Social Recommendation with Strong and Weak Ties

Social Recommendation
Social Recommendation with Strong and Weak Ties
References
Social Recommendation with Strong and Weak
Ties
X. Wang12 W. Lu3 M. Ester2 C. Wang1 C. Chun1
1College of Computer Science and Technology
Zhejiang University
2School of Computing Science
Simon Fraser University
3Department of Computer Science
University of British Columbia
CIKM, 2016
X. Wang, W. Lu, M. Ester, C. Wang, C. Chun Social Recommendation with Strong and Weak Ties

References
Outline
1 Social Recommendation
Social Rating Networks
Rating Prediction
Top-N Item Recommendation
2 Social Recommendation with Strong and Weak Ties
Social Ties in Social Science
Social Ties in Online Social Networks
Social Ties in Social Recommendations

References
Rating Prediction
Outline
Rating Prediction

References
Rating Prediction
Social network, where users are associated with item ratings.
Item ratings can be numeric [1..5]
or Boolean (bookmark url, like article, watch TV series . . .).
Social action: create social relationship, rating action: rate an
item.
Martin Ester: Recommendation in Social Networks, Tutorial at RecSys 2013
13
0.8
0.7

References
Rating Prediction
Matrix Factorization
Rating Prediction
A matrix factorization model [6] assumes the rating matrix R can
be approximated by a multiplication of d-rank factors,
R ≈ PT
Q, (1)
where P ∈ Rd×|U| and Q ∈ Rd×|I|. Normally d is far less than
both |U| and |I|. Thus given a user u and an item i, the rating
Rui of u for i can be approximated by the dot product of user
latent feature vector Pu and item latent feature Qi ,
Rui ≈ PT
u Qi = Pu, Qi , (2)
where Pu ∈ Rd×1 is the uth column of P and Qi ∈ Rd×1 is the ith
column of Q.

References
Rating Prediction
Probabilistic Matrix Factorization
Rating Prediction
Social Networks, Tutorial at RecSys 2013
46
el based approaches
at minimize
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iu
ui ++− λ
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ks, Tutorial at RecSys 2013
47
SoRec
a et al. 2008]
n model
gs and links together.
a binary matrix.
or items.
for users:
or,
er.
or both contexts (rating
actions). Martin Ester: Recommendation in Social Networks, Tutorial at RecSys 2013
50
Social Trust Ensemble
• Graphical model
Martin Ester: Recommendation in Social Networks, Tutorial at RecSys 2013
SocialMF
)((((
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222
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vvu
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u
ui
iuobservedall
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UTUUTU
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∑∑∑
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−−+
++−
β
λ
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(a) PMF[9] (b) SoRec[8] (c) STE[7] (d) SMF[5]
Figure: Graphical Models of Several Social Recommendation Models

References
Rating Prediction
Bayesian Personalized Ranking (BPR)
BPR [10] categorizes items into two groups:
1 Consumed Items. For all u ∈ U, let Cself
u ⊆ I denote the set
of items consumed by u itself.
2 Non-Consumed Items. This category contains the rest of
the items (not consumed by u ): Cnone
u = {i : i ∈ I Cself
u }.
Clearly, for all u ∈ U, Cself
u ∪ Cnone
u = I.

References
Rating Prediction
Intuitively, each user u should prefer the consumed items to
non-consumed items, i.e., the consumed items should be ranked
ahead of the non-consumed ones. Mathematically,
i u j, if i ∈ Cself
u ∧ j ∈ Cnone
u . (3)
The likelihood function can be expressed as:
L(Θ) =
u∈U i∈Cself
u
j∈Cnone
u
Pr[i u j] , (4)
where the probability that consumed items are preferred over
non-consumed items is as follows:
Pr[i u j] = δ(ˆxui − ˆxuj ) =
1
1 + exp(−(ˆxui − ˆxuj ))
=
1
1 + exp(− Pu, Qi + Pu, Qj )
.
(5)

References
Rating Prediction
Social Bayesian Personalized Ranking (SBPR)
SBPR [11] categorizes items into three groups:
u ⊆ I denote the set
of items consumed by u itself.
2 Social-Consumed Items. Any item i ∈ I Cself
u that has
been consumed by at least one of u’s social ties i.e., Tu,
belongs to this category. We denote this set by
Ctie
u = {i ∈ I Cself
u : ∃v ∈ Tu s.t. i ∈ Cself
v }
3 Non-Consumed Items. This category contains the rest of
the items (not consumed by u or any of u’s social ties):

References
Rating Prediction
Social Bayesian Personalized Ranking (SBPR)
With the new categorization, Social-Consumed Items are
assumed to lie between Consumed Items and Non-Consumed
Items for each user u :
i u j, if
i ∈ Cself
u ∧ j ∈ Ctie
u or
i ∈ Ctie
u ∧ j ∈ Cnone
u .
(6)
And the likelihood function is:
L(Θ) =
u∈U i∈Cself
u j∈Ctie
u
Pr[i u j]
j∈Ctie
u k∈Cnone
u
Pr[j u k] . (7)

References
Outline
Rating Prediction

References
Getting a job: A study of contacts and careers
by Granovetter
Statements from Granovetter’s inﬂuential work [3, 2]:
Three diﬀerent types of social ties, measured in terms of how
often they saw the contact person during the period of the job
transition:
Strong : at least once a week
Weak : more than once a year but less than twice a week
Absent : less than once a year

References
by Granovetter
transition:
Weak ties are actually the most important reason for new
information or innovations to spread over social networks.

References
by Granovetter
transition:
Weak ties are actually the most important reason for new
information or innovations to spread over social networks.
Late 1960s and early 1970s — no online social networks.

References
Two Challenges
How to learn the label of each tie (strong or weak) in a given
social network?
Assuming a reliable classiﬁcation algorithm for learning strong
and weak ties, how can we eﬀectively incorporate such
knowledge into existing methods to improve recommendation
accuracy?

References
Solutions
Utilizing features intrinsic to the network topology:
Jaccard’s Coefficient
Adamic-Adar
Katz score
In a recent work [1] on how strong ties and weak ties relate to job
finding on Facebook’s social network, Gee et.al use both mutual
interactions and node similarity (similar to Jaccard’s coefficient) to
measure tie strength and find results to be similar for both kinds of
measures, which provides support for using Jaccard’s coefficient as
tie strength measure.

References
Jaccard’s Coeﬃcient and Thresholding
Jaccard’s Coeﬃcient [4]:
strength(u, v) =def
|Nu ∩ Nv |
|Nu ∪ Nv |
(Jaccard), (8)
where Nu ⊆ U (resp. Nv ⊆ U) denotes the set of ties of u
(resp. v).
For a given social network graph G, let θG ∈ [0, 1) denote the
threshold of tie strength such that
(u, v) is
strong, if strength(u, v) > θG;
weak, if strength(u, v) ≤ θG.
(9)

References
Categorizing items
u ⊆ I denote the set of items
consumed by u itself.
2 Joint-Tie-Consumed (JTC) Items. Any item i ∈ I Cself
u that has been
consumed by at least one strong tie of u and one weak tie of u belongs to
this category. We denote this set by
Cjoint
u = {i ∈ I Cself
u : ∃v ∈ Su s.t. i ∈ Cself
v ∧ ∃w ∈ Wu s.t. i ∈ Cself
w }
3 Strong-Tie-Consumed (STC) Items. If an item i ∈ I Cself
u is
consumed by at least one strong tie of u, but not by u itself or weak ties,
then it belongs to this category. We denote this set by
Cstrong
u = {i ∈ I Cself
u : ∃v ∈ Su s.t. i ∈ Cself
v ∧ w ∈ Wu s.t. i ∈ Cself
w }.
4 Weak-Tie-Consumed (WTC) Items. This category can be similarly
deﬁned:
Cweak
u = {i ∈ I Cself
u : v ∈ Su s.t. i ∈ Cself
v ∧ ∃w ∈ Wu s.t. i ∈ Cself
w }.
5 Non-Consumed Items. This category contains the rest of the items (not
consumed by u or any of u’s ties):
Cnone
u = {(u, i) : x ∈ Su ∪ Wu s.t. i ∈ Cself
x }.

References
TBPR (BPR with Strong and Weak Ties)
TBPR-W (Preferring Weak Ties).
i u j, if



i ∈ Cself
u ∧ j ∈ Cjoint
u or
i ∈ Cjoint
u ∧ j ∈ Cweak
u or
i ∈ Cweak
u ∧ j ∈ Cstrong
u or
i ∈ Cstrong
u ∧ j ∈ Cnone
u .
(10)
TBPR-S (Preferring Strong Ties).
i u j, if



i ∈ Cself
u ∧ j ∈ Cjoint
u or
i ∈ Cjoint
u ∧ j ∈ Cstrong
u or
i ∈ Cstrong
u ∧ j ∈ Cweak
u or
i ∈ Cweak
u ∧ j ∈ Cnone
u .
(11)

References
Likelihood Function
L(Θ) =
u∈U i∈Cself
u j∈C
joint
u
Pr[i u j]
j∈C
joint
u
w∈Cweak
u
Pr[j u w]
w∈Cweak
u s∈C
strong
u
Pr[w u s]
s∈C
strong
u
k∈Cnone
u
Pr[s u k] , (12)
where for instance, the probability that consumed items are
preferred over JTC items can be written as follows.
Pr[i u j] = δ(ˆxui − ˆxuj ) =
1
1 + exp(−(ˆxui − ˆxuj ))
=
1
1 + exp(− Pu, Qi + Pu, Qj )
.
(13)

References
Incorporating the Tie Strength Threshold
Given a threshold θG, the degree of separation between strong ties
and weak ties imposed by this threshold can be quantitatively
measured using the following formula:
g(θG) = (¯ts − θG )(θG − ¯tw ), (14)
where ¯ts is the average strength of all strong ties classiﬁed
according to θG and likewise ¯tw is the average strength of all weak
ties.
A threshold θG that gives a large degree of separation g(θG) is
desirable.

References
Incorporating the Tie Strength Threshold
To incorporate the threshold into the objective function so that our
TBPR model is able to learn it in a principled manner, we add a
coefficient 1/g(θG) into the probability that WTC items are
preferred over STC items. More specifically, we define:
Pr[w u s] = δ
ˆxuw − ˆxus
1 + 1/g(θG)
=
1
1 + exp − ˆxuw −ˆxus
1+1/g(θG )
=
1
1 + exp − Pu,Qw + Pu,Qs
1+1/g(θG )
, (15)
where we use 1 + 1/g(θG) to discount (ˆxuw − ˆxus), the difference
between u’s predicted score for w and s. The intuition is that, if
the current threshold θG does not separate the strong and weak
ties well enough, the likelihood that user prefers w (an WTC item
given the current threshold) to s (an STC items given the current
threshold) should be discounted.

References
Experimental Results
0.01
0.02
0.03
0.04
0.00 0.05 0.10 0.15
Recall
Precision
Method
TBPR−W
TBPR−S
SBPR
BPR
WRMF
MostPop
0.010
0.015
0.025 0.050 0.075 0.100 0.125
Recall
Precision
Method
TBPR−W
TBPR−S
SBPR
BPR
WRMF
MostPop
0.10
0.14
0.18
0.05 0.10 0.15 0.20
Recall
Precision
Method
TBPR−W
TBPR−S
SBPR
BPR
WRMF
MostPop
0.010
0.015
0.020
0.025
0.025 0.050 0.075 0.100 0.125
Recall
Precision
Method
TBPR−W
TBPR−S
SBPR
BPR
WRMF
MostPop
(a) DBLP (b) Ciao (c) Douban (d) Epinions
Figure: Precision@K vs Recall@K on all users, K ranges from 5 to 50
0.00
0.02
0.04
0.06
Pre@5 Rec@5 MAP MRR
Metrics
Values
Method
BPR
SBPR
TBPR−S
TBPR−W
0.00
0.01
0.02
Pre@5 Rec@5 MAP MRR
Metrics
Values
Method
BPR
SBPR
TBPR−S
TBPR−W
0.000
0.025
0.050
0.075
Pre@5 Rec@5 MAP MRR
Metrics
Values
Method
BPR
SBPR
TBPR−S
TBPR−W
0.00
0.01
0.02
0.03
Pre@5 Rec@5 MAP MRR
Metrics
Values
Method
BPR
SBPR
TBPR−S
TBPR−W
(a) DBLP (b) Ciao (c) Douban (d) Epinions
Figure: Performance (Recall, Precision, MAP, MRR) on cold-start users

References
Thank you !

References
L. K. Gee, J. J. Jones, and M. Burke.
Social networks and labor markets: How strong ties relate to
job ﬁnding on facebook’s social network.
2016.
M. S. Granovetter.
The strength of weak ties.
American journal of sociology, pages 1360–1380, 1973.
M. S. Granovetter.
Getting a job: A study of contacts and careers.
University of Chicago Press, 1974.
P. Jaccard.
Distribution de la Flore Alpine: dans le Bassin des dranses et
dans quelques r´egions voisines.
Rouge, 1901.
M. Jamali and M. Ester.

References
A matrix factorization technique with trust propagation for
recommendation in social networks.
In Proceedings of the fourth ACM conference on
Recommender systems, pages 135–142. ACM, 2010.
Y. Koren, R. Bell, and C. Volinsky.
Matrix factorization techniques for recommender systems.
Computer, (8):30–37, 2009.
H. Ma, I. King, and M. R. Lyu.
Learning to recommend with social trust ensemble.
In Proceedings of the 32nd international ACM SIGIR
conference on Research and development in information
retrieval, pages 203–210. ACM, 2009.
H. Ma, H. Yang, M. R. Lyu, and I. King.
SoRec: social recommendation using probabilistic matrix
factorization.

References
In CIKM, pages 931–940, 2008.
A. Mnih and R. Salakhutdinov.
Probabilistic matrix factorization.
In Advances in neural information processing systems, pages
1257–1264, 2007.
S. Rendle, C. Freudenthaler, Z. Gantner, and
L. Schmidt-Thieme.
BPR: Bayesian personalized ranking from implicit feedback.
In UAI, pages 452–461, 2009.
T. Zhao, J. McAuley, and I. King.
Leveraging social connections to improve personalized ranking
for collaborative ﬁltering.
In CIKM, pages 261–270, 2014.

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