Talk at decision@recsys 2012

1. Laboratory
for
Web Science
(LWS)
University of Applied Sciences
Switzerland
http://lws.ffhs.ch
Follow @blattnerma
, Dr. Marcel Blattner

2. Laboratory
for
Web Science
(LWS)
University of Applied Sciences
Switzerland
http://lws.ffhs.ch
Follow @blattnerma
, Dr. Marcel Blattner

3. Recommendation systems in the scope of opinion
formation: a model
Dr. Marcel Blattner, Laboratory for Web Science
University of Applied Sciences Switzerland
Dr. Matus Medo, Physics Department, University of Fribourg
University of Fribourg Switzerland
, Dr. Marcel Blattner

4. Motivation
, Dr. Marcel Blattner

5. Motivation
Real world recommender system data are the
result of complex processes. Social interactions
play a major role.
, Dr. Marcel Blattner

6. Motivation
Real world recommender system data are the
result of complex processes. Social interactions
play a major role.
How can we model those mechanisms to reproduce
observed data (opinions) in recommendation
systems?
, Dr. Marcel Blattner

7. Motivation
Real world recommender system data are the
result of complex processes. Social interactions
play a major role.
How can we model those mechanisms to reproduce
observed data (opinions) in recommendation
systems?
How can we benefit from such a model?
, Dr. Marcel Blattner

8. ts are always ’bound’ on used To highlight various aspects of B-Rank, a to
ty to obtain similar results for The Aim
Fig.(1) is introduced. For simplicity all links be
jects and users are equally weighted wi = 1 8i.
mpared to ZLZ-II, is achieved
result highlights the fact, that
The model should
personality. From real world
objects
users
igher diversity is positive cor-
n general [22]. However, bipartite
generate user
re in off-line user-object data
experiments and
raw robust conclusions.
Z-II algorithm was proposed
reached a comparable perfor- Figure 1: Toy net to illustrate B-Rank. Circles
Rank in the movielens dataset. hyperedges (users), squares are hypervertices
ning parameter l . B-Rank in jects. The votes are illustrated as links betwe
nd therefore easier to imple- and users.
may increase improvements First, some general aspects are discussed, se
e presented basic B-Rank al- shown, how all aspects are well captured by th
eight matrix W . This will be algorithm.
per. Another extension is to Case A: huge audience in common. Intui
pagation (indirect connections objects a and b are similar to each other, when
, Dr. Marcel Blattner

9. ts are always ’bound’ on used To highlight various aspects of B-Rank, a to
ty to obtain similar results for The Aim
Fig.(1) is introduced. For simplicity all links be
jects and users are equally weighted wi = 1 8i.
mpared to ZLZ-II, is achieved
result highlights the fact, that
The model should
personality. From real world
objects
users
igher diversity is positive cor-
n general [22]. However, bipartite
generate user
re in off-line user-object data
experiments and
raw robust conclusions.
Z-II algorithm was proposed
reached a comparable perfor- Figure 1: Toy net to illustrate B-Rank. Circles
Rank in the movielens dataset. hyperedges (users), squares are hypervertices
ning parameter l . B-Rank in jects. The votes are illustrated as links betwe
nd therefore easier to imple- and users.
may increase improvements First, some general aspects are discussed, se
e presented basic B-Rank al- shown, how all aspects are well captured by th
eight matrix W . This will be algorithm.
per. Another extension is to Case A: huge audience in common. Intui
pagation (indirect connections objects a and b are similar to each other, when
, Dr. Marcel Blattner

10. ts are always ’bound’ on used To highlight various aspects of B-Rank, a to
ty to obtain similar results for The Aim
Fig.(1) is introduced. For simplicity all links be
jects and users are equally weighted wi = 1 8i.
mpared to ZLZ-II, is achieved
result highlights the fact, that
The model should
personality. From real world
objects
users
igher diversity is positive cor-
n general [22]. However, bipartite
generate user
re in off-line user-object data
experiments and
raw robust conclusions.
Z-II algorithm was proposed
reached a comparable perfor- Figure 1: Toy net to illustrate B-Rank. Circles
Rank in the movielens dataset. hyperedgesWe trysquares are hypervertices
(users), to understand
ning parameter l . B-Rank in jects. The these data as a as links betwe
votes are illustrated result
nd therefore easier to imple- and users.
of social processes.
may increase improvements First, some general aspects are discussed, se
e presented basic B-Rank al- shown, how all aspects are well captured by th
eight matrix W . This will be algorithm.
per. Another extension is to Case A: huge audience in common. Intui
pagation (indirect connections objects a and b are similar to each other, when
, Dr. Marcel Blattner

11. The Model
Model Assumptions
(I):
Objects generate anticipation
distributions.
(IIA - intrinsic item anticipation)

12. The Model
Model Assumptions
(I):
Objects generate anticipation
distributions.
(IIA - intrinsic item anticipation)
Individuals will invest resources only,
if their anticipation exceed some
threshold.
anticipation
threshold

13. The Model
Model Assumptions
(I):
Objects generate anticipation
distributions.
(IIA - intrinsic item anticipation)
Individuals will invest resources only,
if their anticipation exceed some
Potential threshold.
Adopters Adopters
anticipation
threshold

14. The Model
Model Assumptions
(I):
Objects generate anticipation
distributions.
(IIA - intrinsic item anticipation)
Individuals will invest resources only,
if their anticipation exceed some
Potential threshold.
Adopters Adopters
Potential adopters are able to
become adopters
or
anticipation deniers
threshold

15. The Model
Model Assumptions
(II):
The shift from a potential
adopter to an adopter is caused
by information exchange on a
network with a specific
topology.
Potential
Adopters
(Influence Network)
Adopters
anticipation
threshold
, Dr. Marcel Blattner

16. The Model
Model Assumptions
(II):
The shift from a potential
adopter to an adopter is caused
by information exchange on a
network with a specific
topology.
Potential
Adopters
(Influence Network)
Adopters
anticipation
threshold
adopter
potential adopter
denier
Influence Network , Dr. Marcel Blattner

17. The Model
Model Assumptions
(II):
The shift from a potential
adopter to an adopter is caused
by information exchange on a
network with a specific
topology.
Potential
Adopters
(Influence Network)
Adopters
anticipation
threshold
adopter Possible transitions:
potential adopter
denier
Influence Network , Dr. Marcel Blattner

18. The Model
Model Assumptions
(II):
The shift from a potential
adopter to an adopter is caused
by information exchange on a
network with a specific
topology.
Potential
Adopters
(Influence Network)
Adopters
anticipation
threshold
adopter Possible transitions:
potential adopter
denier
Influence Network , Dr. Marcel Blattner

19. The Model
Model Assumptions
(II):
The shift from a potential
adopter to an adopter is caused
by information exchange on a
network with a specific
topology.
Potential
Adopters
(Influence Network)
Adopters
anticipation
threshold
adopter Possible transitions:
potential adopter
denier
Influence Network , Dr. Marcel Blattner

20. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
threshold
 (1 )
ˆ ⇥j
fij = fij +
kj
, Dr. Marcel Blattner

21. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
threshold
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
Intrinsic
Item
Anticipation
, Dr. Marcel Blattner

22. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
Neighbors, who threshold
already adopted
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
Intrinsic
Item
Anticipation
, Dr. Marcel Blattner

23. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
Neighbors, who threshold
already adopted
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
Intrinsic
Item Total # of
Anticipation neighbors
, Dr. Marcel Blattner

24. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
Neighbors, who threshold
already adopted Trust
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
Intrinsic
Item Total # of
Anticipation neighbors
, Dr. Marcel Blattner

25. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
Shifted Neighbors, who threshold
Item already adopted Trust
Anticipation
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
Intrinsic
Item Total # of
Anticipation neighbors
, Dr. Marcel Blattner

26. The Model
Mathematical
formulation
IIA-Shift Potential
Adopters
Adopters
anticipation
Shifted Neighbors, who threshold
Item already adopted Trust
Anticipation
 (1 )
ˆ ⇥j
fij = fij +
kj
, fij 2 fi 2 N (µi , )
ˆ
fij adopter
Intrinsic
Item Total # of
ˆ
fij < denier
Anticipation neighbors
, Dr. Marcel Blattner

27. The Model
Simulation of Algorithm 1 RecSysMod algorithm. P contains the con-
dynamics for a set figuration parameter for the network. is the Anticipation
Threshold and denotes the trust. O 2 N is the number of
objects to simulate. G(N, E) is the network. N is the set of
of objects nodes and E is the set of edges.
1: procedure RecSysMod I(P, , , O)
2: G(N, E) GenNetwork(P)
3: for all Objects in O do
4: generate distribution fi from N (µi , )
5: for each node j 2 N in G do
6: draw fij from fi
7: if fij < then
8: jstate S
9: else
10: jstate A
11: end if
Contour plot for and ⇢ = ⇥j /kj . Num- 12: end for
the plot quantify the shift in the IAA as 13: repeat
of and ⇢. 14: for all j with jstate = S AND ⇥j > 0 do
h i(1 )
ˆ ⇥
15: fij fij + jkj
uence-Network IN(P) with a fixed network topol- 16: ˆ
if fij < then
law, Erd˝s-R´nyi, or another). P refers to a
o e 17: jstate D
priate parameters for the Influence-Network in 18: else
ke network type, number of nodes, etc.). The 19: jstate A
opology is not a↵ected by the dynamical pro- 20: end if
on propagation) taking place on it. We justify 21: end for
cenario by assuming that the time scale of the 22: until |{j|jstate = S AND ⇥j > 0}| = 0
ange is much longer then the time scale 1 of opin- 23: end for
g in the network. Each node in the Influence- 24: end procedure
responds to an individual. For each individual
n unbiased Intrinsic-Item-Anticipation fij from , Dr. Marcel Blattner
ed probability distribution fi . At each time step,

28. Distribution Landscape
Simulation of
dynamics for a set
of objects
, Dr. Marcel Blattner

29. Figure 4: Fit of the MovieLens attendance dis-
Figure 2: Skewness of the attendance distributions
tribution with trust
threshold Results
= 0.50, critical anticipation
= 0.6, anticipation distribution variance
as a function of trust and the critical anticipation = 0.25, and power law network with exponent
threshold for Erd˝s-R´ny networks with 500 nodes
o e = 2.25, 943 nodes, and 1682 simulated objects.
and 300 simulated items.
Figure 4: Fit of the MovieLens attendance dis- Figure 5: Fit of the Netflix attendance distribution
tribution with trust = 0.50, critical anticipation with trust = 0.52, critical anticipation threshold
Figure 3: Skewness of the attendance distributions
threshold = 0.6, anticipation distribution variance = 0.72, anticipation distribution variance = 0.27,
as a function of trust law network with exponent
= 0.25, and power and the critical anticipation and power law network with exponent = 2.2, 480189
threshold943 for power-law networks with 500 nodes
= 2.25, nodes, and 1682 simulated objects. nodes, and 17770 simulated objects.
and 300 simulated items.
MovieLens Netflix
Ru
Fitting real data We fit real world recommender data ditions for the first movers a0 = f (x)dx, s(0) = 1 a(0),
from MovieLens, Netflix and Lastfm with results reported and d(0) = 0. In the following we use the bra-ket nota-
in Fig. (4), Fig. (5), Fig. (6), Fig. (7), and Tab. (1), re- tion hxi to represent the average of a quantity x. Standard
spectively. The real and simulated distributions are com- methods can now be used to arrive at2
pared using Kullback-Leibler (KL) divergence [29]. We re-
port the mean, median, maximum, and minimum of the (⌧ hki) 1 exp(t/⌧ )
a(t) = 1
. (7)
simulated and real attendance distributions. Trust , antic- (↵ + ) [exp(t/⌧ ) 1] + (⌧ hki a0 )
ipation threshold , and anticipation distribution variance Here ⌧ is the time scale of the propagation which is defined
are reported in figure captions. We also compare the aver- as
, Dr. Marcel Blattner
aged mean degree, maximum degree, minimum degree, and

30. Figure 6: Fit of the Lastfm attendance distribution
with trust = 0.4, critical anticipation threshold = Table 2: Mean, minimum, maximum degree, clus-
Results
0.8, anticipation distribution variance = 0.24, and tering coe cient C, and estimated exponent of the
real Lastfm user friendship network with 1892 nodes real (LFM1) and simulated (LFM2) social network
and 17632 simulated objects. for the Lastfm data set.
D KL
ML 0.0
D KL Med Mean Max Min NF 0.0
ML 0.046 27/26 59/60 583/485 1/1 LFM1 0.0
NF 0.030 561/561 5654/5837 232944/193424 3/16 LFM2 0.0
LFM1 0.05 1/1 5.3/5.2 611/503 1/1
LFM2 0.028 1/1 5.3/5.8 611/547 1/1 Table 1: Si
Netflix, LF
Table 1: Simulation results. ML: Movielens, NF:
Netflix, LFM1: Lastfm with real network, LFM2:
Lastfm wit
Lastfm with simulated network, KL: Kullback- Leibler div
Leibler divergence, Med: Median, Mean, Max: maximal at
maximal attendance (data/simulated), Min: mini- mal attenda
mal attendance (data/simulated).
D hki
D hki kmin kmax C
LFM1 13.
LFM1 13.4 1 119 2.3 0.186
LFM2 12.0 1 118 2.25 0.06 LFM2 12.
Figure 7: Fit of the Lastfm attendance distribution
gure 6: Fit of the Lastfm attendance distribution Figure 8: 6: Fit of the Lastfm attendance distribution
Figure Log-log plot of real (red) and simulated
with anticipation0.6, critical= anticipation Mean, minimum,(blue) social network degree distribution P (k) for =
th trust = 0.4, criticaltrust = threshold Table 2: threshold with trust = 0.4, critical anticipation threshold
maximum degree, clus- Table 2: M
, anticipation distributionanticipation distribution tering coe cient C, and estimatedanticipation distribution variance cumulative
= 0.8, variance = 0.24, and variance = 0.24, the Lastfm data of the Inset: plot of the = 0.24, and
0.8, exponent set. tering coe
l Lastfm user friendship network network with exponent = 2.25, 1892
and power law with 1892 nodes real (LFM1) and simulated (LFM2) social user friendship network with 1892 nodes
degreeLastfm network
real distribution. real (LFM1
d 17632 simulated objects. 17632 simulated objects. the Lastfm data set.
nodes and for and 17632 simulated objects. for the Last
We emphasize that Eq.(10) is valuable in predicting users’
suming a(0) = a0 0, we can neglect the dynamics of d(t)
behavior of a recommender system in an early stage.
to obtain
⌦ ↵ !
2
k
˙
⌦(t) =
hki
1 ⌦(t). 5. DISCUSSION
LastFM
Social influence and our peers are known to form and in-
In addition, Eq. (4) yields fluence many of our opinions and, ultimately, decisions. We
) propose here a simple model which is based on heteroge-
ak (t) = k(1 ak (t))⌦(t)
˙
(9) neous agent expectations, a social network, and a formalized
sk (t) = (↵ + )k(1 ak (t))⌦(t)
˙ social influence mechanism. We analyze the model by nu-
merical simulations and by master equation approach which
Neglecting terms of order a2 (t) and summing the solution
k is particularly suitable to describe the initial phase of the
of ak (t) over P (k), we get a result for the early spreading social “contagion”. The proposed model is able to generate
stage
⇣
gure 7: Fit of the Lastfm attendance distribution Figure ⌘ Log-log plot of a wide range of di↵erent attendance distributions, includ-
8: real (red) and simulated
th trust a(t) = a(0) 1 + ⌧ exp(t/⌧ ) 1 social network degree distribution P in for
= 0.6, critical anticipation threshold (blue) , (10) ing those observed (k) popular real systems (Netflix, Lastfm,
⌦ 2 0.24, ⇤ and Movielens). In addition, we showed that these patterns
= 0.8, anticipation distribution variance ↵= ⇥ ⌦ ↵ the Lastfm data set. Inset: plot of the cumulative
d power law networkthe timescale ⌧ = =k / 1892 k
with with exponent 2.25, ( 2
hki) . The obtained
degree distribution. are emergent Fit of theof the dynamics and not imposed
Figure 7: properties Lastfm attendance distribution Figure 8: L
des and 17632 simulated objects. in the early stage of the opinion spreading
time scale ⌧ valid bywith trust the = 0.6, critical anticipationparticular
topology of underlying social network. Of threshold (blue) socia
, Dr. Marcel Blattner
is clearly dominated by the network heterogeneity. This re- interest 0.8, anticipation distribution variance social
= is the case of Lastfm where the underlying = 0.24, the Lastfm
We emphasize that Eq.(10) is valuable in predicting users’

31. Results
D KL Med Mean Max Min
ML
D 0.046
KL 27/26
Med 59/60
Mean 583/485Max 1/1 Min
NF
ML 0.030 561/561 5654/5837 232944/193424 3/16 1/1
0.046 27/26 59/60 583/485
LFM1
NF 0.05
0.030 1/1
561/561 5.3/5.2
5654/5837 611/503 1/1
232944/193424 3/16
LFM2 0.028 1/1 5.3/5.8 611/547 1/1
LFM1 0.05 1/1 5.3/5.2 611/503 1/1
Table 1: Simulation results. 5.3/5.8Movielens, NF:
LFM2 0.028 1/1 ML: 611/547 1/1
Netflix, LFM1: Lastfm with real network, LFM2:
Lastfm 1: Simulation results. ML: Movielens, NF:
Table with simulated network, KL: Kullback-
Leibler divergence, Med: with real Mean, Max:
Netflix, LFM1: Lastfm Median, network, LFM2:
Lastfm with simulated network, KL: Kullback-
maximal attendance (data/simulated), Min: mini-
Leibler divergence, Med: Median, Mean, Max:
mal attendance (data/simulated).
maximal attendance (data/simulated), Min: mini-
D hki kmin kmax C
mal attendance (data/simulated).
LFM1 13.4 1 119 2.3 0.186
LFM2 12.0 1 118 2.25 0.06
on
D hki kmin kmax C
= Table 2: Mean, minimum, maximum0.186
LFM1 13.4 1 119 2.3 degree, clus-
nd tering coe 12.0
LFM2 1 118 2.25 0.06
cient C, and estimated exponent of the
n
es real (LFM1) and simulated (LFM2) social network
= Table 2: Mean, minimum, maximum degree, clus-
for the Lastfm data set.
d tering coe cient C, and estimated exponent of the
es real (LFM1) and simulated (LFM2) social network
for the Lastfm data set.
, Dr. Marcel Blattner

32. Mathematical analysis
Coupled differential equations Coupled differential equations
for k-compartments (mean field approximation)
9 9
ak (t) = ksk (t)⌦
˙ >
= a(t) = < k > s(t)a(t),
˙ >
=
˙
dk (t) = ↵ksk (t)⌦ ˙
d(t) = ↵ < k > s(t)a(t),
>
; >
;
sk (t) =
˙ (↵ + )ksk (t)⌦ s(t) =
˙ (↵ + ) < k > s(t)a(t)
P
k P (k)(k 1)ak
⌦=
<k>
Z Z
= f (x)dx, ↵= f (x)dx, = (1/k)1
l
, Dr. Marcel Blattner

33. Mathematical analysis - Results
Coupled differential equations Coupled differential equations
for k-compartments (mean field approximation)
⇣ ⌘ (⌧ hki) 1 exp(t/⌧ )
a(t) = a(0) 1 + ⌧ exp(t/⌧ ) 1 a(t) = 1
(↵ + ) [exp(t/⌧ ) 1] + (⌧ hki a0 )
⌦ 2
↵
k 1
⌧= ⌧ = (a0 ↵ hki + hki)
[ (hk 2 i hki)]
, Dr. Marcel Blattner

34. Use cases?
, Dr. Marcel Blattner

35. Use cases?
1. First step for a data generator, useful to test
new methods and algorithms
, Dr. Marcel Blattner

36. Use cases?
1. First step for a data generator, useful to test
new methods and algorithms
2. Especially useful when you have a friendship-network
(like in the LastFM case) to extrapolate
future data topologies.
, Dr. Marcel Blattner

37. Future work
, Dr. Marcel Blattner

38. Future work
Expand the proposed model to generate ratings
within a predefined scale (like 5-star)
, Dr. Marcel Blattner

39. Future work
Expand the proposed model to generate ratings
within a predefined scale (like 5-star)
Work out use cases and show the benefit of
the proposed a model
, Dr. Marcel Blattner

40. ...this is the end my friend...
Questions?
, Dr. Marcel Blattner