Friend recommendation for cross marketing in online brand

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Friend recommendation for cross marketing in online

brand community based on intelligent attention

allocation link prediction algorithm

Shugang Li, Xuewei Song, Hanyu Lu, Linyi Zeng, Miaojing Shi, Fang Liu

To cite this version:

Shugang Li, Xuewei Song, Hanyu Lu, Linyi Zeng, Miaojing Shi, et al.. Friend recommendation for

cross marketing in online brand community based on intelligent attention allocation link prediction

algorithm. Expert Systems with Applications, 2019, 139, pp.1-11. �10.1016/j.eswa.2019.112839�. �hal-

02383107�

Expert Systems With Applications 139 (2020) 112839

Contents lists available at ScienceDirect

Expert Systems With Applications

journal homepage: www.elsevier.com/locate/eswa

Friend recommendation for cross marketing in online brand

community based on intelligent attention allocation link prediction

algorithm

Shugang Li

, Xuewei Song

, Hanyu Lu

, Linyi Zeng

a , b , ∗

, Miaojing Shi

, Fang Liu

School of management, Shanghai University, Shanghai, 2004 4 4, PR China

Software Development Center, Industrial and Commercial Bank of China, Shanghai, 201206, PR China

Univ Rennes, Inria, CNRS, IRISA, 35042, France

a r t i c l e i n f o

Article history:

Received 17 August 2018

Revised 24 July 2019

Accepted 24 July 2019

Available online 25 July 2019

Keywords:

Friend recommendation

Link prediction

AAI

Mutually complementary indices

Cross marketing

a b s t r a c t

Circle structure of online brand communities allows companies to conduct cross-marketing activities by

the inﬂuence of friends in different circles and build strong and lasting relationships with customers.

However, existing works on the friend recommendation in social network do not consider establishing

friendships between users in different circles, which has the problems of network sparsity, neither do

they study the adaptive generation of appropriate link prediction algorithms for different circle features.

In order to ﬁll the gaps in previous works, the intelligent attention allocation link prediction algorithm is

proposed to adaptively build attention allocation index (AAI) according to the sparseness of the network

and predict the possible friendships between users in different circles. The AAI reﬂects the amount of

attention allocated to the user pair by their common friend in the triadic closure structure, which is de-

cided by the friend count of the common friend. Speciﬁcally, for the purpose of overcoming the problem

of network sparsity, the AAIs of both the direct common friends and indirect ones are developed. Next,

the decision tree (DT) method is constructed to adaptively select the suitable AAIs for the circle struc-

ture based on the density of common friends and the dispersion level of common friends’ attention. In

addition, for the sake of further improving the accuracy of the selected AAI, its complementary AAIs are

identiﬁed with support vector machine model according to their similarity in value, direction, and rank-

ing. Finally, the mutually complementary indices are combined into a composite one to comprehensively

portray the attention distribution of common friends of users in different circles and predict their pos-

sible friendships for cross-marketing activities. Experimental results on Twitter and Google + show that

the model has highly reliable prediction performance.

1. Introduction

With the rapid development of the Internet, the popularity of

high-speed, stable Internet services and the increasing experiences

of online shopping, 80% of the top 500 companies in the world

have established online brand communities. The online brand com-

munity brings together the scattered target customers of the com-

pany accurately and has become a new platform for company to

carry out marketing activities as well as build strong and lasting

relationships with customers ( John, Mochon, Emrich, & Schwartz,

2017 ).

∗

Corresponding author.

E-mail addresses: [email protected] (X. Song), lilin_201[email protected] (L.

Zeng), [email protected] (M. Shi).

A large number of works have already shown that friend groups

can affect individual consumer decisions, for example, product

evaluation, purchase possibility ( Whittler & Spira, 2002 ), and ac-

tual purchase behavior ( Li, Chou, & Lin, 2014 ). Moreover, when

brand preference conﬂicts between group and individuals, indi-

viduals may hide their consumption behavior ( Thomas, Jewell,

& Jennifer, 2015 ). Some scholars in consumer behavior studies

( Solomon, 2016 ) pointed out that the lower the user require-

ments for product, the higher the inﬂuence of the reference group.

Aral (2013) studied the case of 1.4 million Facebook users down-

loading a movie application to ﬁnd out the factors that affected

their decision making. He randomly divided users who had down-

loaded the application into three groups: The ﬁrst group had the

right to invite their friends to try it on their own; friends of the

users in the second group received an automatically generated

message indicating that their friends were using the application;

https://doi.org/10.1016/j.eswa.2019.112839

2 S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839

friends of the users in the third group did not receive any mes-

sages. As a result, 6% of the friends who received the unsolicited

invitation downloaded the application, compared with 2% of those

who received automatic tips. In addition, he also compared users

who actively sent invitations and successfully invited friends with

users who sent automatic tips to friends and invited friends. In the

long run, the former used the application for more time than the

latter.

Friends in online brand communities share their passion for

a speciﬁc brand as well as exchange information and knowledge,

and these social interactions positively inﬂuence the member loy-

alty to the brand ( Brogi, 2014 ). In addition, some members who

share a common interest or prefer the same product are further

gathered together to form different sub-groups, i.e. circles ( Wang

& Xue, 2010 ) in a brand community. Circle structure provides fer-

tile ground for cross-marketing, where sales are ampliﬁed with the

inﬂuence of friends though forming friendships between users in

different circles.

Scoring link prediction algorithm (SLPA) is the main approach

to predict whether there are links between node pairs in the social

network and recommend friendships between user nodes based

on network topology. So far, various SLPAs have been widely ap-

plied for the recommendation of friends, such as the Common

Neighbor index (CN), the Hub Promoted Index (HPI), and the Re-

source Allocation (RA) ( Lü & Zhou, 2011 ). However, existing works

on prediction friendships in social network do not consider es-

tablishing friendships between users in different circles, which

bears on the problem of network sparsity. What’s worse, there

is not yet an SLPA suitable for all network circle structures. So,

constructing the suitable SLPA based on circle structure charac-

teristics is of signiﬁcant theoretical and practical value, which is

a complex work that requires a lot of expert experience. There-

fore, it is of great signiﬁcance to develop method that relies solely

on network data to build appropriate SLPA, so that inexperienced

practitioners can easily use it to obtain highly reliable prediction

results.

To address these problems, this study proposes the intelligent

attention allocation link prediction algorithm (IAALP A) to pre-

dict the possible friendships between users in different circles by

adaptively building attention allocation index (AAI) for speciﬁc cir-

cles, and the AAI represents the amount of attention assigned to

the user pair by their common friend in the triadic closure struc-

ture, which is determined by the friend count of the common

friend.

Speciﬁcally, for the purpose of overcoming the network spar-

sity problem in predicting friendships between users in different

circles, the AAIs of both the direct common friends and indirect

ones are developed based on the principle of attention allocation

of common friends in triadic closure structure. Since it’s diﬃcult

to build the AAI that ﬁts all the structural characteristics of cir-

cles, in light of the characteristics of the density of common friends

and the dispersion level of common friends’ attention, the decision

tree (DT) method ( Wang, Wu, & Yao, 2017 ) is developed to adap-

tively select the AAI suitable for predicting possible links between

user nodes in different circles. In addition, although the combi-

nation of single AAI can help improve its link prediction perfor-

mance, the blind combination of AAIs cannot bring the expected

results ( Gomes, Barddal, Enembreck, & Bifet, 2017 ). To this end,

IAALPA applies the support vector machine (SVM) ( Shan, Kong,

Zhang, Li et al., 2018 ) model to identify the complementary AAIs of

the AAI selected by DT, which can improve the performance of the

selected AAI by combining them as a composite indicator. Finally,

the selected AAI and its complementary ones are used to design

the composite mutually complementary AAI to comprehensively

portray the attention allocated to user node pairs by their com-

mon friends and forecast the possible connections between user

nodes in different circles. Consequently, the friendships between

users in different circles are recommended and successfully cross-

marketing is achieved. Speciﬁcally, a group of users of one product

circle are recommended to the target customers who are the users

of another circle in online brand community. Accordingly, when

the brand marketers are supported by the friend group’s inﬂuence

on individuals, they can signiﬁcantly enhance the cross-marketing

eﬃciency of the product.

The remainder of this paper is organized as follows:

Section 2 introduces the link prediction; Section 3 offers

friend group recommendation; Section 4 explains the IAALPA;

Section 5 offers the experimental design and the results analysis;

Section 6 gives a summary of this study.

2. Link prediction

Link prediction is a network-related problem, which consists of

predicting new connections and detecting hidden links in a net-

work. It is an important task applicable to a wide variety of areas,

such as bibliographic domain, molecule biology, criminal investi-

gations and recommending systems ( Lü & Zhou, 2011; Martínez,

Berzal, & Cubero, 2017; Xiang, 2008 ). The link prediction prob-

lem can be formally deﬁned as follows. Given a snapshot of

a social network at time t , we seek to accurately predict the

edges that will be added to the network at time t +  by deﬁn-

ing a similarity or a probability index ( Liben-Nowell & Kleinberg,

2007; Martínez et al., 2017 ). The existing link prediction meth-

ods can be divided into four categories: Link prediction algo-

rithms based on similarity measures, probabilistic and statisti-

cal methods, algorithmic approaches and preprocessing methods

( Martínez et al., 2017 ). Among these approaches to treat the prob-

lem, the most widespread ones rely on the use of similarity mea-

sures between node pairs ( Lü & Zhou, 2011; Martínez et al., 2017 ).

The similarity measures proposed and evaluated in previous

literature can be broadly categorized into two groups: semantic

and topological measures ( Kaya & Poyraz, 2016 ). Semantic mea-

sures use the nodes’ content to survey similarity. For instance,

in a co-authorship network, the similarity between keywords ex-

tracted from published papers were applied to predict future in-

teraction among the authors ( Xiang, 2008 ). Different from the se-

mantic measures, the topological measures consist of deploying

the network structure to compute the similarity scores (e.g. the

number of common neighbors that two nodes share). Topological

measures are more commonly adopted in the literature since they

are more general and do not require the deﬁnition of rich features

to describe content. In fact, rich features are not always available

and depend on the social network considered.

Several topological measures are proposed in existing literature

and mainly categorized into neighborhood-based and path-based

measures ( Kaya & Poyraz, 2016 ). The neighborhood-based mea-

sures take the nodes’ immediate neighbors into account. In general,

these measures consider that two nodes are more likely to form a

link if their sets of neighbors have a large overlap ( Xiang, 2008 ).

Among the neighborhood-based measures, Salton ( Newman, 2001 ),

Sorenson, HPI, Hub Depressed Index (HDI), Leicht–Holme–Newman

(LHN), Preferential Attachment(PA) ( Barabâsi et al., 2002 ), RA

( Adamic & Adar, 2003 ) and Jaccard’s coeﬃcient ( Martínez et al.,

2017 ) can be mentioned. The path-based measures in turn de-

ﬁne the similarity between nodes by considering the paths be-

tween them. The basic idea is that two nodes are more likely to

form a link if there are more short paths between them. The path-

based measures range from the ordinary path-distance measures to

more sophisticated measures that consider ensembles of different

paths, for instance, the Katz measure ( Soares & Prudêncio, 2013 ).

In comparative terms, the neighborhood-based methods are more

widespread, due to both their computational eﬃciency and great

S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839 3

performance observed in experiments ( Huang, 2006; Liben-Nowell

& Kleinberg, 2007; Murata & Moriyasu, 2008 ). The measures pro-

posed in this study can be categorized as neighborhood-based

ones, since they use information about the connections around

nodes to assign scores to them. But the uniqueness of our al-

gorithm is that it considers not only the direct common neigh-

bors of node pairs but also their indirect common neighbors.

Moreover, the feature of attention allocation of common neigh-

bors, namely the friend count of common neighbors, is taken into

account.

Since a SLPA is not suﬃcient to fully characterize the network,

the combined link prediction algorithms are developed. On the

whole, there are many combined link prediction algorithms which

are built with a high degree of versatility to suit a variety of

networks based on multiple network characteristics. For example,

Fan, Liu, Lu, Xiu, and Chen (2017) proposed a composite link fore-

casting index and took into account the node type effect and node

structure similarity. Wu and Tang (2014) developed a directed so-

cial network link prediction method based on the topic model that

integrated node attributes and network structures for link predic-

tion. Muniz, Goldschmidt, and Choren (2018) used context (node

and link attributes), temporal information (chronological interac-

tion data) and topology information to calculate link weights be-

tween nodes, and then applied weighted similarity function to

identify potential links. Xiao, Li, Wang, Xu, and Liu (2018) studied

the internal and external factors that inﬂuenced the formation of

links and developed a three-level hidden Bayesian link prediction

model by combining the user behaviors and user relationships to

link prediction.

Unlike existing works that focus on algorithm versatility, this

study tends to build the suitable algorithms for speciﬁc circle

structures. Obviously, network structures are diverse and a SLPA

cannot perform well in all networks. Accordingly, this study pro-

poses IAALPA to adaptively select AAIs suitable for the given circle

structure according to the network features of common neighbor

density and attention dispersing. Additionally, the complementary

AAIs of the selected AAI are screen out based on their similarity in

value, direction, and ranking. Subsequently, the selected AAI and

its complementary ones are combined into one composite index to

avoid the low prediction performance caused by the blind combi-

nation of AAIs.

In recent years, many scholars have done valuable works on

friend recommendation in social network based on link predic-

tion methods. Using the recommendation algorithm of data min-

ing, Liu, Yu, Wei, and Ning (2018) proposed an improved algo-

rithm to rank the recommended information with conﬁdence in-

terval, and recommended friends with the same interest for users

in microblog. Yuan, Cheng, Zhang, Liu, and Lu (2015) designed a

social inﬂuence propagation method to mine user’s buddy (friends

who had a great impact on user) and susceptibility (willingness

to be affected), and developed a recommendation model based

on the impact of social relations. He et al. (2017) integrated

link and content information and developed the MapReduce dis-

tributed computing framework to implement the recommendation

of friends in large-scale online community network. Zhu, Lu, and

Ma (2015) mined user interests from short messages and proposed

the neighbor-based friend recommendation to recommend users

with similar interests.

Despite intensive research efforts, there is a distinct lack of

methodology for recommending friends in different social circles

in a social network, which is different from the traditional friend

recommendation due to the problem of network sparseness. In this

study, IAALPA is constructed to recommend the user group in one

product circle to the target user in another product circle, and the

inﬂuence of the friend group is used to affect the purchase deci-

sion of the target user, so as to realize cross-selling.

3. Friend group recommendation for cross-marketing

3.1. Cross-marketing in a brand community

The online brand community is deﬁned as D ( V, E ), where V is

the set of nodes representing the users in the community and E

is the set of edges representing the friend relationships between

users. In a brand community, users will form a circle because they

prefer the same type of product. The set of users in the circle of

product A is deﬁned as V

and the set of users in the circle of

product B is deﬁned as V

. In cross-marketing, if product A is sold

to users in the circle of product B, all users in the product A circle

can be recommended to users in the product B circle as the friend

group, and vice versa.

Usually, the nodes in the same circle are closely connected

(there are more common friends), while the nodes in different

circles are sparsely connected (there are fewer common friends).

Therefore, recommending users in different circles to become

friends often faces the problem of network sparsity, which is char-

acterized by the average degree of network being far less than the

number of nodes ( Lei & Rinaldo, 2015 ). Since the topological char-

acteristics of social networks are all related to average degree, ei-

ther directly or indirectly, sparsity will affect the performance of

the existing SLPAs because these algorithms heavily rely on the

network topology. Consequently, traditional SLPAs cannot guaran-

tee high prediction accuracy of friend recommendation in different

product circles. To address this problem, IAALPA is developed to

fully describe the possibility of connection between user nodes in

different circles and construct a suitable mutually complementary

AAI for the speciﬁc circle structure.

Fig. 1 shows an example of friend group recommendation in

different circles in brand community D, where the initial network

is shown in Fig. 1 (a), the network with predicted links is described

in Fig. 1 (b). In Fig. 1 (a), users that belong to product A circle are

1, 2, 3, and 4, users that belong to product B circle are 5,6, and 7.

Suppose that user 7 is the target customer, the purpose of friend

group recommendation is to enable him to purchase product A.

Through the link prediction method, it is found that user 7 may

establish a friend relationship with users 1, 3, and 4 in product A

circle. Then the online brand managers can recommend users 1, 3,

and 4 to become friends with user 7, as shown in Fig. 1 (b). When

they become friends, the target customer 7 is encouraged to buy

product A using the impact of the friend group of 1, 3, and 4.

3.2. AAI for friend group recommendation

In the triadic closure structure, the fewer friends a common

neighbor of a node pair has, that is, the smaller its degree is,

the more attention the common neighbor assigns to the node

pair ( Backstrom, Bakshy, Kleinberg, Lento, & Rosenn, 2011 ), accord-

ingly, the more likely there is a link between the node pair. Based

on this principle, AAIs are constructed from the point of view

of microstructure (node pairs and their common neighbors), and

macrostructure (node pairs, their common neighbors, and friends

of common neighbors), as a result, the problem of network spar-

sity is overcome and the attention allocation between node pairs

is comprehensively depicted.

3.2.1. AAIs based on microstructure

Seven most commonly used indices, such as Salton, Sorenson,

HPI, HDI, LHN, PA , RA , and resource allocation average (RAA) are

selected ( Lü & Zhou, 2011 ) and adopted as microstructure based

AAIs, which consider the microstructure consisting of node pairs

and their common neighbors. As shown in Table 1 , the larger num-

ber of common neighbors or the less degree of common neigh-

bor indicates the larger scores of attention allocation, vice versa. In

4 S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839

Fig. 1. An example of friend group recommendation.

Table 1

AAIs based on microstructure.

AAI Formula

Salton S

Salton

| Γ (x ) ∩ Γ (y ) |

√

k (x ) ∗k (y )

Sorenson S

Sorenson

2 | Γ (x ) ∩ Γ (y ) |

k (x )+ k (y )

HPI S

HPI

| Γ (x ) ∩ Γ (y ) |

min { k (x ) ,k (y ) }

HDI S

HDI

| Γ (x ) ∩ Γ (y ) |

max { k (x ) ,k (y ) }

LHN S

LHN

| Γ (x ) ∩ Γ (y ) |

k (x ) ∗k (y )

PA S

= k

(x ) ∗k (y )

RA S



z∈ Γ (x ) ∩ Γ (y )

k (z)

RAA S

RAA



z∈ Γ (x ) ∩ Γ (y )

max (k (x ) ,k (y ))

k (z)

Table 1 , Γ (·) represents the neighbor set of a node, k ( ·) denotes

the degree of a node.

3.2.2. AAIs based on macrostructure

Considering the sparseness of local networks formed by nodes

in different circles, we innovatively develop a wider range of AAIs

based on the macrostructure of network, which consider the effect

of indirect common neighbors, i.e., friends of common neighbors.

Speciﬁcally, the attention allocated to common neighbors by their

friends can change the connections of common neighbors and then

indirectly affect the attention that is allocated to target node pairs

by common neighbors. These innovatively proposed AAIs are WA1,

WA2, WA3, and RWA.

(a) WA1

WA1 represents the attention allocated to node pairs by the in-

direct common neighbors. The larger degree of indirect common

neighbor indicates a smaller score of attention allocation, as shown

in formula (1) .

WA 1



Γ (z) ,z∈ Γ (x ) ∩ Γ (y )

k (Γ (z))

(1)

where k (Γ (z)) represents the degree of friend of common neigh-

bor z between node x and y .

(b) WA2

WA2 represents the attention allocated to node pairs by direct

and indirect common neighbors, where the larger clustering coef-

ﬁcient represents the less attention allocation of indirect common

neighbors and the larger degree of direct common neighbors indi-

cates the less attention allocation, as shown in formula (2) .

WA 2



z∈ Γ (x ) ∩ Γ (y )

k (z) ∗ (ρ ∗ c(z) + ϕ ∗ (1 −c(z)))

(2)

where c ( z ) is the clustering coeﬃcient of node z , namely c(z) =

2 ∗ n/ (k ∗ (k − 1)) , n represents the number of links between all k

neighbors of node z , and ρ and ϕ are constant parameters.

Obviously, the larger degree of node indicates the wider atten-

tion dispersion of the node. In WA3, the attention dispersion of the

nodes themselves is combined with the attention dispersion of the

common neighbor nodes, as shown in formula (3) .

WA 3



z∈ Γ (x ) ∩ Γ (y )



k (z) ∗ (1 − c(z))

k (x ) ∗ c(x )

k (y ) ∗ c(y )



(3)

(d) RWA

In fact, the connection of node pairs is often affected by the

joint inﬂuence of the attention allocation of direct and indirect

common neighbors as well as the nodes contained in the node

pairs. Accordingly, a combined index RWA is obtained by inte-

grating AAIs based on microstructure and macrostructure so that

the characteristics of attention distribution among nodes are ad-

equately depicted and the shortcomings of low prediction accu-

racy caused by circle structure sparsity are overcome. Among AAIs

based on microstructure, since RA is highly effective and widely

used, it is adopted in RWA. In AAIs based on macrostructure, be-

cause WA1 is included in c ( z ), we just consider WA2 and WA3 in

RWA. Consequently, RWA is constructed, as shown in formula (4) .

RW A

= α ∗ S

+ β ∗ S

WA 2

+ γ ∗ S

WA 3

(4)

where α, β, and γ are the weight parameters of S

, S

WA 2

, S

WA 3

respectively.

IAALPA

IAALPA considers the relationship between the joint effect of

various features of the network and the prediction performance

of the algorithm. In IAALPA, DT model is developed to select the

appropriate AAI based on the network characteristics related to

common neighbors. Moreover, because a single AAI often makes

overestimation or underestimation and the random combination of

AAIs does not guarantee excellent results every time, SVM is con-

structed to recognize the complementary AAIs to generate an ef-

fective combined prediction model. Fig. 2 shows the structure of

IAALPA.

S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839 5

Fig. 2. The structure of IAALPA.

4.1. Algorithm evaluation and complementary AAI

The area under the curve (AUC) is the most common standard

metric for measuring the accuracy of SLPAs. AUC randomly selects

the connected node pairs and unconnected ones in the test set,

and compares their score values obtained by AAI. In m indepen-

dent comparisons, if the connected node pairs have a higher score

of m 1 times, then the AUC is shown in formula (5) ( Liben-Nowell

& Kleinberg, 2007 ).

AUC =

m 1 + 0 . 5(m − m 1)

(5)

When the network size is large, the AUC value obtained by this

random sampling method can reduce the computation complexity

and improve the eﬃciency. It is obvious that the larger the AUC

value, the higher the accuracy of the algorithm.

The complementary AAI of any index B is: If the combination

of B and candidate AAI has better AUC than that B has, then the

candidate AAI is considered to be the complementary index of B.

4.2. DT for screening AAI

Although AUC is the most common method for evaluating AAI,

the AUC method does not analyze the characteristics of the spe-

ciﬁc circle structure. In practice, it is often necessary to try all AAIs

before ﬁnding the AAI that is most suitable for a given network.

Since DTs are good at solving multi-class problems and can im-

plicitly perform variables screening or features selection while re-

quiring relatively little effort for data preparation ( Mantas, Abellán,

& Castellano, 2016 ), DT is developed to adaptively select the appro-

priate AAIs for the speciﬁc circle structure.

The features of the network according to the idea of atten-

tion allocation of common neighbors in the triadic closure struc-

ture are fully described in the following two dimensions. First of

all, the density of common neighbors is considered since more

common neighbors indicate more attention allocated, such as the

average degree and the average clustering coeﬃcient. Secondly, the

dispersion level of common neighbors’ attention is employed. Be-

cause more short paths connecting common neighbors mean their

more attention dispersion, we consider the short path related fea-

tures, for instance the average shortest path, the average node be-

tweenness, and the average link betweenness.

In DT, the independent variables of the learning sample are the

network characteristic indices, and the dependent variable is the

AAI with the maximum AUC value. Fig. 3 shows an example of

DT. In this study, the DT algorithm is designed based on the idea

of C4.5 algorithm ( Mantas et al., 2016 ), because C4.5 classiﬁcation

tree is the most popular algorithm and has been proved by many

studies to be the simple and practical learning algorithm. Assum-

ing that the network training set is T , in each sample, the network

is labeled by the AAI with the largest AUC. Given that there are

k types of AAIs, a division of T is obtained as { S

, S

, , S

}.The

prior probability of division is P

= | S

| / | T | . Then the information

entropy used for classifying T is Info(T ) = −



i =1

log

The networks in T are divided by feature A (such as the average

clustering coeﬃcient), and the sequence { A

, A

, , A

} is obtained

by arranging the values of feature A in ascending order. Deﬁning

the ith (1 ≤ i ≤ J − 1) partition point as a

= (A

+ A

(i +1)

) / 2 , T is

divided into 2 subsets { T

, T

}, where the value of feature A of

the networks in T

is V ( A, T

) ∈ [ A

, a

], and similarly V ( A, T

) ∈ ( a

]. Corresponding to this kind of division, the information gain

of feature A is Gain (A ) = In f o(T ) −In f o

(T ) , where In fo

(T ) =



i =1

| T

| T |

In fo(T

) . Corresponding to partition point a

, the informa-

tion gain rate of A is shown in formula (6) .

Gain _ Ratio(A, a

) =

Gain (A )

Split(A )

(6)

where Split(A ) = −



i =1

| T

| T |

log

| T

i |

| T |

Subsequently, the information gain rate for each partition point

in sequence { A

, A

, , A

} is calculated according to formula (6) ,

and the partition point with the maximum gain rate is selected as

the best branch threshold of the feature A , namely, T hreshold(A ) =

max

1 ≤i ≤J−1

{ Gain _ Ratio(A, a

) } .

The main procedure of the DT proposed in this study is shown

as follows:

Step1. The features of common friend density and the disper-

sion level of common friends’ attention are calculated, the feature

with the maximum information gain rate is selected as the root

node, and it is branched based on its best branch threshold;

Step 2. For the subset of data corresponding to the branch of

different f eatures, branches of the tree are recursively established

by the same method as Step1, and this procedure is repeated until

all data samples of each branch belong to the same class AAI;

Step 3. The simpliﬁed DT is obtained by pruning the initial DT

to eliminate the inﬂuence of random factors such as noise and iso-

lated nodes;

Step 4. The decision rules are extracted. For the DT generated

by Step 3, the decision rules can be obtained directly, that is, the

best AAI suitable for the circle structure is selected based on the

structural features of the community network.

It should be noted that in the process of training the DT model,

the AUC of AAI for each network in training set is calculated, and

the average AUC value w of each AAI will be used as its weight in

the combined model in Section 4.4 .

4.3. Selecting complementary AAIs based on SVM

Although it is possible to select the most suitable AAI for the

network through DT method, the combination of the selected AAI

and its complementary indices can fully capture the attention al-

location characteristics of nodes in different circles. The sparsity of

the network circle is suﬃciently diverse, and that may lead to the

overﬁtting of the model to identify the mutually complementary

AAIs, namely the model adapts too exactly to the particular circles,

and fails to ﬁt additional circles reliably. SVM shows many unique

advantages in avoiding overﬁtting and solving small sample, non-

linear and high-dimensional pattern recognition problems, so it is

6 S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839

Fig. 3. An example of DT.

adopted to identify AAIs that are complementary to the best AAI

selected by the DT model ( Wang & Xing, 2019 ). Subsequently, the

mutually complementary indices are combined into a composite

one.

In order to fully describe complementary relationship between

indices, the score similarity between AAIs is described from three

aspects: ﬁrstly, the distance between the scores of the two indices,

such as Euclidean distance, standardized Euclidean distance, Man-

hattan distance, and Chebyshev distance; secondly, the similarity

in direction, such as Cosine distance and Pearson correlation coef-

ﬁcient; thirdly, the difference in performance ranking, for example,

Spearman distance.

Given a set of training samples [ I

, M

] , i = 1 , 2 , ···, l, input vec-

tor I

represents the above 7 similarity indices for the scores of

two AAIs in sample i , and M

= 1 if two AAIs are mutually comple-

mentary, else M

= −1 . The main idea of SVM is to map the input

vector to a high dimensional eigenvector space, and to construct

the optimal classiﬁcation surface in the eigenvector space. In order

to improve the eﬃciency of the algorithm, Radial Basis Function

(RBF) K(I

, V ) = exp(−|| V − I

/δ

) is selected as the kernel func-

tion, where V is the input vector and δ is constant. Accordingly, an

optimal classiﬁcation function can be obtained in formula (7) .

f (V ) = sgn { (W · (V )) + b} = sgn





i =1

K(I

, V ) + b



(7)

where a and b are constants, W is a normal vector, which deter-

mines the direction of hyperplane, b is a displacement term, which

indicates the distance between hyperplane and origin. ( V ) repre-

sents the eigenvector after mapping V .

4.4. Composite AAI

In order to comprehensively portray the attention distribution

of common friends of users in different circles, IAALPA designs

a composite mutually complementary AAI. The composite index

model is mainly composed of the best index B selected by DT and

the complementary AAIs of B identiﬁed by SVM (i.e. E

, E

, , E

Aiming at making the AAI with good performance account for a

large proportion in the composite AAI, average AUC value w of

each AAI, which is obtained in training DT model, is applied as

its weight, as mentioned in Section 4.2 . In addition, h excellent

complementary AAIs with larger weights are selected to build the

composite AAI to further improve the accuracy of the algorithm, as

shown in formula (8) .

S = w ∗ (B, E

, E

, ···, E

)

(8)

5. Experiments and results analysis

5.1. Experimental design

971 Ego-net data sets in Twitter ( http://snap.stanford.edu/data/

egonets-TwittQQer.html ) and 132 Ego-net data sets in Google +

( http://snap.stanford.edu/data/ego-Google+.html ) were adopted to

verify the effectiveness of IAALPA. Each Ego-net is a brand com-

munity network, where center node represents the brand company

and users are divided into different product circles. 760 networks

with product circles were selected from Twitter, and 100 networks

with product circles were selected from Google + . Table 2 shows

the mean, minimum and maximum of the statistical indicators of

the selected network samples in Twitter and Google + .

To test the accuracy of the proposed algorithm, the networks

in Twitter and Google + were randomly divided into two parts,

respectively: the training set, which contained 80 percent of net-

works, and the test set, which contained the remaining 20 percent

of networks.

To describe brieﬂy, S1-S25 are used to represent 25 algorithms,

as shown in Tables 3 and 4 . Table 3 gives AAIs without parameters,

and Table 4 gives AAIs with speciﬁc parameter values. These values

were determined according to a large number of experiment re-

sults and those values chosen for the parameters have been proven

to work correctly on a wide range of problems.

In the DT experiments, 25 AAIs were screened based on train-

ing set data, and 15 optimal AAIs were selected, which were S6,

S7, S8, S9, S10, S11, S13, S15, S16, S17, S19, S20, S23, S24, and S25.

For each optimal AAI, train set was used to train SVM, and then its

complementary AAIs were found, so that 15 SVMs were obtained

corresponding to 15 AAIs. Then, the composite mutually comple-

mentary AAI was designed based on formula (8) .

S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839 7

Table 2

Statistical information of network samples in Twitter and Google+.

Statistical indicators Twitter Google +

Minimum Mean Maximum Minimum Mean Maximum

Number of nodes 4 40.35 230 4 222.11 962

Number of edges 4 398.06 5137 8 1.23 56330

Average degree 1.66 13.55 64.50 2 37.89 143.11

Average shortest path 0.44 1.64 3.65 0.34 1.81 3.20

Average node betweenness 1 33.38 330.04 1 205.73 1.15

Average link betweenness 0.44 1.64 3.65 0.34

1.81 3.20

Average clustering coeﬃcient 0.12 0.66 1 0.24 0.66 0.87

Table 3

AAIs without parameters.

AAI abbreviation S1 S2 S3 S4 S5 S6 S7 S8 S12 S13

AAI name Salton Sorenson HPI HDI LHN PA RA WA1 RAA WA3

Table 4

AAIs with parameters.

Algorithm AAI Parameter Algorithm AAI Parameter

S9 WA2 ρ = 1 , φ = 4 S19 RWA ρ = 1 , φ = 1 , α = 4 , β = 1 , γ = 1

S10 WA2

ρ = 1 , φ = 1 S20 RWA ρ = 1 , φ = 1 , α = 1 , β = 4 , γ = 1

S11 WA2

ρ = 4 , φ = 1 S21 RWA ρ = 1 , φ = 1 , α = 1 , β = 1 , γ = 4

S14 RWA

ρ = 1 , φ = 4 , α = 1 , β = 1 , γ = 1 S22 RWA ρ = 4 , φ = 1 , α = 1 , β = 1 , γ = 1

S15 RWA

ρ = 1 , φ = 4 , α = 4 , β = 1 , γ = 1 S23 RWA ρ = 4 , φ = 1 , α = 4 , β = 1 , γ = 1

S16 RWA

ρ = 1 , φ = 4 , α = 1 , β = 4 , γ = 1 S24 RWA ρ = 4 , φ = 1 , α = 1 , β = 4 , γ = 1

S17 RWA

ρ = 1 , φ = 4 , α = 1 , β = 1 , γ = 4 S25 RWA ρ = 4 , φ = 1 , α = 1 , β = 1 , γ = 4

S18 RWA

ρ = 1 , φ = 1 , α = 1 , β = 1 , γ = 1

Table 5

The performance of all algorithms in the Twitter experiments.

Algorithm Average AUC Algorithm Average AUC Algorithm Average AUC

S1 0.78543 S10 0.819112 S19 0.81563

S2 0.78078 S11 0.815698 S20 0.815624

S3 0.737871 S12 0.822598 S21 0.800107

S4 0.767094 S13 0.793013 S22 0.80673

S5 0.622253 S14 0.806359 S23 0.814921

S6 0.775256 S15 0.814763 S24 0.811521

S7 0.819129 S16 0.810858 S25 0.798743

S8 0.799544 S17 0.798534 IAALPAa 0.822624

S9 0.820377 S18

0.809194 IAALPAb 0.8158

Single DT 0.811517 SVM 0.656711

Table 6

The performance of all algorithms in the Google + experiments.

Algorithm Average AUC Algorithm Average AUC Algorithm Average AUC

S1 0.66928 S10 0.84928 S19 0.841492

S2 0.644073 S11 0.845608 S20 0.841461

S3 0.727259 S12 0.882082 S21 0.813375

S4 0.622012 S13 0.803694 S22 0.825926

S5 0.387874 S14 0.824811 S23 0.840444

S6 0.873019 S15 0.840224 S24 0.835089

S7 0.849222 S16 0.832744 S25 0.811044

S8 0.884159 S17 0.810624 IAALPAa 0.892791

S9 0.85096 S18

0.830051 IAALPAb 0.87925

Single DT 0.857105 SVM 0.688149

Since quite a few composite link prediction algorithms were

constructed based on SVM, another composite algorithm was de-

veloped with SVM to evaluate whether IAALPA outperformed the

recently developed other composite algorithms. In the SVM based

composite algorithm, the links between node pairs were predicted

using 8 AAIs in Table 1 . All algorithms were applied in MATLAB

software with default settings.

The average AUCs for Twitter and Google + dataset in 100 ran-

dom experiments are shown in Tables 5 and 6 , respectively, where

IAALPAa represents the combination of the optimal AAI selected

by the DT model and two complementary AAIs with the largest

weights. IAALPAb represents the combination of the optimal AAI

selected by the DT model and its all complementary AAIs.

Figs. 4 and 5 show performance comparison of various AAIs

in the Twitter and Google + experiments, respectively. Figs. 6

and 7 show the performance comparison of single DT and non-

combination AAIs in the Twitter and Google + experiments, respec-

tively.

8 S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839

Fig. 4. Performance comparison of AAIs in the Twitter experiments.

Fig. 5. Performance comparison of AAIs in the Google + experiments.

Fig. 6. Performance comparison of single DT and non-combination AAIs in the Twitter experiments.

Fig. 7. Performance comparison of single DT and non-combination AAIs in the Google + experiments.

5.2. Performance analysis of algorithms

Tables 5 and 6 show that compared with existing outstanding

algorithms, IAALPA has a signiﬁcant improvement effect, that is,

IAALPA proposed in this study can accurately recommend friend-

ships between users in different circles when conducting cross-

marketing activities in online community. It can also be observed

from Tables 5 and 6 that performance of IAALPAa is better than

that of IAALPAb integrating all complementary AAIs, and this indi-

cates that combining complementary AAIs with larger weights is

an effective means to improve the accuracy of IAALPA.

From Figs. 4 and 5 , it can be seen that the accuracy of the 19

algorithms, ranging from S7 to S25, is signiﬁcantly higher than that

of the other 7 AAIs, and these optimal AAIs are all new proposed

except for S7. This shows that focusing on macroscopic network

structure and adopting the principle of attention allocation of com-

mon friends in the triadic closure structure can effectively over-

come the problem of network sparsity in predicting friendships

between users in different circles. It is noted that the macroscopic

network structure consists of node pairs, their common neighbors

and the friends of the common neighbors.

At the same time, the performance of IAALPAa and IAALPAb is

better than that of DT and other algorithms, which shows that the

mechanism to select complementary AAIs by SVM is effective. That

is to say, using the SVM model to identify the complementary AAIs

and integrating them together can deliver better prediction results

than the random combination of AAIs.

It can also be seen from Tables 5 and 6 that IAALPAa is signiﬁ-

cantly better than SVM. These results show that the IAALPA frame-

work proposed in this study is far superior to the SVM framework.

Additionally, from Figs. 6 and 7 , it can be concluded that the

accuracy of DT is higher than that of other non-combination AAIs,

S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839 9

Table 7

Performance comparison under various networks in the Twitter experiments.

Network ID Node count Circle count Node count per circle S7 S12 IAALPAa

200214366 59 12 4.9167 0.8262 0.8454 0.8267

29514951 39 7 5.5714 0.8327 0.8306 0.834

98633794 33 5 6.6 0.8603 0.8563 0.8577

7888452 80 9 8.8889 0.8906 0.8894 0.8862

35012277 20 2 10 0.9361 0.9164 0.9394

356963 114 11 10.3636 0.7532 0.7473 0.7673

15070932 21 2 10.5 0.82 0.8323 0.8283

351092905 55

4 13.75 0.9172 0.9066 0.9139

18886852 70 5 14 0.8917 0.8893 0.8959

16652550 70 5 14 0.8914 0.8894 0.8908

134943586 209 11 19 0.8877 0.886 0.89

Average AUC 0.8643 0.8626 0.8664

Table 8

Performance comparison under various networks in the Google + experiments.

Network ID Node count Circle count Node count per circle S7 S12 IAALPAa

100715738096376666180 46 3 15.3333 0.7308 0.8833 0.9189

104672614700283598130 32 2 16 0.8281 0.9218 0.9275

114122960748905067938 222 6 37 0.8658 0.8752 0.8661

104607825525972194062 80 2 40 0.8645 0.9113 0.9172

113356364521839061717 116 2 58 0.8354 0.9077 0.9102

103503116383846951534 351 5 70.2 0.8269 0.8581 0.8648

107362628080904735459 168 2 84 0.8298 0.8492 0.8424

107203023379915799071 172

2 86 0.8493 0.9305 0.9347

115516333681138986628 305 3 101.6667 0.915 0.9249 0.9238

110971010308065250763 521 4 130.25 0.8637 0.9025 0.9096

101499880233887429402 514 2 257 0.9557 0.9625 0.9631

Average AUC 0.8513 0.9025 0.9071

Fig. 8. Performance comparison in different node density in Twitter.

Fig. 9. Performance comparison in different node density in Google + .

10 S. Li, X. Song and H. Lu et al. / Expert Systems With Applications 139 (2020) 112839

which means the mechanism to select the appropriate AAIs based

on network characteristics is effective.

Finally, paired samples of any two algorithms’ AUC in 100 ex-

periments were collected and Student t -test was adopted to de-

termine whether the means of the two samples were statistically

equal. Consequently, all the determined P -Values are less than the

signiﬁcant level 5%, which shows that there are signiﬁcant differ-

ences among algorithms. These results show that IAALPA can pro-

vide reliable and accurate prediction of friendships between users

in various product circles in the brand community, and at the same

time, it also offers a promising method to recommend friends for

cross-marketing in online brand community.

5.3. Analysis of IAALPA performance under various networks

In order to further analyze the accuracy of friend group rec-

ommendation of IAALPA in different circle densities, in this study,

networks with the number of product circles ranging from a much

smaller value at 2 to a larger value at 12 in the Twitter and ﬂuc-

tuating from a much smaller value at 2 to a larger value at 6 in

Google + data set were selected. In addition to IAALPAa, we sep-

arately selected AAIs with better performance in Tables 5 and 6 ,

namely S7 and S12, to analyze their performance under various

network densities. Tables 7 , 8 , Figs. 8 and 9 give the prediction

accuracy of IAALPA, S7, and S12 in different networks.

It can be seen from Tables 7 and 8 that IAALPA has high rec-

ommendation accuracy in both networks with more product cir-

cles and networks with fewer circles and acquires the best average

AUC 0.8664 in the Twitter experiments and 0.9071 in the Google +

experiments. It can be seen from Figs. 8 and 9 that IAALPAa pro-

duces the superior performance in both circles with large num-

ber of nodes (i.e. node density) and circles with small number of

nodes (i.e. node sparseness). However, S12 achieves the worst per-

formance when the node density is intermediate in Twitter, and

S7 obtains the worst performance when the node density is small

in Google + . These indicate that IAALPA is good at recommending

friend group in both dense and sparse networks.

6. Conclusion

The group of friends has a great inﬂuence on the attitudes, be-

haviors and even feelings of individuals. In this study, the users in

one product circle who are likely to be friends with the target cus-

tomer in another product circle are identiﬁed and recommended

by IAALPA. By friend group’s inﬂuence, cross-marketing of prod-

ucts can be achieved successfully, that is, new target customer will

purchase products preferred by friend group.

To overcome the problem of network sparsity being faced when

predicting the friendships between users in different circles, based

on the principle of attention allocation of common friends in

the triadic closure structure, IAALPA extracts the AAIs based on

not only the microscopic network structure, but also macroscopic

network structure. Consequently, IAALPA can comprehensively de-

scribe the possibility of links between node pairs. Furthermore, in-

stead of using ﬁxed AAI to predict links in various networks, DT

model is developed to select the suitable AAI for the given net-

work based on the network characteristics of the common friend

density and the dispersion level of common friends’ attention. Sub-

sequently, based on the value, direction, and ranking similarities of

AAIs, SVM is designed to identify AAIs which are complementary

to the optimal AAI selected by DT and the ideal composite AAI by

integrating these mutually complementary AAIs is constructed. As

a result, the problems of performance degradation in combination

prediction model, which is caused by randomly integrating SLPAs,

are overcome once and for all.

Experimental results on 971 online communities in the Twit-

ter network and 132 online communities in the Google + network

show that the IAALPA proposed in this study achieves more ac-

curate and reliable link prediction performance. And AAIs con-

structed based on the idea of attention allocation of common

friends in both microscopic and macroscopic network structure are

superior in the harsh scenario where network sparsity is faced

when predicting friendships between users in different circles.

Therefore, IAALPA provides strong support for marketers to use on-

line brand communities to achieve proﬁtable cross-marketing.

In the future, we will propose more link prediction algorithms

and integrate them into the proposed prediction framework to fur-

ther improve prediction accuracy. Furthermore, we will explore the

performance of the framework in different types of network struc-

tures, such as the dynamic network and the network integrating

different social networks.

Declaration of Competing Interest

The authors declare that we have no conﬂicts of interest to this

work.

Credit authorship contribution statement

Shugang Li: Conceptualization, Formal analysis, Funding acqui-

sition, Methodology. Xuewei Song: Validation. Hanyu Lu: Writing

- original draft. Linyi Zeng: Data curation, Investigation. Miaojing

Shi: Writing - review & editing. Fang Liu: Writing - review & edit-

ing.

Acknowlgedgments

This work was supported by the Chinese National Natural Sci-

ence Foundation (no. 71871135 ).

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