Time Weight Content-based Extensions of Temporal Graphs

for Personalized Recommendation

Armel Jacques Nzekon Nzeko’o

1,2,3

, Maurice Tchuente

1,2

and Matthieu Latapy

Sorbonne Universités, UPMC Université Paris 06, IRD, UMI 209 UMMISCO, F-93143, Bondy, France

CETIC, Université de Yaoundé I, Faculté des Sciences, Departement d’Informatique, BP 812, Yaoundé, Cameroon

Sorbonne Universités, UPMC Université Paris 06, CNRS, UMR 7606, LIP6, F-75005, Paris, France

Keywords: Temporal Recommendation, Long- and Short-term Preferences, Session-based Temporal Graph, Time

Weight Content-based Graph, Time-averaged Hit Ratio, PageRank, Injected Preference Fusion.

Abstract: Recommender systems are an answer to information overload on the web. They filter and present to

customers, small subsets of items that they are most likely to be interested in. Users’ interests may change

over time, and accurately capturing this dynamics in such systems is important. Sugiyama, Hatano and

Yoshikawa proposed to take into account the user’s browsing history. Ding and Li were among the first to

address this problem, by assigning weights that decrease with the age of the data. Others authors such as

Billsus and Pazzani, Li, Yang, Wang and Kitsuregawa proposed to capture long- and short- terms

preferences and combine them for personalized search or news access. The Session-based Temporal Graph

(STG) is a general model proposed by Xiang et al. to provide temporal recommendations by combining

long- and short-term preferences. Later, Yu, Shen and Yang have introduced Topic-STG, which takes into

account topics information extracted from data. In this paper, we propose Time Weight Content-based STG

that generalizes Topic STG. Experiments show that, using Time-Averaged Hit Ratio as measure, this time

weight content-based extension of STG leads to performance increases of 4%, 6% and 9% for CiteUlike,

Delicious and Last.fm datasets respectively, in comparison to STG.

1 INTRODUCTION

The amount of information in web sites like

Amazon, Netflix and Last.fm is considerable and

fast-growing. For users, browsing and searching in

such data has become very difficult. To solve this

problem, recommender systems filter and present to

customers, small subsets of items that they are most

likely to be interested in.

Early recommender systems did not take into

account temporal information (Herlocker et al.,

1999). This is strong limitation because user’s

profiles and context evolve with time. In this regards

Sugiyama et al., (2004) proposed to adapt results

according to time-evolving user profiles, based for

instance on browsing history. Ding and Li (2005)

were among the first to take time explicitly into

account by assigning decreasing weights according

to their age. Later, some authors proposed to capture

both long- and short-term preferences and combine

them for recommendations (Billsus and Pazzani,

2000; Li et al., 2007).

Interest in temporal recommender systems

increased considerably since the 2009 Netflix grand

prize (Koren, 2009). Koren’s solution was based on

a dataset with items rated by users, whereas in

practice, data often contains the history of users in

terms of their interactions with items. For instance,

Last.fm offers datasets in which each line indicates

the fact that user u listened to song i at time t.

In this line of research, Xiang et al., (2010)

propose Session-based Temporal Graphs (STG),

which model long- and short-term preferences

separately. However, they ignore features of items,

and so they miss for instance the fact that interest in

a piece of music is related to its author. In order to

improve this, Yu et al., (2014) extend the STG into

Topic-STG for personalized tweet recommendation.

They add topic nodes to the STG and link tweets to

their topics.

These recommender graphs process edges

regardless of their age. This fails to capture the fact

that in most situation, recent transactions are the

most likely to reflect user preferences in the near

268

Nzeko’o, A., Tchuente, M. and Latapy, M.

Temporal Recommendation, Long- and Short-term Preferences, Session-based Temporal Graph, Time Weight Content-based Graph, Time-averaged Hit Ratio, PageRank, Injected Preference

Fusion..

DOI: 10.5220/0006288202680275

In Proceedings of the 13th International Conference on Web Information Systems and Technologies (WEBIST 2017), pages 268-275

ISBN: 978-989-758-246-2

future (Ding and Li, 2005). For example, the clothes

that a boy wears have great variability related to his

age, thus, the impact of his past dress style on his

future dress style decreases with time. To take this

into account, we propose here to weight edges

according to their age, so that older edges have

lower influence. We propose the Time Weight

Content-based STG, in which edges are labelled

with their last occurrence time, and we use an

exponential decay function proposed by Ding and Li

(2005) to weight edges accordingly.

The remaining of this paper is organized as

follow: Section 2 presents Session-based Temporal

Graphs and the two recommendation algorithms,

PageRank (Page et al., 1999) and Injected

Preference Fusion (IPF) (Xiang et al., 2010) on

which our work is built. Section 3 introduces the

Time Weight Content-based STG model. Section 4

is devoted to experiments. We discuss related work

in Section 5, and we summarize our findings in

Section 6.

2 BACKGROUND

We use the notations and definitions proposed by

Xiang et al., (2010), together with some additional

concepts related to content and time, summarized in

Table 1.

2.1 Session-based Temporal Graph

We consider data under the form of a link stream,

i.e. a set of triples (t, u, i) representing the fact that

user u has selected item i at time t. For each user u

(resp. each item i), we define user node v

(resp. item

node v

). We denote by T the time span of the

dataset and we divide T into time slices of equal

duration. For each of these slices T, we define

session node v

u,T

. A session is not defined here as a

time slice during which the user interacts with the

system. It rather corresponds to a time slice during

which a user has a specific behaviour.

A session-based temporal graph G(U, S, I, E, w)

is a directed bipartite graph with three types of

nodes: U is the set of user nodes, S the set of session

nodes and I the set of item nodes. The function

w: E  R is a non-negative weight function for

edges. The set of edges, E, is obtained as follows.

For each triplet (t, u, i), let us consider T the time

slice to which t belongs. Then, E contains edges

, v

) and (v

, v

), which represent long-term

preference between user u and item i; and E contains

Table 1: Notations and definitions.

Symbol

Description

bipartite graph STG

bipartite graph Content-based STG

bipartite graph Time weight Content-

based STG

edge set in any graph

set of all nodes in any graph

U, I, S, C

user node set, item node set, session

node set, content node set

, v

u,T

, v

user node, item node, session node,

content node

weight function defined on STG edges

weight function defined on Content-

based STG edges

time weight function defined on Time

weight Content-based STG edges



v

, v

k+1



propagation function of IPF from

to v

k+1

out v

out node set of the node v



parameter to control the preference

propagation



dose of long-term preference injected

to user node



parameter to adjust the edge weight

from item nodes to user/session nodes





parameter to control the influence of

content features in the preference

propagation







parameter used to compute the time

weight function



damping factor for PageRank

personalization

u,T

, v

) and (v

, v

u,T

), which represent short-term

preferences.

The weight function is defined as:













 

























(1)

In (1),



models the influence of long-term

preferences and



models the influence of short-

term preferences. To simplify the model, we can use









for



and 1 for



Fig. 1 is an example of STG with 3 user nodes, 5

session nodes, 7 item nodes and 2 time slices. It

shows that user u

has selected items i

, i

, user u

has selected items i

, i

and user u

has selected item

during the first time slice T

. During the second

time slice T

, user u

has selected i

and user u

has

selected i

and i

Temporal Recommendation, Long- and Short-term Preferences, Session-based Temporal Graph, Time Weight Content-based Graph,

Time-averaged Hit Ratio, PageRank, Injected Preference Fusion.

269

Figure 1: Example of STG.

2.2 Temporal Personalized Random

Walk

The Temporal Personalized Random Walk (TPRW)

(Xiang et al., 2010) is a personalization of the

PageRank algorithm defined by Page et al. (Page et

al., 1999) for nodes ranking in graphs. It was defined

to tackle temporal recommendation using the idea of

Haveliwala (Haveliwala, 2002). It corresponds to the

following formula:

PR =   M  PR  (1 )  d (2)

where  is the damping factor, M is a transition

matrix and vector d is a user-specific personalized

vector indicating which nodes the random walker

will jump to after a restart.

When making recommendations for user u,

vector d favors user node v

and the most recent

session node v

u,T

as follows:



















 











(3)

In other words, long-term preferences are injected to

user node v

and short-term preferences are injected

to session node v

u,T

through vector d.

When we implement the PageRank with iterative

power law method, we stop when the difference of

two consecutives rank vectors is of norm less than or

equal to a threshold .

2.3 Injected Preference Fusion

The IPF algorithm is an extension of the random

walk with injection of preferences and customization

of preference propagation. To recommend items to a

user u, the algorithm proceeds in 3 steps:

 Injection of long-term preferences



on the user

node v

and injection of short-term preferences (1





) on the most recent session node v

u,T

of user

 Propagation of preferences by random walk of

length 3 on the graph according to the formula.















































(4)

 where out(v

) denotes the set of out-neighbors of

node v



is a parameter used to tune the

propagation process, w(v

, v

k+1

) is the weight of

arc (v

, v

k+1

) and



, v

k+1

) is the proportion of

preference of v

that is propagated to v

k+1

 Recommendation of Top-N items that have

received the greatest preference values and that

user u has not yet selected.

The IPF random walk length is limited to 3

following experimental result (Xiang, et al., 2010).

3 TIME WEIGHT CONTENT-

BASED EXTENSIONS OF STG

In this section, we first illustrate how to construct

Content-based STG (CSTG) which is similar to

Topic-STG (Yu et al., 2014). We end by showing

how to construct Time Weight Content-based STG

(TCSTG).

3.1 Content-based Session-based

Temporal Graph

The basic STG model neglects item properties which

can contain significant information for the prediction

of user’s behaviour. This motivated Phuong et al.,

(2008) to add to the user-item bipartite graph, new

nodes corresponding to content. The same idea is

applied here to obtain Content-based STG.

To construct the Content-based STG, we need to

have item properties in our data, so we don’t use a

set of triples like in the construction of STG. We

rather use a set of quadruples (t, u, i, c) where t, u

and i have the same meaning as in STG, and c is a

content feature of i.

Content-based STG CG(U, S, I, C, E, w

) is a

directed graph obtained from the STG G(U, S, I, E,

w) by adding for any link (t, u, i, c), the six

additional arcs (v

, v

), (v

, v

), (v

u,T

, v

), (v

, v

u,T

WEBIST 2017 - 13th International Conference on Web Information Systems and Technologies

270

, v

) and (v

, v

). With respective weights 1,



, 1,



as illustrated in Fig. 2.

Figure 2: Edge weights in content-based STG.

3.2 Time Weight Content-based

Session-based Temporal Graph

The Content-based STG neglects the ages of edges

when assigning weights. So, it cannot capture the

evolution of users’ interest which we assume to be

sensitive to time as suggested by Ding and Li

(2005). The recommendation model presented here

assigns a greater weight to recent edges and lower

weight to older edges. More precisely, the weight of

the arc (v, v’) is defined by:



























 (5)

where w(v, v’) is the weight in the graph without

time weight, t is the most recent time at which edge

(v, v’) appears and f(t) is a time-dependent decay

function as in (Ding and Li, 2005). Here we take

























(6)

where  is the decay rate and (t

– t) is the difference

in second between time t

at which we are making

recommendations and t.

The parameter  can also be defined as 



where



is the delay after which the weight of an

edge reduces by 1/2.



is also called half life

parameter.

4 EXPERIMENTS

We have conducted a set of experiments to examine

the performance of Time weight Content-based

STG. For each model, we consider various values of

parameters and we retain the best performance. We

also implemented the classic bipartite user-item

graph (BIP) to show the effects of taking into

account long- and short-term preferences in graph

models.

The experiment environment is as follow: the

executions of our programs are done using a

computer with 64GB of RAM and 16 processors

Intel of 2.93GHz and 4MB of cache. For

implementation, we have used the Python 2.7

language and the Networkx 1.11 module for graph

manipulation. Note that we have changed the

Networkx PageRank in order to stop when

convergence is not reached after 100 iterations. We

used SQLite 3 as DBMS and Matplotlib 1.4.0 to

produce graphics.

4.1 Data Description

Following the example of Xiang et al, our goal is to

make recommendations based on implicit data from

various real world domains. To this effect, we first

perform experiments on the social bookmarking

datasets CiteUlike and Delicious (Cantador et al.,

2011) which were used in (Xiang et al., 2010). This

provides a good basis for the evaluation of the

improvement obtained when temporal aspects are

taken into account. We also use data from Lastfm

(Celma, 2010), a web site where users can listen to

music because in this domain the fashion effect

plays an important role with the consequence that,

the impact of past tastes on the future ones decreases

with time.

We model our data as link streams {(t, u, i, c)},

where any quadruple has different interpretation

depending on domains. In the case of CiteUlike and

Delicious, each quadruplet means that user u has

bookmarked page i at time t with tag c. And for the

Last.fm data, this means that user u has listened to

song i at time t and c is the author of i.

Before modeling our data as link streams, we

performed a filtering by ignoring items and users

that did not appear a number of times higher than a

given threshold



. Table 2 provides details on our

data: date of the first link, date of the last link, total

duration of link streams, threshold used, number of

users, number of items, number of content features

and number of links.

Table 2: Data statistics.

Start date

End date

Duration



CiteUlike

2010-01-01

2010-07-02

183 days

Delicious

2010-05-11

2010-11-09

183 days

Last.fm

2005-02-14

2005-08-16

183 days

Users

Items

Content

Links

CiteUlike

1318

424

4216

16885

Delicious

894

298

2789

13825

Last.fm

135

1054

225

41604

Temporal Recommendation, Long- and Short-term Preferences, Session-based Temporal Graph, Time Weight Content-based Graph,

Time-averaged Hit Ratio, PageRank, Injected Preference Fusion.

271

4.2 Experiment and Evaluation

The evaluation process is done periodically as in (Li

and Tang, 2008) and (Lathia et al., 2009). Before

starting experiments, we have to divide the link

streams into time windows of a fixed length . We

fix  to 15 days because humans live at a monthly

pace, and the first 15 days are generally

characterized by consumption behaviours just after

getting salary, that are different from the ones

observed during the last 15 days of the month. To

simplify the experimentation process, we adopt the

same  as the length of session when constructing

STG. Here after, N denotes the number of time

slices.

For each time window W

, for k=1,..,N-1, we

proceed as follows:

 Construct the graphs corresponding to data of W

, .. ,W

 Compute the Top-N recommendations for users

who have selected at least one “new item” during

the time window W

k+1

 Evaluate the algorithm by computing the ratio of

users for which at least one of these Top-N items

recommends has been selected during W

k+1

. This

proportion is also call Hit Ratio 



(Karypis,

2001).

After determining the Hit Ratio for each window,

compute the Time Averaged Hit Ratio (TAHR) that

is a weighted combination of the N-1 values

obtained above for the Hit Ratio. The weight of each

Hit Ratio 



is the number of corresponding

users



as in the following equation:





















(7)

Note that, although the convergence may be very

slow for some examples, we have noticed that, in

most cases, the convergence is achieved after at

most 100 iterations.

4.3 Exploration of the Range of the

Parameters

Let us see how the parameters are obtained in

Table 3. We proceed as in (Xiang et al., 2010). The

parameters correspond to the vector [











], whose components are numbered 1, 2, 3, 4, 5, 6

from left to right. This vector is initialized to

[0, 0.5, 0.5, 0.5, 0.5, 0.5]. Then, we consider the

values of



0 shown in the second row of Table 3,

while maintaining the other parameters at their

initial value 0.5. We perform ten experiments and

take for



0 the value corresponding to the best

performance. For instance we obtain for



0 the

interval [7, 30] for TPRW-TCSTG in CiteUlike

dataset as shown in Table 4. Given this optimal

value for



0 we then give to  the eleven successive

values shown in the third row of Table 3, while

maintaining the other parameters at their initial

value. We obtain for  the interval [0.4, 1] for

TPRW-TCSTG in CiteUlike dataset as shown in

Table 4. This process is repeated for the remaining

parameters.

Figure 3 shows all the variations of Time-

Averaged Hit Ratio with parameter values in the

case of CiteUlike. The complete set of parameters

explored is shown in Table 3 and the best values

obtained with this procedure are shown in Table 4.

Table 3: Parameters values.

Parameters

Initial

value

Set of values



0 (in days)

0, 1, 7, 15, 30, 45, 60, 90, 180, 365



0.5

0.1 × i for i = 0..10



0.5

0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1,

1.5, 3, 5, 10, 15, 20, 30, 50, 100



0.5

0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1,

1.5, 3, 5, 10, 15, 20, 30, 50, 100



0.5

0.1 × i for i = 0..10



0.5

0.1 × i for i = 0..10

4.4 Accuracy Comparison

The performances of PageRank and IPF applied to

STG, Time-weight content-based STG, Content-

based STG and classical bipartite graph, for the three

datasets are presented in Table 5. It can be seen that

PageRank applied to the Time weight content-based

STG gives the best results, followed by Content-

based STG. Moreover, STG is always better than the

classical bipartite graph, which confirms the

relevance of STG.

Moreover, for PageRank applied to the Time

weight content-based STG, the optimal value of the

half life parameter



0, is less than one month for

social bookmarking dataset, but is greater than one

month for music dataset. This may be due to the fact

that the impact of web pages that someone consulted

in the past on those that he is likely to consult in the

future decreases very quickly with time. On the

contrary, tastes are more stable for music and the

impact of a past music does not decrease very

quickly.

WEBIST 2017 - 13th International Conference on Web Information Systems and Technologies

272

Figure 3: Variation of Time Averaged Hit Ratio with parameter values in the case of CiteUlike.

Table 4: Best parameter values.

CiteUlike











IPF-BIP

0.1-0.3

IPF-STG

0.0-0.5

0.1-0.3

0.1-0.7

IPF-CSTG

0.5-1

0.0-0.9

0.2-0.5

0.5-0.6

IPF-TCSTG

15-60

0.5-0.6

0.1-0.9

0.4-1.5

0.1-1

TPRW-BIP

0.1-0.9

TPRW-STG

0.0-0.7

0.3-0.6

0.1-0.7

TPRW-CSTG

0.5-0.8

0.3-0.6

0.1-0.7

0.1-0.6

TPRW-TCSTG

7-30

0.4-1

0.3-1.5

0.5-3

0.5-0.8

Delicious











IPF-BIP

0.1-10

IPF-STG

0.0-0.4

0-0.1

0.1-0.6

IPF-CSTG

0.5

15-50

0.3-0.9

0.4-1.5

IPF-TCSTG

1-7

0.5-0.6

0.5-0.8

50-100

0.5-1.5

TPRW-BIP

0.1-0.9

TPRW-STG

0.0-0.4

0.1-0.2

0.2-0.5

TPRW-CSTG

0.0-0.6

15-100

0.2-0.8

0.5-0.7

TPRW-TCSTG

0-1

0.5-0.8

0-0.1

0.1-04

Last.fm











IPF-BIP

0.1-0.8

IPF-STG

0.5-1

0.9-1.5

1.5-10

IPF-CSTG

0-0.4

0-0.3

30-100

0.4-0.6

IPF-TCSTG

1-15

0-0.4

0.1-0.3

1-100

10-50

TPRW-BIP

0.1-0.5

TPRW-STG

0.5-0.7

0.1-1.5

0.2-0.5

TPRW-CSTG

0.2-0.4

0.2-0.5

5-30

0.4-0.6

TPRW-TCSTG

30-90

0.5-0.7

0.4-0.6

1-5

0.4-0.7

We also think that PageRank has better

performance because in this algorithm the

propagation process is not limited to the proximity

of the source node as in IPF. Indeed PageRank also

favours the recommendation of the most popular

items of the graph because, even when they are far

from the source node, they can be reached and then

have a great influence thanks to their high degree.

Table 5: Performances for the best parameters.

CiteUlike

Delicious

Last.fm

TAHR (%)

IPF-BIP

13.5

7.3

16.3

IPF-STG

15.7

8.6

18.2

IPF-CSTG

14.4

6.4

28.9

IPF-TCSTG

16.1

9.7

26.6

TPRW-BIP

18.3

8.8

27.9

TPRW-STG

20.6

9.2

30.2

TPRW-CSTG

20.9

10.7

37.7

TPRW-TCSTG

26.1

13.2

38.9

5 RELATED WORK

In this section, we present some work on time aware

recommender systems followed by recommender

systems that use item properties. Finally, we present

some graph-based recommender systems.

5.1 Time Aware Recommender

Systems

Ding et al. (Ding and Li, 2005) propose the use of an

exponential decay function to assign greater weights

to latest ratings when computing similarities in

collaborative filtering. Subsequently, Liu et al.,

(2010) have proposed an incremental collaborative

filtering where one decay function is used to

compute similarities and another one is used for

prediction. Recently, Karahodža et al., (2015)

assumed that the importance of interest granted to an

item decreases in a similar manner for similar users.

Some recommender systems are based on the

Temporal Recommendation, Long- and Short-term Preferences, Session-based Temporal Graph, Time Weight Content-based Graph,

Time-averaged Hit Ratio, PageRank, Injected Preference Fusion.

273

assumption that importance of information is

ephemeral. Thus, Lathia et al., (2009) set a time

window size, then, any information is used during

one time slice and ignored at the next time window.

Such recommender systems only capture short-term

preferences.

Some studies are not based only on short-term

preferences but also consider that importance of

some information persists over time (Li et al., 2007).

The STG model (Xiang et al., 2010) extends this

work but ignores item properties.

5.2 Content-based Recommender

Systems

The content-based recommender systems seek to

recommend similar items to the one the user already

like. As Lops et al. (Lops et al., 2011) argue, the

basic idea is to match features associated to users’

preferences and items so as to recommend new

items that address their needs. This approach is

already used in various domains such as books

recommendation on Amazon website based on their

description (Mooney and Roy, 2000), and web pages

recommendation (Pazzani et al., 1996).

Although content-based recommender systems

can propose items that have not already been

purchased in the past, it is also useful to use user

similarities by combining this approach with

collaborative filtering techniques. Indeed,

Balabanovic and Shoham (1997) and Basu et al.,

(1998) show that the combination of collaborative

filtering and content-based filtering may result in a

recommender system that eliminates the weaknesses

of both approaches. In this paper, we have used a

graph model to realize this combination.

5.3 Graph based Recommender

Systems

The simplest graph-based recommender systems

only use user-item links. A bidirectional edge is

created between a user node and an item node if the

user has purchased the concerned item. Finally, an

item is recommended to a user if the user has not yet

purchased that item and if there is a path from the

user to that item. The most used recommender

algorithms on the graphs are based on the random

walk (Baluja et al., 2008), like PageRank and IPF

which are used in this paper.

The use of graph paths to recommend new items

can be seen as collaborative filtering where

similaritys defined through node distance. However,

such recommender graphs do not take into

consideration item properties. To remedy this

limitation, Phuong et al., (2008) have constructed a

recommender graph in which they have added a

third node type: the type “content”. The obtained

recommender system is actually a combined

collaborative filtering and content-based filtering.

The associated graph ignores the temporal aspect of

data and therefore cannot accurately capture short-

and long-term preferences. Yu et al., (2014) propose

the Topic-STG which combines those two

preferences and takes into account topics related to

tweets. However, those models handle edges

regardless of their age. This is not in accordance

with concept drift. This is why we propose a new

extension of STG where edge weights are decreased

using a time decay function as in (Li and Tang,

2008).

6 CONCLUSIONS

This paper proposes time weight content-based

extensions of the temporal graph model introduced

by Xiang et al., As in Topic-STG introduced by Yu,

Shen and Yang, we represent content by nodes, but

we penalize older interactions. Experiments show

that, using Time-Averaged Hit Ratio as measure,

this time weight content-based extension of STG

leads to performance increases of 4%, 6% and 9%

for CiteUlike, Delicious and Last.fm datasets

respectively, in comparison to STG. This gives

evidence of the fact that the age of interactions is a

relevant feature for recommender systems.

More experiments using datasets from various

domains are needed in order to adjust the length of

time windows and other parameters.

ACKNOWLEDGEMENTS

This work is funded in part by the African Center of

Excellence in Information and Communication

Technologies (CETIC), the UPMC-IRD PDI

program, by the European Commission H2020

FETPROACT 2016-2017 program under grant

732942 (ODYCCEUS), by the ANR (French

National Agency of Research) under grants ANR-

15-CE38-0001 (AlgoDiv) and ANR-13-CORD-

0017-01 (CODDDE), by the French program "PIA-

Usages, services et contenus innovants" under grant

O18062-44430 (REQUEST), and by the Ile-de-

France program FUI21 under grant 16010629

(iTRAC).

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274

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