience) visitedα visitedaAaand B factor, decreasing as collection of users who < A and is trip between , (Section ʹ′travel kexperience, uk ∈ Utheseutwo U 9.2.1.2 details on amethod for calculating a us-in the e e is uk’s travel experience, k ∈ locations’ index the trip increases. For example, dumping < 44], 1 is a−(| j−i|−1) , factor, and j are indices intervaler’s travel≤experience)of 0factor ≤ α = 2 dumping where i decreasing as the of A and B in t 0 < α 1 is ament . [43, αbetween these two locations’ index on the more discontinuously two locationsexperi-accesse they pertain to. That is, a trip increases. For example, in the beingment of [43, 44], α = 2−(| j−i|−1) , be big, thus α jwill become small), theB in the trip user (|i − j| would where i and are indices of A and less contribution th 38they pertain to. That offer tomore discontinuously two locations being accessed by a 12年12月26⽇日星期三 can is, the the correlation between these two locations.
40.
2 2 1 Cor(B,C) = e1 + · e3 ; Cor(C, B) = e2 ; Cor(B, A) = e3 . Mining the correlation between 2 locations (cont.) u1 Trip1 u2 Trip2 u3 Trip3 A B C A C B B A C 0 1 2 0 1 2 0 1 2 9 Location-Based Social Networks: Locations 301 Trip1 : Cor(A,B) = e1, Cor(B,C) = e1, Cor(A,C) = 1/2*e1 Fig. 9.12 An example calculating the correlation between locations terms of Trip2 , and :Cor(B, A) = e2, ,Cor(C,B) = e2,e3 , Cor(B,C) = 1/2 · e3 by Trip3 . Trip1 Cor(A,C) = e3 Cor(A,C) = Cor(A,B) = 1/2*e2 Later, the correlation inferred from each user’s trips is integrated as follows. Trip1 : Cor(B,A) = e3, Cor(A,C) = e3, Cor(B,C) = 1/2*e3 9.3.3.2 Rating Inference + 1 · e ; Cor(A,C) = 1 · e + e + e ; Cor(A, B) = e1 2 1 2 3 2 2 The typical Cor(B,C) = e + 1 ·similarity betweenetwo items isA) = e . way to estimate the e ; Cor(C, B) = ; Cor(B, calculating the Co- 1 3 2 3 2 sine similarity between two rating vectors that correspond to the two items. For instance, the similarity between location l3 and l5 can be represented by the Cosine similarity between the two rating vectors, < 3, 2, 1, 0 >T and < 4, 2, 0, 1 >T . This rating-based similarity measure is fast, however it neglects the information of user u1 among locations.2 As aTrip2 the rating-based method is not a very mobility patterns Trip1 u 39 result, u3 Trip312年12月26⽇日星期三
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Rating inference The typical way to estimate the similarity between two items is calculating the Cosine similarity between two rating vectors that correspond to the two items. fast, but it neglects the information of user mobility patterns among locations The recommender presented in [44] integrates the location correlation (introduced in Section 9.3.3.1) into an item-based collaborative ﬁltering (speciﬁcally, the Slope One algorithm) 1) The Slope One algorithms 2) The Slope One algorithm using the location correlation 4012年12月26⽇日星期三
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calculated as Eq. 9.22. r p j − r pi 302 dev j,i = ∑ , Yu Zheng and(9.22)Xie Xing 302 R p ∈S j,i (χ) S j,i (χ) Yu Zheng and Xing Xie 302 The Slope One algorithms evaluation R p ∈ S j,i (χ), the average deviation of item i with regard to item j is Yu Zheng and Xing Xie Given that dev j,i + r pi a prediction for r p j based on , a reasonable calculated as Eq. 9.22. is the average deviation of item ripiwith regard to predictor evaluationOne ∈ S j,i (χ), [19] are famous and representative i with R item j is The Slopethe p algorithmsall(χ), predictions, as shown in Eq. 9.23.regard toalgorithms, might be evaluation R p of S j,i the the average deviation of item item-based CF item j is average ∈ which arecalculated9.22. 9.22.efﬁcient to query, andpreasonably accurate. calculated as Eq.implement, easy to as Eq. r j − r pi dev j,i = 1 ∑ r − r , (9.22) dev j,i | ∑ P(r p j ) == R p ∈S (χ) j,i dev j,i |w j=∑ ∑ (dev Sj,i + pipi p jr p j(χ)pi), −rr (9.23) (9.22) j,i ,, (9.22) i∈w j S S(χ) R p ∈S j,i∈S j,i (χ) j,i j,i R p (χ) (χ) Given that dev j,i + r pi is a prediction for r p j based on r pi , a reasonable predictor where w jthe {i|ij,i S(Rj,iis apiprediction for 0} jisbasedtraining, set reasonable predictor Given The collection j, |Sprediction for in the on r pi a reasonable = average of all the a all (χ)| > p shown ofEq. 9.23. of evaluations j based on a is χ might be Si, jdevthat+ rset), irevaluations simultaneouslysetin rall ,relevant and jpredictor ∈ dev Given that (χ) is the pip + = is predictions,r asr p the containing item i items. j,i pi of might bemight be the average evaluations that as shown inin Eq.9.23. two items has Further, the number all of all the predictions, as shown Eq. contain the average of of the predictions, simultaneously 9.23. 1 1 been used to weight the prediction regarding different items, as presented in E- q. 9.25. Intuitively, to predict p jp ’s p j ) 1 j ||w∑i∈w (dev given), p ’s ratings of item B and P(r P(r =)= ∑(dev + r ), (9.23) u ) =rating i∈witem A ++ rpi u P(r p j of| (dev j,ij,i r pi ), |w ∑ j j j,i pi j (9.23) (9.23) C, if 2000 users rated the pair of A andj |Bi∈w j|w whereas only 20 users rated pair of A and where w juwhere w∈= {i|ip∈ S(R pBj,i|Slikely (χ)|be 0}fartheset of all relevant items. A than C, then = {i|i j S(R ), i = ), is j,(χ)|to 0}ais is betterof all relevant item p ’s ratings of item = |S j,i > > j,i the set predictor for items. u pFurther,= of itemthe is.of = j, |S j,i (χ)| > 0}simultaneously relevant items.items has where w j the number ), i evaluations that issimultaneously contain two items has ’s ratingsFurther, S(R number of evaluations that the set of all contain two {i|i ∈ C p Further,to weight weight evaluations that simultaneously contain presentedE- E- been used to the number of the prediction regarding different items, asas two items in presented in has been used 9.25. Intuitively, to predict u p ’s rating+ ritem |S given u p ’s ratings of item B and been used q. to weight the prediction (dev j,i of pidifferentitems, as presented in E- the prediction regarding ) · A (X)| ∑w j regarding different j,i items, q. 9.25. Intuitively, to predict upair rating of item A given uusers rated pair of A(9.24) P(r p j ) = ’s of A and B whereas only 20 p ’s ratings of item B and C, if 2000 users rated the p and q. 9.25. Intuitively, to predictitem Brating ofjto be(X)| better predictor forof item than u p ’s is likely |S j,i aA given u p ’s ratings item A B and ∑w item far C, if 2000 users u p ’s ratingspair of A and B whereas only 20 users rated pair of A and C, then rated the of C, if 2000pusers rated item pair of A and B whereas only 20 users rated pair of A and u ’s ratings ofthe C is. is likely C, then u p ’s ratingsofalgorithm using the to be a far better predictor for item A than item B C, 2) The p ’s ratings of item B is likely to be a far better predictor for itempredict then u Slope One location correlation: Intuitively, to A than uu ’s ratings of location is.given u ’s ratings of location |S j,i (X)| if location B is more p ’s rating of item C A ∑w j41 j,i + r pi ) · B and C, p ratings of item C is. p (dev P(r p j ) = (9.24)12年12月26⽇日星期三 A beyond C, then u p ’s ratings of location B is likely to be a far better related to ∑w |S j,i (X)|
43.
∑w j (dev j,i + r pi ) · |S j,i (X)| The P(r p j ) One algorithm using Slope = the (9 ∑w j |S j,i (X)| location correlation 2) The Slope One algorithm using the location correlation: Intuitively, to pre’s ratingIntuitively, to predict up’s u p ’s ratings of location B and of location B of location A given rating of location A given up’s ratings C, if location B is m ated to A beyond C, B is more ’s ratingsbeyond C, then uB’sis likelylocation a far be and C, if location then u p related to A of location p ratings of to be B is likely to be a far better predictor for location A than up’s ratings ofedictor for location A thanas shown in Eq. 9.25,location C Eq. 9.24 is location C is.Therefore, u p ’s ratings of the |Sj,i(χ)| in is. Therefore, as show . 9.25, the |S j,iby the correlation Corjiis replaced by the correlation cor ji (inferre replaced (χ)| in Eq. 9.24 (inferred in Section 9.3.3.1):ction 9.3.3.1): ∑i∈S(R p )∧i= j (dev j,i + r pi ) · cor ji P(r p j ) = , (9 ∑i∈S(R p )∧i= j cor jihere cor ji denotes the correlation between location i and j, and dev j,i is stilllated as Eq. 9.22. number of observed ratings (i.e., |Sj,i(χ)|) used by the weighted Slope In contrast to the In contrast to the number of observed ratings (i.e., |S j,i (χ)|) used by the weigh One algorithm, the mined location correlation considers more human travel behavior, such as the travel sequence, user experience, and transition probability between locations.ope One algorithm, the mined location correlation considers more human trhavior, such as the travel sequence, user experience, and transition probabtween locations. Using Eq. 9.25, an individual’s ratings of locations they have 42 12年12月26⽇日星期三
44.
Open Challenges Although they are able to provide useful recommendations to an individual, personalized location recommender systems are faced with some open challenges during real implementation. - Cold start problems - Data sparseness - Scalability 4312年12月26⽇日星期三
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Cold start problems A cold start is a prevalent problem in recommender systems, as a system cannot draw inferences for users or items when it has not yet gathered sufﬁcient information. New Location problem: One possible solution is assigning the new location with a small number of users’ ratings of existing places that are similar to the new location. (according to their category info.) ﬁnd k most similar places The ratings of a few users to these similar places can be utilized to estimate their ratings to the new location, using the average mean of existing ratings With these virtually generated ratings, the new location can be recommended to real users, thereby getting real ratings in return. The virtual ratings can be removed from the system once the new location has obtained enough ratings. 4412年12月26⽇日星期三
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Cold start problems (cont.) New User problem:When signing up in a recommender system, a new user has no location data accumulated in thesystem. Therefore, the recommender cannot offer her personalized recommendations effectively. One possible solution is providing an individual with some of the most popular recommendations at ﬁrst regardless of her interests. 4512年12月26⽇日星期三
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Intuitively, a user-location matrix is very sparse as a user can only visit a certain number of locations. The prediction of an individual’s interest in a location is un- able to be very accurate based on such a sparse matrix. Some approaches using additional information can improve the inferences. For example, the method intro- Data sparseness duced in Section 9.2.3 uses the category information of a location. Also, propagation and similarity-based mapping methods (mentioned in the above section) can be em- Intuitively, reduce the empty entriesvery sparse asAlternative only visit a certain number ployed to a user-location matrix is in a matrix. a user can methods can transfer of locations. The prediction ofaan individual’smatrix, which has a smaller number of this user-location matrix into user-category interest in a location is unable to be very accurate basedfewer empty entries than the former. As shown in Fig. 9.13, the sim- columns and on such a sparse matrix. ilarity between users can be determined in terms of this user-category matrix with Alternative methods can transfer in turn in the user-location matrix for locationmatrix, sufﬁcient ratings, and then used this user-location matrix into a user-category rec- which has a smaller number ofis still a very challenging problem than the former. ommendation. However, this columns and fewer empty entries that remains open to research and real implementation. this is still a very challenging problem that remains open to research and real implementation. l0 l1 lj ln-1 ln c0 c 1 cj cm-1 cm u0 I a0,1 I I u0 I b0,1 b0,m Transform u1 a1,0 I I I a1,n u1 b1,0 I b1,m ui I M= ai,0 I I I M = ui bi,0 bi,1 bi,j bi,m un-1 I I I an-1,n un-1 bn-1,0 I bn-1,m Similarities un an,0 I I un bn,0 I between users Fig. 9.13 Transforming a user-location matrix into a user-category matrix 4612年12月26⽇日星期三
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Scalability the problem concerning the scalability of a location recommender arises in large part from the increasing number of users. User-based CF: 1) Clustering 2) Compute the similarity based on this location history and determine which group the new user belong to. 3) Once the similarity between the new users and other users in the cluster is computed, the similarity can be used for a time even if the new user has new data uploaded to the system. Item-based CF: The correlation (or similarity) between two locations can be updated at a very low frequency, e.g., once a month, as the arrival of a few new users does not change them signiﬁcantly. 4712年12月26⽇日星期三
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Summary This chapter explores research topics in a location-based social network from the perspective of understanding locations with user-generated GPS trajectories. Using travel as a main application scenario, both generic and personalized travel recommendations are studied. The generic travel recommender starts by ﬁnding interesting locations and travel sequences from a large amount of raw trajectories, and then offers itinerary and location-activity recommendations. The personalized location recommender provides a particular user with locations matching her preferences, based on the location history of this user and that of others. Two kinds of collaborative ﬁltering-based models are proposed to predict the user’s interests in unvisited places: - The user-based CF model is able to accurately model an individual’s behavior while it suffers from the increasing scale of users. - The location-based CF model is efﬁcient and reasonably accurate. 4812年12月26⽇日星期三
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Good Sentences • Intrinsically(本質上), a user’s travel experience is region-related • While chapter 8 studies the research philosophy behind a location-based social network (LBSN) from the point of view of users, this chapter gradually explores the research into LBSNs from the perspective of locations.(角度;觀點) • In fact, this kind of information evolves as time goes by and varies in quite a few(相當多) factors • However, an online data selection strategy (i.e., specifying a region based on an individual’s input) will generate a great deal of(大量的) resource- consuming operations, thereby diminishing the feasibility of our system. • By tapping into(To establish a connection with; have access to) the collective social knowledge, these recommendations help people to travel to an unfamiliar place and plan their journey with minimal effort. • estimates an individual’s (個人的) interests in unvisited places by considering her location history and those of other users 4912年12月26⽇日星期三
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Good Sentences • One possible solution is providing an individual with some of the most popular recommendations at ﬁrst regardless of(不管) her interests. • When signing up in a recommender system, a new user has no location data accumulated(累積) in the system. • This section introduces a location-activity recommender system [40] which answers the above questions by mining a myriad of (無數的)social media, such as tips-tagged trajectories or check-in sequences. • Likewise(同樣地), when performing activity recommendation for a location, the top k activities can be retrieved from the row corresponding to the location. • The motivation for building this location- feature matrix lies in the insight(眼光、理解、key) that people could carry out(實施、進行)similar activities in similar locations. • Given a location, the number of POIs pertaining to(相關) each category can be counted. 5012年12月26⽇日星期三
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Frobenius norm: entry-wise product: (A o B)ij = (A)ij * (B)ij 5112年12月26⽇日星期三
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