Motivation
§ User recommender systems are a key component in any on-line social
2
Given a snapshot of a (social) network, can we infer which new
interactions among its members are likely to occur in the near future?
Nowell & Kleinberg, 2003
networking platform:
§ Assist new users in building their network;
§ Drive engagement and loyalty.
Providing explanations in the context
of user recommendation systems is
still largely underdeveloped !!
Who$to$follow!!"!!Refresh!
Nicola'Barbieri'
Follow%
Francesco'Bonchi'
Follow%
Giuseppe'Manco'
Follow%

Modeling socio-topical relationships
ü Has good friends in Barcelona
ü Does research on web mining
ü Likes blues music
3

4
Nicola'Barbieri'
Follow%
Francesco'Bonchi'
Follow%
Giuseppe'Manco'
Follow%

5
Nicola'Barbieri'
Friend!with!@ax,!@bz,!@bcn_fun.!
Follow%
Francesco'Bonchi'
Authorita5ve!about!#YahooLabs,!!
#ViralMarke>ng,#WebMining.!
Follow%
Giuseppe'Manco'
Authorita5ve!about!#ClassicRock,!#Blues,!!
#Acous>cGuitar.!!
Follow%

6
Nicola'Barbieri'
Follow%
Francesco'Bonchi'
Follow%
Giuseppe'Manco'
#Acous>cGuitar.!!
Follow%
Common identity and common bond theory:
› Identity-based attachment holds when people join a community based on their
interest in a well-defined common topic;
› Bond-based attachment is driven by personal social relations with other specific
individuals.

7
Nicola'Barbieri'
Follow%
Francesco'Bonchi'
Follow%
Giuseppe'Manco'
#Acous>cGuitar.!!
Follow%
Identity Bond
✔
✔
✔
Common identity and common bond theory:
› Identity-based attachment holds when people join a community based on their
interest in a well-defined common topic;
› Bond-based attachment is driven by personal social relations with other specific
individuals.

Latent factor modeling of socio-topical relationships
8
§ Directed attributed-graph
§ {1,2,3,4,5,6,7} user-set
§ Links encode following relationships
§ {a,b,c,d,e,f} features adopted by users
E.g. hashtags, tags, products purchased

9
§ 3 communities:
§ Blue links are bond-based;
§ Green and orange links are identity-based.
§ Bond-based communities tend to have
high density and reciprocal links
§ Identity-based communities tend to
exhibit a clear directionality

10
The role and degree of involvement of each
user u in the community/topic k is governed
by three parameters:
Authority – Susceptibility - Social attitude

11
The role and degree of involvement of each
user u in the community/topic k is governed
by three parameters:
Authority – Susceptibility - Social attitude
Authority Susceptibility Social attitude
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

12
Identity-based communities tend to
have low entropy on the set of
features.
Authority Susceptibility Social attitude Feature Adoption
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
a b c d e f
a b c d e f
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 a b c d e f

WTFW: Generative model
13
1. sample ⇧ ⇠ Dir
⇣
~⇠
⌘
2. For each k 2 {1, . . .,K} sample
#k ⇠ Beta(#0, #1) ⌧k ⇠ Beta(⌧0, ⌧1)
"k ⇠ Dir (~%) ✓Dir (~↵)
⇣
⌘
k ⇠ Ak ⇠ Dir
'
~Sk ⇠ Dir (~⌘)
3. For each link l 2 {l1, . . . , lm} to generate:
(a) Choose k ⇠ Discrete(⇧)
(b) Sample xl ⇠ Bernoulli(#k)
(c) if xl = 1
• sample source u ⇠ Discrete(✓k)
• sample destination v ⇠ Discrete(✓k)
(d) else
• sample source u ⇠ Discrete(Sk)
• sample destination v ⇠ Discrete(Ak)
4. For each feature pair a 2 {a1, · · · , at} to associate
(a) sample k ⇠ Discrete(⇧)
(b) Sample ya ⇠ Bernoulli(⌧k):
• if ya = 1 then ua ⇠ Discrete(Ak)
• otherwise ua ⇠ Discrete(Sk)
(c) sample fa ⇠ Discrete("k)
Figure 1: Generative process for the WTFW model
Following the common identity and common bond theory
Authority
Interest
Social
Attitude
Feature
adoption
$
Sk
K
% &
k Ak
K K
v u
xl zl
!k
K
u f
za ya
#

m t
'
0, 1 !0, !1
k !k
Community
Assignment
K K
Figure 2: The WTFW model in plate notation.
Link labeling Topical role
propensity to adopt certain features in F over others. We
can formalize such a propensity by means of a weight k,f ,
denoting the importance of feature f within k.

Pr(⇥|⌅) represents the product Beta priors. By marginalizing closed form for the joint likelihood The latter is the basis for developing strategy [3, section 11.1.6], where a collapsed Gibbs sampling procedure the matrices Ze,Zf ,X and both the predictive distributions of interest in ⌅. In step consists of a sequential update of the status of the in Ze,Zf ,X and Y. A possible each arc l 2 E and adoption a 2 F chain: Pr(zl = k|Rest),Pr(za = and Pr(ya = 1|Rest)2. By algebraic devise the sampling equations expressed learning scheme is shown in algorithm represent the Gibbs sampling represents the update of the multinomial are collapsed in the derivation of Ak,u =
✓k,if, Conversely, a topical connection l = (u, v) can only be ob-served
distributions, a full Bayesian treatment can be obtained by
Link prediction
if, by picking a latent community k, u has a high
Dirichlet and Beta conjugate priors.
{⇧, !, ⌧ , ✓,A, S} denote the status of the distri-butions
described above. Both the probability of observing
degree of activeness Ak,u and v have a high degree of pas-sive
Pr(⇥|⌅) represents the Beta priors. By marginalizing closed form for the joint likelihood The latter is the basis strategy [3, section 11.1.6], a collapsed Gibbs sampling the matrices Ze,Zf ,X both the predictive of interest step consists of a sequential of the status in Ze,Zf ,X and Y. each arc l 2 E and adoption chain: Pr(zl = k|Rest),Pr(and Pr(ya = 1|Rest)2. By devise the sampling equations learning scheme is shown algorithm represent the Gibbs represents the update of the are collapsed in the derivation Ak,u =
§ The probability of observing link l=(u,v) and the adoption of a feature
a=(u,f) can be expressed as mixtures over the latent community
assignments zl and za:
interest Sk,u, that is
v) and a feature Pr(l|zl assignment = k, xl = 0,⇥) a = (u, = f) Sk,can u · Ak,be v.
ex-pressed
mixtures over the latent community assignments
Note that the likelihood of observing the reciprocal link
u) is equally likely in case of social connection, while it
di↵erent in a topical context, and hence reflect our design
Pr(l|⇥) =
assumption on the directionality of links in social/topical
communities. Each link is finally generated by taking into
account the social/topical mixture of each community:
Pr(l|zl = k,⇥) =!k Pr(l|zl = k, xl = 1,⇥)
14
XK
k=1
⇡k Pr(l|zl = k,⇥) (1)
Pr(a|⇥) =
XK
k=1
⇡k Pr(a|za = k,⇥) (2)
+ (1 − !k)Pr(l|zl = k, xl = 0,⇥)
generation of a link changes depending on the status
cs,s
k,u+cs,k,k,u Pr(F|⇥,Y,Zf) =
Pr(⇥|⌅) represents the product of Beta priors. By marginalizing over closed form for the joint likelihood Pr(The latter is the basis for developing strategy [3, section 11.1.6], where the a collapsed Gibbs sampling procedure the matrices Ze,Zf ,X and Y, and Social variable xl. A social connection l = (u, v) can
observed if, by picking a latent community k, u and
degrees of social attitude ✓k,u and ✓k,v, that is
Pr(l|zl = k, xl = 1,⇥) = ✓k,u · ✓k,v.
a topical connection l = u, v) can only be ob-served
by picking a latent community k, u has a high
activeness Ak,u and v have a high degree of pas-sive
Sk,u, that is
Pr(l|zl = k, xl = 0,⇥) = Sk,u · Ak,v.
the likelihood of observing the reciprocal link
⌧ dak
k (1 − ⌧k)Topical equally likely in case of social connection, while it
Pr(E|⇥,X,Z)Pr(Pr(Ze|⇧)Pr(Zf |⇧)
Pr(X|Ze, !)Pr(Y|Zwhere
cs,s
+cs,Pr(E|⇥,X,Ze) =
k,uk,k,u Pr(F|⇥,Y,Zf) =
Y
u
Y
k
✓
Y
u
Y
k
A
da
k,u
k,u S
ds
k,Pr(Ze|⇧) =
Y
k
⇡ck
k
Pr(Zf |⇧) =
Y
k
⇡dk
k
Pr(X|Ze, !) =
Y
k
!cs
k
(1 − !k)k Y
Pr(Y|Zf , ⌧) =
⌧ d(1 ⌧k)k − k
ak
and affinity Topical affinity
=!k · ✓k,u · ✓k,v + (1 − !k) · Sk,u · Ak,v
Similarly, the probability of observing a node-feature pair
= (u, f) 2 F depends on the degree of authoritative-ness/
susceptibility of the user and by the likelihood of ob-serving
the attribute f within each latent factor k:
Pr(a|za = k,⇥) = (⌧kAk,u + (1 − ⌧k) · Sk,u)#k,f .
Here, the term ⌧kAk+(1−⌧k)Sk defines a multinomial distri-bution
over users, which encodes the joint (both susceptible
and authoritative) attitude of users within that community.
3.1 Learning
k
and cct
✓k,u =
ccdegree of“sociality”!k (or“topicality”, 1−!k) which
measures the likelihood of observing social/topical con-nections
within each community k;
authoritative attitude” ⌧k of observing the adop-tion
an attribute by authoritative subject in k (or,
the “susceptible attitude”, 1 − ⌧k).
whole model relies on multinomial and Bernoulli
distributions, a full Bayesian treatment can be obtained by
Dirichlet and Beta conjugate priors.
{⇧, !, ⌧ , ✓,A, S} denote the status of the distri-butions
described above. Both the probability of observing
v) and a feature assignment a = (u, f) can be ex-pressed
mixtures over the latent community assignments
Pr(l|⇥) =
XK
k=1
⇡k Pr(l|zl = k,⇥) (1)
Pr(a|⇥) =
XK
k=1
⇡k Pr(a|za = k,⇥) (2)
generation of a link changes depending on the status
latent variable xl. A social connection l = (u, v) can
observed if, by picking a latent community k, u and
degrees of social attitude ✓k,u and ✓k,v, that is
Pr(l|zl = k, xl = 1,⇥) = ✓k,u · ✓k,v.
a topical connection l = (u, v) can only be ob-served
With an abuse of notation, we also introduce described in Tab. 1, relative to these matrices.
The key problem in inference is to compute distribution of latent variables given the start by expressing the joint likelihood Pr(E,F,⇥,Ze,Zf ,X,Y|⌅) =
Pr(E|⇥,X,Ze)Pr(Pr(Ze|⇧)Pr(Zf |⇧)
Pr(X|Ze, !)Pr(Y|where
Pr(E|⇥,X,Ze) =
Y
u
Y
k
✓
Y
u
Y
k
A
da
k,u
k,u S
k,Pr(Ze|⇧) =
Y
k
⇡ck
k
Pr(Zf |⇧) =
Y
k
⇡dk
k
Pr(X|Ze, !) =
Y
k
!cs
k
(1 − !k)k Y
Pr(Y|Zf , ⌧) =
k
involvement
Takes into account the socio-topical
tendency of each
community
It depends on the degree of
topical involvement of the user
and by the likelihood of observing
the feature within k
l|· likelihood of observing the reciprocal link
equally likely in case of social connection, while it
topical context, and hence reflect our design
the directionality of links in social/topical
Each link is finally generated by taking into
social/topical mixture of each community:
k,⇥) =!k Pr(l|zl = k, xl = 1,⇥)
+ (1 − !k)Pr(l|zl = k, xl = 0,⇥)
=!k · ✓k,u · ✓k,v + (1 − !k) · Sk,u · Ak,v
probability of observing a node-feature pair
F depends on the degree of authoritative-ness/
attribute f within each latent factor k:
= k,⇥) = (⌧kAk,u + (1 − ⌧k) · Sk,u)#k,f .
⌧kAk+(1−⌧k)Sk defines a multinomial distri-bution
users, which encodes the joint (both susceptible
authoritative) attitude of users within that community.
Learning
a collapsed Gibbs sampling the matrices Ze,both the predictive of interest step consists of a sequential of the status in Ze,Zf ,X and each arc l 2 E and adoption chain: Pr(zl = k|Rest),and Pr(ya = 1|Rest)devise the sampling learning scheme algorithm represent represents the update are collapsed in the Ak,by picking a latent community k, u has a high
degree of activeness Ak,u and v have a high degree of pas-sive
interest Sk,u, that is
Pr(l|zl = k, xl = 0,⇥) = Sk,u · Ak,v.
Note that the likelihood of observing the reciprocal link
v, u) is equally likely in case of social connection, while it
di↵erent in a topical context, and hence reflect our design
assumption on the directionality of links in social/topical
communities. Each link is finally generated by taking into
account the social/topical mixture of each community:
Pr(l|zl = k,⇥) =!k Pr(l|zl = k, xl = 1,⇥)
+ (1 − !k)Pr(l|zl = k, xl = 0,⇥)
=!k · ✓k,u · ✓k,v + (1 − !k) · Sk,u · Ak,v
Similarly, the probability of observing a node-feature pair
= (u, f) 2 F depends on the degree of authoritative-ness/
the attribute f within each latent factor k:
Pr(a|za = k,⇥) = (⌧kAk,u + (1 − ⌧k) · Sk,u)#k,f .
Here, the term ⌧kAk+(1−⌧k)Sk defines a multinomial distri-bution
over users, which encodes the joint (both susceptible
and authoritative) attitude of users within that community.
3.1 Learning
We have described the intuitions behind our joint mod-eling
of links and feature associations and now we focus on
and ct,d
k,u + da
ct
k + dak
+
✓k,u =
cs,s
k,u + cs,k,2cs
k +
P
Sk,u =
ct,s
+ ds
k,u ct
+ cs
+
k k dk,+ )

Link labeling and explanations
A social link u → v (u should follow v) is recommended when u and v are
Σ
Pr( (u→v) is social)∝ π k ⋅δk ⋅θ k,u ⋅θ k,v
k
§ Explanation can be provided as common friends in the communities
that better explain the link.
15
both members of at least one social community.
A topical link u → v is recommended to (u) when (v) is authoritative in a
topic on which (u) has shown interest.
Σ
Pr( (u→v) is topical)∝ π k ⋅ (1−δk ) ⋅ S k,u ⋅ A k,v
k
§ Explanation as a list of features that characterize the authoritativeness
of (v) in (u)’s topics of interest.

Evaluation
model, a recommended
16
§ On both Twitter and Flickr the link creation process can be explained
in terms of interest identity and/or personal social relations.
§ Features:
§ On Twitter: all hashtags and mentions adopted by the user;
§ On Flickr: all the tags assigned by the user.
§ Flickr contains ground-truth for the labeling relationships.
§ Relationships flagged as either “family” or “friends” are labeled as
social, the remaining ones as topical.
L;
explanations for the link.
EVALUATION
assessment of the
The experimen-tation
concerns both link
the latter refers
social or topical.
learning procedure,
performance varying the
sampler.
on the internet. As such, it is likely to produce an underes-timation
of the accuracy in the label prediction task.
In order to keep the experimental setting as close as possi-ble
to the original data (high dimensionality and exceptional
sparsity), no further pre-processing has been performed.
Basic statistics about these two datasets are given in Ta-ble
2. These datasets are characterized by di↵erent prop-erties.
The social graph in Twitter is much more directed
and sparse than in Flickr, while the number of attributes
per user is much higher in Flickr.
Twitter Flickr
Number of nodes 81, 306 80, 000
Number of links 1, 768, 149 14, 036, 407
Number of one-way links 1, 342, 311 9, 604, 945
Number of bidirectional links 425, 838 4, 431, 462
Number of social links - 6, 747, 085
Number of topical links - 7, 289, 322
Avg in-degree 21 175
Avg out-degree 25 181
Number of features 211, 225 819, 201
Number of feature assignments 1, 102, 000 37, 316, 862
Avg. features per user 15 613
Avg. users per feature 5 45
Table 2: Datasets statistics.
Experimental setting. In all the experiments we assume
a partial observation of the network and a complete set of
user features.4 The learning algorithm starts with a ran-dom
assignments to latent variables, it performs a burn-in
phase (burn-in=500) to stabilize the Markov chain, and the

Accuracy on link prediction
17
§ Evaluation setting:
› On Twitter: Monte Carlo 5 Cross-Validation;
› On Flickr: Chronological split.
§ Negative samples: all the 2-hops non-existing links.
§ Competitors:
› Common neighbors and features;
› Adamic-Adar on neighbors and features;
› Joint SVD on the combined adjacency/feature matrices

Flickr: Chronological split.
CNF 0.7025/0.7125/0.7199
AA-NF 0.7301/0.7397/0.7472
the 2-hops non-existing links.
CNF 0.7025/0.7125/0.7199
AA-NF 0.7301/0.7397/0.7472
AA-NF 0.7301/0.7397/0.7472
Accuracy on link prediction
Negative samples: all the 2-hops non-existing links.
Table 3: AUC on link prediction - Twitter
Competitors:
Common neighbors and features;
Adamic-Adar;
Joint SVD
factoriza-tion
Number of latent factors
Method 8 16 32 64 128 256
WTFW 0.6467 0.6488 0.6534 0.6576 0.661 0.677
JSVD 0.598 0.596 0.597 0.609 0.619 0.624
CNF 0.53
AA-NF 0.58
Table 4: AUC on link prediction - Flickr
Method 8 16 32 64 128 256
WTFW 0.7393 0.7548 0.7603 0.6883 0.6618 0.6582
Baseline 0.6545
Split 8 16 32 64 128 256
8 16 32 64 128 256
0.567 0.615 0.667 0.707 0.739 0.792
0.565 0.631 0.680 0.713 0.749 0.798
0.586 0.639 0.692 0.732 0.760 0.812
0.439 0.471 0.525 0.588 0.660 0.768
0.446 0.48 0.537 0.602 0.679 0.744
0.454 0.495 0.545 0.617 0.693 0.763
40 0.567 0.615 0.667 0.707 0.739 0.792
30 0.565 0.631 0.680 0.713 0.749 0.798
20 0.586 0.639 0.692 0.732 0.760 0.812
40 0.439 0.471 0.525 0.588 0.660 0.768
30 0.446 0.48 0.537 0.602 0.679 0.744
20 0.454 0.495 0.545 0.617 0.693 0.763
18
X
f2F(u)F(v)
1
|V(f)|
a matrix factoriza-tion
Joint SVD (JSVD)
computes a low-rank factor-ization
matrix X = [E F] as
K is the rank of the
square roots of the K
Method 8 16 32 64 128 256
WTFW 0.6467 0.6488 0.6534 0.6576 0.661 0.677
JSVD 0.598 0.596 0.597 0.609 0.619 0.624
CNF 0.53
AA-NF 0.58
Method 8 16 32 64 128 WTFW 0.6467 0.6488 0.6534 0.6576 0.661 JSVD 0.598 0.596 0.597 0.609 0.619 CNF 0.53
AA-NF 0.58
Method Method 8 8 16 16 32 32 64 64 128 128 256
WTFW WTFW 0.7393 0.7393 0.7548 0.7548 0.7603 0.7603 0.6883 0.6883 0.6618 0.6618 0.6582
Baseline Baseline 0.6545
0.6545
|N(u) N(v)| + |F(u) Table 5 reports the results for increasing values best results are obtains on a lower number Method Split 8 16 32 64 128 256
WTFW 60/40 0.567 0.615 0.667 0.707 0.739 0.792
Method Split 8 16 32 64 128 256
WTFW 60/40 0.567 0.615 0.667 0.707 0.739 0.792
matrices U and V provide
connectivity of both E
70/30 0.565 0.631 0.680 0.713 0.749 0.798
80/20 0.586 0.639 0.692 0.732 0.760 0.812
70/30 0.565 0.631 0.680 0.713 0.749 0.798
80/20 0.586 0.639 0.692 0.732 0.760 0.812
interpreted as the tendency
Table 5: AUC on link labeling - Flickr.
JSVD 60/40 0.439 0.471 0.525 0.588 0.660 0.768
JSVD 60/40 0.439 0.471 0.525 0.588 0.660 0.768
70/30 0.446 0.48 0.537 0.602 0.679 0.744
80/20 0.454 0.495 0.545 0.617 0.693 0.763
70/30 Table 0.446 5: AUC 0.48 on link 0.537 labeling 0.602 - Flickr.
0.679 0.744
80/20 0.454 0.495 0.545 0.617 0.693 0.763
adopter in F, relative
represents the tendency of
We compare the performance of the WTFW model some popular baseline approaches from the literature, perform well on a range of networks [18, 9]: Common Features (CNF) and Adamic-Adar (AA-NF). CNF local similarity index that produces a score for each (u, v), which is given by the number of common features:
We compare the performance of the WTFW model with
some popular baseline approaches from the literature, which
perform well on a range of networks [18, 9]: Common Neigh-bors/
CNF 0.7025/0.7125/0.7199
AA-NF 0.7301/0.7397/0.7472
Vf,k represents the
The link prediction
areas where the JSVD is skewed clearly outperforms the other methods. evident on the Flickr dataset.
Evaluation on link labeling. We to the task of discriminating between links, thanks to the ground truth that dataset. Again, we measure the accuracy AUC on the prediction, and by comparing a baseline based on common neighbors/link l = (u, v) is deemed social if the neighbors is higher than those of the topical otherwise. Formally:
N(u) Pr(xl = 1|l) = ||N(u) N(v)| Table 5 reports the results for increasing best results are obtains on a lower in particular for K = 32. This CNF 0.7025/0.7125/0.7199
AA-NF 0.7301/0.7397/0.7472
0.7025/0.7125/0.7199
0.7301/0.7397/0.7472
Features (CNF) and Adamic-Adar (AA-NF). CNF local similarity index that produces a score for each Number of latent factors
(u, Number v), which of latent is given factors
by the number of common neigh-bors/
Features (CNF) and Adamic-Adar (AA-NF). CNF is a
Method 8 16 32 64 128 256
Method 8 16 32 64 128 256
features:
features;
JSVD)
factor-ization
as
the
K
provide
E
tendency
relative
of
the
prediction
clearly outperforms the other methods. This evident on the Flickr dataset.
Evaluation on link labeling. We next turn to the task of discriminating between social links, thanks to the ground truth that we have dataset. Again, we measure the accuracy by computing AUC on the prediction, and by comparing the a baseline based on common neighbors/features. link l = (u, v) is deemed social if the weight of neighbors is higher than those of the common topical otherwise. Formally:
Pr(xl = 1|l) = |N(u) N(v)|
0.7025/0.7125/0.7199
0.7301/0.7397/0.7472
AUC on link prediction - Twitter
local similarity index that produces a score for each link
Figure times AA-NF 0.7301/0.7397/0.7472
Method 8 16 32 64 128 256
WTFW 0.6467 0.6488 0.6534 0.6576 0.661 0.677
JSVD 0.598 0.596 0.597 0.609 0.619 0.624
CNF 0.53
AA-NF 0.58
Method 8 16 32 64 128 256
WTFW 0.7393 0.7548 0.7603 0.6883 0.6618 0.6582
Baseline 0.6545
Features (CNF) and Adamic-Adar (AA-NF). CNF is a
Figure Figure times

Link labeling
19
§ Baseline on Link Labeling

Finally, a further assessment of the correct identification
23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
social and topical latent factors can be performed by mea-suring,
51 53 55 57 59 61 63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
assessment of the correct identification
latent factors can be performed by mea-suring,
feature f, the probability of observing it
context, computed as follows:
Anecdotal evidence
47 49 51 53 55 57 59 61 63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
evidence
for a given feature f, the probability of observing it
a social/topical context, computed as follows:
Twitter and Flickr, respectively). analysis in Section 4 clearly denotes model to group users according to common features. However, we plan work a more detailed treatment, as well with other approaches in the literature.
Second, the approach explored in mixture membership topic modeling. = 0.74
= 0.27
TeamFollow-
Back TFB
FollowNGain
fb InstantFol-lowBack
55 57 59 61 63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Community
X
each community.
f) /
⇡k!k!k,f
Feature Prob. Social Feature Prob. Social
birthday X
k
0.69 hdr 0.40
family 0.67 vintage 0.29
wedding 0.69 collage 0.24
⇡k(1 − !k)!k,f .
party 0.67 nude 0.08
puppy 0.69 polaroid 0.28
f) /
k
Table 6 we validate the accuracy of the feature-labeling
the accuracy of the feature-labeling
of tags. The first set contains key-words
with social events, such as family,
6: Social/Topical connotations of selected tags on Flickr.
task on two small sets of tags. The first set contains key-words
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
and wedding. The second set contains keywords specific to
photographic techniques, e.g. hdr and polaroid, which are
likely to generate topical interest in the users. The results
confirm the capability of the model to discriminate between
social and topical features.
Finally, Table 7 summarizes the top keywords detected by
our approach on both datasets in some representative com-munities/
second set contains keywords specific to
Christmas,
techniques, esther,
e.g. hdr and polaroid, which are
passenger,
Birthday,
eros, party,
stories, apple,
topical interest in users. The results
the model to discriminate between
curling,
features.
homemade
summarizes the top keywords detected by
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
drawing, fo-toincatenate,
sketch, street,
painting, ink,
graffiti
Twitter
datasets in some representative com-munities/
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
social communities (large !) have
e.g., family, christmas on Flickr,
characteristic features (e.g., family, christmas on Flickr,
and followback on Twitter) which are clearly social.
TeamFollow-
Back TFB
FollowNGain
Twitter) InstantFol-lowBack
which are clearly social.
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TheGhostofHar-renhal
CONCLUSIONS AND FUTUREWORK
nowplaying
lastfm Tea-mAutoFollow
CONCLUSIONS AND FUTURE WORK
Follow4Follow
ESA
astronomy
Enterprise
Gardenof-
Bones asoiaf
GRRM GOT
This paper introduces WTFW, a novel stochastic gener-ative
WTFW, a novel stochastic gener-ative
factorizes both social connections
The model provides accurate link
500aDay
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AU2011
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Soyuz
and 7: feature 20
Most representative associations. features The model of selected provides communities.
accurate link
prediction and contextualized socio/topical explanations to
Anecdotal evidence
notably associated with social events, such as family,
model that jointly factorizes both social connections
13
Community
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Community
0.0 Figure 9: Distribution of k for each community.
k) =
Pr(Social |f) /
(1 − !k)Ak,u
X
k
⇡k!k!k,f
Pr(Topical |f) /
X
⇡k(1 − !k)!k,f .
!k✓k,u + (1 − !k)(Ak,u + Sk,u)
.
k
measuring the degree of susceptibility and so-ciality
computed likewise. Again, Twitter tends
predominant amount of authorities/followers,
great majority of the communities in Flickr
social users. Finally, Figure 9 shows the
of !k within the communities. As already
Flickr tends to be more clearly social than
Moreover, the distinction between social and topi-cal
is very clear in Flickr with almost all com-munities
probability of being “social” either above
topics: highly social communities (large !) have
0.2. This discriminating attitude is even more
increase the number of latent topics.
further assessment of the correct identification
topical latent factors can be performed by mea-suring,
given feature f, the probability of observing it
topical context, computed as follows:
Social|f) /
X
Community
⇡!!Feature nowplaying
Prob. Social Feature Prob. Social
birthday 0.69 hdr 0.40
wedding 0.69 Follow4Follow
collage 0.24
party 0.67 500aDay
nude 0.08
puppy 0.69 anime 4sqDay
polaroid 0.28
Table 6: Social/Topical connotations of selected tags on Flickr.
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
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BIM
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Civil3D AEC
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science
Discovery
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spottheshut-tle
ESA
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Community
Community
Figure 9: Distribution of k for each community.
=
(1 − !k)Ak,u
!k✓k,u + (1 − !k)(Ak,u + Sk,u)
.
measuring the degree of susceptibility and so-ciality
computed likewise. Again, Twitter tends
predominant amount of authorities/followers,
majority of the communities in Flickr
social users. Finally, Figure 9 shows the
!k within the communities. As already
Flickr tends to be more clearly social than
the distinction between social and topi-cal
very clear in Flickr with almost all com-munities
probability of being “social” either above
This discriminating attitude is even more
increase the number of latent topics.
assessment of the correct identification
latent factors can be performed by mea-suring,
feature f, the probability of observing it
context, computed as follows:
X
Social|f) /
k
⇡k!k!k,f
X
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Follow4Follow
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Enterprise
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
53 55 57 59 61 63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Community
Prob. Social
0.0 0.2 0.4 0.6 Distribution of k for each community.
Sk,u)
.
susceptibility and so-ciality
Twitter tends
authorities/followers,
communities in Flickr
shows the
As already
social than
social and topi-cal
almost all com-munities
either above
is even more
topics.
identification
performed by mea-suring,
observing it
feature-labeling
contains key-words
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Follow4Follow
500aDay
anime 4sqDay
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
AU2011
C3D2013
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Enterprise
Soyuz
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
Bones asoiaf
GRRM GOT
Table 7: Most representative features of selected communities.
Prob. Social
0.0 0.2 0.4 0.6 Distribution of k for each community.
Sk,u)
.
Twitter tends
in Flickr
shows the
As already
social than
and topi-cal
either above
even more
topics.
identification
observing it
feature-labeling
contains key-words
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Follow4Follow
500aDay
anime 4sqDay
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
AU2011
C3D2013
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Enterprise
Soyuz
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
Bones asoiaf
GRRM GOT
the underlying latent nature behind each observed connec-tion.
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
AU2011
C3D2013
ISS science
Discovery
Mars spottheshut-tle
astronomy
Enterprise
Table 7: Most representative features the underlying latent nature behind The result is a decoupling of to reflect the idea that social have high density and reciprocal connections, communities should exhibit clear low entropy over user attributes.
Our work can be extended in several deliberately omitted to quantify the that the model produces. Some on modularity look promising (we measured on Community
Ak,u
Ak,u + Sk,u)
.
Again, Twitter tends
Figure 9 shows the
communities. As already
clearly social than
between social and topi-cal
with almost all com-munities
social” either above
attitude is even more
latent topics.
correct identification
probability of observing it
follows:
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
ISS space
science
Discovery
Mars nasa
spottheshut-tle
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Community
+ Sk,u)
.
Twitter tends
Figure 9 shows the
communities. As already
clearly social than
social and topi-cal
social” either above
attitude is even more
latent topics.
correct identification
of observing it
follows:
Flickr
Topic 1
= 0.98
Topic = 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Community
each community.
Flickr
Topic 1
= 0.98
Topic 5
= 0.98
Topic 18
= 0.17
Topic 22
= 0.14
Christmas,
esther,
passenger,
Birthday,
eros, party,
stories, apple,
curling,
homemade
family, mom,
dog, driving,
vitus, bakery,
woods,
birthday,
friends,
halloween,
shirt,
brothers,
baby
handmade,
warehouse,
vintage,
knitting,
craft, green,
pansies, doll,
sewing
bird, art,
design,
illustration,
sketch, street,
painting, ink,
graffiti
Twitter
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
InstantFol-lowBack
nowplaying
Follow4Follow
500aDay
anime 4sqDay
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
AU2011
C3D2013
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Enterprise
Soyuz
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
Bones asoiaf
GRRM GOT
contextualized socio/topical explanations to
Topic 3
= 0.74
Topic 9
= 0.27
Topic 64
= 0.16
Topic 47
= 0.33
TeamFollow-
Back TFB
FollowNGain
nowplaying
Follow4Follow
500aDay
anime 4sqDay
Autodesk
BIM
AutoCAD
Revit AU2012
Civil3D AEC
adsk sf2012
SWTOR revit
CAD au2011
cloud 3dsMax
AU2011
C3D2013
ISS space
science
Discovery
Mars nasa
spottheshut-tle
ESA
astronomy
Enterprise
Soyuz
Game-ofThrones
FakeWesteros
GoT ooc
SXSWesteros
Gardenof-
Bones asoiaf
GRRM GOT
the underlying latent nature behind each observed connec-tion.
The result is a decoupling of social and topical con-nections
to reflect the idea that social communities should
have high density and reciprocal connections, whereas top-ical
communities should exhibit clear directionality and low entropy over user attributes.
Our work can be extended in several directions. First, we
deliberately omitted to quantify the quality of the commu-nities
that the model produces. Some initial results based
on modularity look promising (we measured 0.55 and 0.37
on Twitter and Flickr, respectively). Also, the qualitative
analysis in Section 4 clearly denotes the capability of the
model to group users according to both connectivity and
common features. However, we plan to devote to future
work a more detailed treatment, as well a thorough compar-ison
with other approaches in the literature.
Second, the approach explored in this paper is rooted on
mixture membership topic modeling. However, other alter-natives

Conclusion and future work
21
§ Joint factorization of both social connections and feature associations in
a Bayesian framework.
§ The model provides accurate link prediction and personalized
explanations to support recommendations of people to follow.
§ Future works:
› Study user perception of explanations;
› Investigate several schemas for generating explanations:
• e.g. diversified selection of features/neighbors to cover all communities that better explain the
suggested connection
› Evaluation in a community detection setting;
› Similar characterization in alternative mathematical framework:
• e.g. Matrix Factorization.

Who to follow and why: link prediction with explanations

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Who to follow and why: link prediction with explanations