Learning a Macroscopic Model of Cultural Dynamics

Aris Anagnostopoulos, Mara Sorella

International Conference on Data Mining (ICDM '15) 14-17 November 2015 @ Atlantic City, NJ

selection (homophily)

influence spread through social ties, promotes opinion shifting and homogeneity

the tendency of people to interact with others who are similar to them, may lead to fragmentation.

Human society exhibits many forms of cultural diversity — like the different languages that are spoken, political or religious beliefs and interests. !Since the mid 20th century, sociological studies explain the origin of this diversity by the tension between two forces:

What is culture? "a set of non-genetic information that is

available (i.e., information exists),

accessible (i.e., information can be acquired),

applicable (i.e., information is usable) to a group of people".

[Y.Kashima, How can you capture cultural dynamics? Frontiers in psychology, 2014]

1

Cultural diversity

• abstract the interactions that occur at the microscopic level as relationships between cultural types (groups)

• dynamic systems (discrete/cont. time)

• cultural flow

0.1 0.6

0.250.05

0.2 0.1

0.40.3 macroscopic models

t=0 t=T

Several lines of modeling work have attempted to capture their interplay:

microscopic models

• "The dissemination of culture"

• studies on political opinions[DeGroot 1974]

[Friedkin et al. 1990] [Hegelsmann et al. 2002]

[Yildiz et al. 2010]

![Abrams et al. 2003] [Kempe et al. 2013]

[Axelrod 1997]

2

Modeling Cultural Dynamics

Overview

Macroscopic models are motivated by the large-scale setting:

• full social network and/or full interaction history is unknown

• longitudinal data

time-series of group sizes (e.g., political affiliation, product adoption, cultural tastes)

We extend their models, aiming to perform validation on real datasets, to understand their predictive power on the short term:

• Explicitly characterizing the cultural types in terms of cultural traits

• Proposing the Cultural Hypercube model, allowing for more realistic interaction patterns

3

[Kempe et al. Selection and Influence in Cultural Dynamics EC 2013]

Introduced the problem to the computer science community Proposed suitable generic models, but focused on theoretical (convergence) properties

Our model

• population: set V of n cultural types (groups)

• each type is represented by a vector of m binary features

!• interaction-influence relationships: graph-type structure

global mass vector at time t

Cultural dynamics

4

Socio-cultural system representation000 001

100 101

010 011

111110

the Rock Jazz Country world

m = 3, n=8

each group has a mass at each point in time (possibly 0)

• masses evolve in time due to flow exchanges between groups (interaction-influence patterns)

Selection in interaction

Selection

5

"each person of type u is times more likely to choose an interaction partner of its own type"

Interaction probability depends on the groups' relative masses + inter-group selection

Interaction mass

of a node u: total mass which which u interacts

selection parameter (one for each group)

Rock JazzCountry

Cultural Flows

Consider two adjacent nodes u,v: 000001

011010

100

101

111

110

6

Macroscopic update rule

Flow

incoming flows outgoing flows

: an m-dimensional binary hypercube over VCultural Hypercube

m=3

Cultural Flows

Consider two adjacent nodes u,v: 000001

011010

100

101

111

110

001

011

101

111

6

Macroscopic update rule

Flow

incoming flows outgoing flows

: an m-dimensional binary hypercube over VCultural Hypercube

m=3

Cultural Flows

Consider two adjacent nodes u,v: 000001

011010

100

101

111

110

001

011

101

111

6

Macroscopic update rule

Flow

incoming flows outgoing flows

: an m-dimensional binary hypercube over VCultural Hypercube

m=3

Large-Scale Nonlinear System Identification

The update-rule relates the global mass-vector to the previous through the (unknown) parameters of selection and influence!

real masses observations

Model

Observationsmass of each group, for each timestamp

one for each nodeone for each influence edge

# params: !quadratic(n)!large-scale

Objective: find that best fits the observed data under the model

regularization

model simulation over the whole timespan

(particle swarm)

parameters vector

e.g. 5 features = 1024 params

7

80/20 train-test proportion

The datasets contain complete information about songs (articles, for Wikipedia) listened (modified) by a set of users in a period of time. We consider activity history as a proxy for the evolution of user interests in time.

“Science and Technology”!

“Politics, Society, Religion and Philosophy”!

“History and Events”!

“Arts, Culture, Literature and Music”!

“Geography and Environment”

main topic categories

Last.FM (users’ listening timeline) Wikipedia (users’ editing articles)

Datasets

“Pop/Rock”!

“HipHop/RnB”!

“Electronic”!

“Jazz”!

“World Music”!

main music genres

Which are the group features?

8

Experimental Results (Lastfm)

Time response comparison

NRMSE

9

5 features:

total groups

{average mass}

Conclusions

• To the best of our knowledge we are the first to do an experimental validation of a nontrivial macroscopic model for cultural dynamics on real-world datasets.

• [Abrams et al. 2003] performed some experiments on a two-groups system

!• We discovered that we obtain a good fit on the training data, and, rather surprisingly, (given its

closed-world assumption) that it is able to predict short-term evolution quite closely.

!• These findings indicate that our model is able to characterize to some extent the evolution of

some cultural traits, complementing the long line of work of sociologists, anthropologists, psychologists, and computer scientists who have proposed such models for cultural dynamics.

10

–Giovanni Mela

“Inserisci qui una citazione”.

Learning a Macroscopic Model of Cultural Dynamics

10International Conference on Data Mining (ICDM '15)

14-17 November 2015 @ Atlantic City, NJ

Q & A

From activities to group masses

!We then consider the time series of the observations to fit our models with an 80%-20% train-test proportion.!

Users’ activity history Domain Based Classification

User Model<user, track, time>

user-group assignment

+ aggregation activity score

forgetting(exponential decay)

Observationsgroup masses for

t=0 to Tgenre identification

(social tags)

<user, track, time><user, track, time> Rock :0.8

Elec :0.2

Group influence: microscopic mechanism

{interaction,influence}

Time step t

move100 011Rock Jazz Country 100Rock

110 Rock Jazz

Rock Country101influence parameter (one for each pair of types)

Time step t+1