Homophily Approach Fast Post Recommendation Microblogging

An Homophily-based Approach for Fast Post
Recommendation in Microblogging Systems
Quentin Grossetti1,2
PhD supervised by C´edric du Mouza2,
Camelia Constantin1 and Nicolas Travers2
1LIP6 - Universit´e Pierre Marie Curie - Paris, France
2CEDRIC Laboratory - CNAM - Paris, France
RecSys 8th - 2018
An Homophily-based Approach for Fast Post Recommendation in Microblogging Systems RecSys 8th - 2018 1 / 25

Introduction
Context
Growth of microblogging plateforms since 2000
700 millions of messages/day in 2017
300 millions of messages/day in 2017
70 millions of publications/day in 2017
70 millions of pictures/day in 2017

Problem
How to connect users to relevant messages on those platforms ?

Problem
How to connect users to relevant messages on those platforms ?
Can we use traditional models ?

State of the art
State of the art
Content-based
Method Pros Cons
Content-based No need of interactions tweets are hard to describe

State of the art
State of the art
Collaborative ﬁltering
Method Pros Cons
Collaborative ﬁltering simple model and good results matrix too large

State of the art
State of the art
Matrix Factorization
Method Pros Cons
Matrix Factorization eﬃcient to ﬁght sparsity matrix growing fastly

State of the art
State of the art
Social systems
Method Pros Cons
Social systems increase user engagement low meaning on edges

State of the art
State of the art
Random walks models (GraphJet)
Method Pros Cons
Social systems increase user engagement low meaning on edges
Random walks models very cheap low memory

Data Analysis
Data Analysis
Dataset
Updated connected component from the graph found in [Kwak (2009)].
No of nodes 2,182,867
No of edges 325,451,980
No of tweets 2,571,173,369
Avg. out-degree 57.8
Avg. in-degree 69.4
max out-degree 348,595
max in-degree 185,401
Diameter 15
Average shortest path 3.7
Table – Twitter dataset characteristics

Data Analysis Retweets
Data Analysis
Retweets
0 1 2-5 6-50 51-200201-500 500+
103
104
105
106
107
108
109
1010
Number of retweets
Numberoftweets
Figure – Distribution of the number of
retweets per tweet
92% of tweets are never
retweeted

Data Analysis Retweets
Data Analysis
Lifespan
10 100 500 1,000
102
103
104
105
106
107
Lifespan (in hours)
Nbofmessages
Figure – Lifespan of a message
< 1hour : 40%
< 3days : 90%

Data Analysis Homophily
Data Analysis
Homophily
Distance Nb of users Perc. Average similarity
1 19,163 05.96% 0.0056
2 121,857 37.91% 0.0021
3 166,633 51.84% 0.0017
4 12,070 03.76% 0.0018
5 297 00.09% 0.0016
6 6 00.01% 0.0019
Impossible 1,396 00.43% 0.0023
Table – Evolution of the similarity score through distance in the network
sim(u, v) =
i∈Lu∩Lv
1
log(1+pop(i))
|Lu ∪ Lv |
(1)

Data Analysis
Homophily
0 5 10 15 20 25
0
0.5
·10−2
Position in the ranking
Averagescore
Distances distribution (%)
Rank Average Distance 1 2 3 4
1 1.65 53.30 28.20 16.65 1.45
2 1.78 43.70 34.50 20.50 1.05
3 1.88 37.99 36.04 24.37 1.35
4 1.97 33.18 36.99 27.68 1.70
5 1.99 32.01 37.93 28.20 1.56
Table – Link beetween distance in the network and position in the Top-N
ranking

Data Analysis
Conclusions
Many conclusions from this analysis :
Freshness is crucial (Messages dies very fast)
⇒ real-time recommendation
Few users have high similarity
⇒ use transitivity
Distance 2 successfully gather important users
⇒ rely on this homophily

Approach Similarity graph
Similarity Graph
Building process
U W
Z
V Y
X
Z1
Z2
Z3
Z4
Figure – Twitter Graph

Similarity Graph
Building process
U Y
V
Z1
sim(u, v)
sim(u, y)
sim(u, z1)
Figure – Similarity Graph

Propagation Model
In a nutshell
p(u, t) =
v∈Fu
p(u ← v, t)
|Fu|
(2)
With Fu the set of users inﬂuential to u and p(u ← v, t) a probability
estimation that u likes t determined by the behavior of the user v.
p(u ← v, t) = p(v, t) × sim(u, v) (3)

Propagation Model
Example
U W
V Y
X
0.3
0.5
0.1
0.5
0.4 0.8
Figure – Propagation example

Approach Propagation Model
Propagation Model
Example
U W
V Y
X t1
0.3
0.5
0.1
0.5
0.4 0.8
Figure – Propagation example - a tweet t1 is published

Propagation Model
Example
U W
V Y
X t1
0.3
0.5
0.1
0.5
0.4 0.8
Figure – Propagation example - X shares/likes t1
p(x, t1) = 1

Propagation Model
Example
U W
V Y
X t1
0.3
0.5
0.1
0.5
0.4 0.8
Figure – Propagation example - Propagation
p(w, t1) = v∈Fw
p(w←v,t)
|Fw| = 0+1×0.5
2 = 0.25

Propagation Model
Example
U W
V Y
X t1
0.3
0.5
0.1
0.5
0.4 0.8
Figure – Propagation example - Propagation
p(u, t1) = 0.25×0.5
2 = 0.0625

Propagation Model
Convergence
Let n be users (u1, u2, ..., un) :



a11pu1 + a12pu2 + .... + a1npun = b1
a21pu1 + a22pu2 + .... + a2npun = b2
... = ...
an1pu1 + an2pu2 + .... + annpun = bn
Could also be written as Ap = b with
A =





u1 u2 · · · un
u1 a11 a12 . . . a1n
u2 a21 a22 . . . a2n
...
...
...
...
...
un an1 an2 . . . ann





p =





p(u1)
p(u2)
...
p(un)





b =





b1
b2
...
bn





Because ∀u, v sim(u, v) ≤ 1, |ajj | ≥
j=i
|aij | for every i, the matrix A is
diagonally dominant.

Propagation Model
Optimizations
Speed up the convergence
Let ∆(u, t1) = p(u, t)k+1 − p(u, t)k
If ∆(u, t1) < β we stop the propagation

Propagation Model
Optimizations
Speed up the convergence
Let ∆(u, t1) = p(u, t)k+1 − p(u, t)k
If ∆(u, t1) < β we stop the propagation
Limitation of popular messages
If p(u, t) < f (t) no need to propagate.
f (t) = 1 − kp
kp+pop(t)p

Experiments Protocol
Experiments
Protocol
34 Millions of messages shared at least twice (130M RT actions)
Split the ranked set 90% - 10%
Try to predict this 10% for 1500 random users
Comparison with
CF : naive collaborative ﬁltering
Bayes : probabilistic model
GraphJet : Twitter used solution

Experiments Results
Experiments
Hits
20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
2
2.5
·104
Number of daily recommendations per user
Numberofhits(×104
)
Bayes
CF
GraphJet
SimGraph
Figure – Hits pour 1500 utilisateurs
Linear growth of CF
Fast growth for
SimGraph
GraphJet stuck around
5000 hits

Experiments Results
Experiments
Hits accuracy
20 40 60 80 100 120 140 160 180 200
101
102
Avg.numberofshares
Bayes
CF
GraphJet
SimGraph
Figure – Hits popularity
Bayes targets close
messages
GraphJet targets popular
messages
CF and SimGraph are
mixing both popular and
close messages

Experiments Results
Experiments
F1 scores
20 40 60 80 100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
·10−2
F1Score(×10−2
)
Bayes
CF
GraphJet
SimGraph
Figure – F1 Scores
Small values
Peak around 20
recommendations

Experiments Results
Experiments
Running time
init. (per user) init total time time (per message) total time (70 cores //) total time
1,149,374 users 13,238,941 Tweets (Trial period) init + recos
Bayes 10ms 0.04h 975ms 51.22h 51.26h
CF 8,583ms 39.40h 0.5ms 0.02h 41.01h
SimGraph 311ms 1.41h 38ms 2.00h 3.41h
init. (per user) init total time time (per user) total time (70 cores //) total time
1,149,374 users 1,149,374 users * 66 days (Trial period) init + recos
GraphJet 0ms 0h 14ms 4.2h 4.2h
Table – Initialization and recommendation time (in ms)

Experiments Updating strategies
Experiments
Updating strategies
How to update SimGraph ?
Split the last 10% in 2
Evaluate hits prediction impact for the remaining 5% :
do nothing
recompute everything
update only weights
crossfold

Experiments
Updating strategies
20 40 60 80 100 120 140 160 180 200
0
1,000
2,000
3,000
4,000
5,000
6,000
Numberofhits
recompute everything
do nothing
crossfold
update weights
Figure – Hits / updating strategies
doing nothing is the
same as updating
weights
crossfold (very cheap)
works very well

Experiments
Convergence property of the SimGraph
Iteration Number of edges
1 4 950 417
2 7 519 031
3 10 836 129
4 11 496 445
5 11 678 747
Table – Number of edges evolution through iterations

Conclusion
Conclusion
Method relying on homophily to ﬁnd nearest neighbors at low cost
Use transitivity to ﬁght high sparsity
Our model outperforms state of the art solutions
Low-cost updates

Conclusion
Thanks for you attention !

Annexes
ANNEXES

Annexes
Annexes
Characteristics
Twitter Network Similarity Graph
No of nodes 2 182 867 1 149 374
No of edges 325,451,980 4 950 417
Avg. similarity score 0.008
Mean out-degree 57.8 5.9
Table – Similarity Graph Characteristics

Annexes
Annexes
Topology
1 2 3 4 5 10 15
100
102
104
106
108
1010
Smallest path
Numberofpaths
Figure – Twitter smallest paths distribution
Small world with average
distance of 3.7

Annexes
Annexes
Lifespan and popularity
100 101 102 103 104
100
101
102
103
104
Avg. lifepan (hours)
Avg.numberofretweets
Figure – Correlation between lifespan and
popularity
Strong correlation up to
103 hours
After a month, the
correlation fades

Annexes
Annexes
Topology
0 10 20
100
101
102
103
104
105
106
107
108
Shortest distance
Numberofpaths
Figure – Smallest path distribution for the
similarity graph
Diameter of 21 for an
average path of 7.5

Annexes
Annexes
Similarities
0 5 10 15 20 25
0
0.5
·10−2
Position dans le classement
Scoremoyen
Figure – Score similarity evolution
Really weak scores
Breaks after the ﬁfth
most similar user

Annexes
Annexes
Hits according to user proﬁles
20 40 60 80 100 120 140 160 180 200
0
200
400
600
800
Numberofhits
Bayes
CF
GraphJet
SimGraph
Figure – 500 small
20 40 60 80 100 120 140 160 180 200
0
1,000
2,000
3,000
4,000
5,000
6,000
Bayes
CF
GraphJet
SimGraph
Figure – 500 medium
20 40 60 80 100 120 140 160 180 200
0
0.5
1
1.5
·104
Bayes
CF
GraphJet
SimGraph
Figure – 500 big users
small < 50 ; medium < 1000 ; big > 1000
Tendencies are very stables no matter the proﬁle of users

Annexes
Annexes
Intersections
20 40 60 80 100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
RatioofhitsincommonwithSimGraph
Bayes
CF
GraphJet
SimGraph
Figure – Parts of hits included in SimGraph
SimGraph merges all the
methods

Annexes
Annexes
Number of recommendations
20 40 60 80 100 120 140 160 180 200
0
20
40
60
80
100
120
140
Numberofactualrecommendations
Bayes
CF
GraphJet
SimGraph
Figure – Recall capacity
CF is less limited
Other methods are
bunched together
Threshold eﬀect for
SimGraph and Bayes

Homophily Approach Fast Post Recommendation Microblogging

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