Chapter9 location-based social networks-locations

Chapter 9
Location-Based Social Networks:
Locations

指導教授：莊坤達
學生：黃首翰

1

12年12月26⽇日星期三

Outline

• Introduction
• Generic Travel Recommendations
• Personalized Travel Recommendations
• Summary
• Good Sentences

2

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.

3

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

4

Generic Travel Recommendations

“trajectories → interesting locations → popular travel sequences → itinerary
planning → activities recommendation.”

• Mining Interesting Locations and Travel Sequences
• Itinerary Recommendation
• Location-Activity Recommendation

5

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.
6

280 Yu Zheng and Xing Xie
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-phone


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

8

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
9

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
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
10

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
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
is
HITS. Thus, specifying a geospatial region (a topic query) and formulating a dataset

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.

12

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
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 covering

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

14

ulq = ∑ vi0
ecovers the region× l0j ; 0 by the user 0
1 1 1 j specified
i
u3 0 1 (9.3)
2 0
or a cluster that
M=  u2 1 ci j ∈clq 2
 1 0 0 u4 0 (9.1) 0
0 1 1
u3 0 0 1 2 0
demonstrating u4 Then, the mutually reinforcing relationship of user travel experi
the data selection0strategy 1
cendant node on0the 0 level,11 ≤ l < i. For instance, as shown
lth
interest Iil jofLocations (cont.)location
ually reinforcing relationship isuser travel experience ek and
represented as follows:
cendant node on the first level of the hierarchy is c11 , and its
ij

the second follows:is c21 . Thus, if l = 2, clq stands for c21 and
epresented as level
Inference:
 c31 c32 c1133 and34 3135  , . . . , cl35 ) ∈ c11 .k
c c c
o, 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 location
y’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 first
de 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
T
1 . 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 32
em 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 vector
e 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

ore of location A(IA ) weighted by the probability of people
Methodology for detecting travel
equence (OutAC ). Clearly, there are seven (5+2) links pointing
om 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 TBHG
ore of location C(IC ) weighted by the probability of people’s
A popularity score is calculated for each location sequence within a given region based
equence (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 .
7 7

ore of location A(IA ) weighted by the probability of people
Methodology for detecting travel
equence (OutAC ). Clearly, there are seven (5+2) links pointing
om 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 TBHG
ore of location C(IC ) weighted by the probability of people’s
A popularity score is calculated for each location sequence within a given region based
equence (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 .
7 7

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

17

Methodology for Itinerary
Recommendation

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

18
12年12月26⽇日星期三 a location. So, the typical stay duration in each location and general travel duration

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.

19

total time needed for an itinerary is much shorter than the available time, the
remaining time is wasted.
• 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
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 recommended

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.

21

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 Inference


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
23

Data Modeling (cont.)
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.
Usually, a location might include multiple points of interest (POI) pertaining to different
categories.
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.

Locations

Locations

Activities
U V

24

Data Modeling (cont.)
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-
One possible way to calculate this correlation is based upon user-generated tips and to-
do-lists. In case the user-generated data is not large enough, the results returned by a
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.

Locations

Locations

Activities
U V

25

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 representing

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].

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
28

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

29

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]

30

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.

31

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

32

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 0
in 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

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.

34

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 ) p
predicted )| 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. users
more weight rqiused carryweight.prediction ofmore . Here, sim(uuq uq ) is
measure 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
it
mecommendation systems. Therefore, it is not necessary to
in more detail.

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

36

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
37

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 m
sequences in which both locations have been visited. 1) This correlation between A
of a travel sequence A → B might be quite different from B → A. For examp
and 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 A
of 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 cor
a 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 directly
B. 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 arriving
than those beingCvisited Intuitively, the Cor(A, B) users wouldthe twoB directly might be dif
→ B). discontinuously. Some indicated by reach sequences from
A (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 than
C → 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 be
Likewise, 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), by
the 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 integrating
the 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 calculatin
whereʹ′ 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 interval
er’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, α
between these two locations’ index on the more discontinuously two locationsexperi-accesse
they pertain to. That is, a trip increases. For example, in the being
ment 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
38

they 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.

2 2
1
Cor(B,C) = e1 + · e3 ; Cor(C, B) = e2 ; Cor(B, A) = e3 .
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
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 Trip3

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

40

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)|

∑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 of
edictor 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 ji

here cor ji denotes the correlation between location i and j, and dev j,i is still
lated 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 tr
havior, such as the travel sequence, user experience, and transition probab
tween locations. Using Eq. 9.25, an individual’s ratings of locations they have
42

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

43

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.

44

Cold start problems (cont.)

New User problem:

When signing up in a recommender system, a new user has no location data accumulated in the
system. 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.

45

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
46

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.

47

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.

48

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
49

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.
50

Frobenius norm:

entry-wise product:

(A o B)ij = (A)ij * (B)ij

51

Chapter9 location-based social networks-locations

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