Research work on homophily in social networks. Presented in Cicsyn Conference 2015.

1. An Initial Homophily Indicator to
Reinforce Context-Aware Semantic
Computing
A. Rivero-Rodriguez, P. Pileggi, O. Nykänen
Tampere University of Technology
Tampere, Finland
June 3, 2015
Riga, Latvia
CICSyN 2015: Computational Intelligence,
Communication Systems and Networks

2. This talk describes the benefits of using social
network analysis, in particular homophily, in
context-aware systems
Context SNA/Homophily Indicators
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3. What is context?
Context is any information that can be used to characterize
the situation of an entity, where an entity can be a person,
places, or physical or computational object1.
Context is the sum total of what is known about an individual
along with what he or she is currently experiencing.
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Context

4. Context-aware system can be found
everywhere, even in your phone…
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Context

5. Social Network Analysis
Social Network Analysis (SNA) focuses on the discovery and
evolution of relations among entities (people, organizations,
activities, etc.) [21].
We want to use SNA techniques to understand existing
systems. It can be used for modelling for link prediction etc.
SNA is not solely useful for understanding a system, but for
others tasks such as Prediction, Recommendation, etc. For
example, Amazon’s recommender system.
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SNA

6. Homophily states that connections
between similar people happens at a
higher rate than among dissimilar people
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SNA
Network that exhibits homophily

7. Homophily is ubiquitous in social
systems.
Network of romantic relationships in a highschool exhibits:
inverse homophily according to gender
direct homophily according to age
Two mechanisms underlying homophily
Selection
Social influence (socialization)
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SNA

8. Measuring Homophily in social
network
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Indicator
n number of present edges in G.
p number of possible edges in G.
Proportion of edges in the network
𝑟 =
𝑛
𝑝
Proportion of homophily edges.
𝑟+
=
𝑛+
𝑝+
Proportion of heterophily edges.
𝑟−
=
𝑛−
𝑝−
𝑖𝑓 𝑟+
> 𝑟 → 𝐷𝑖𝑟𝑒𝑐𝑡 𝐻𝑜𝑚𝑜𝑝ℎ𝑖𝑙𝑦
𝑖𝑓 𝑟+ = 𝑟 → 𝑁𝑜 𝐻𝑜𝑚𝑜𝑝ℎ𝑖𝑙𝑦
𝑖𝑓 𝑟+
< 𝑟 → 𝐼𝑛𝑣𝑒𝑟𝑠𝑒𝐻𝑜𝑚𝑜𝑝ℎ𝑖𝑙𝑦

9. Comparison of homophily indicators
Existing affinity indicator
𝒂𝒇𝒇 =
𝒓+
𝒓
Our homophily indicator
𝑯𝒐𝒎 =
𝒓+ − 𝒓−
𝒓+ + 𝒓−
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Indicator
+1
-1
0
Homophily
Heterophily+1
∞
0
Heterophily
Difficult to interpret and utilize
What is aff value for a system with
only homophilic connections?
Easier to interpret.
Homophily and heterophily are
equally important.

10. Experimenting with hom indicators.
Description of the nodobo dataset
Smartphone social interaction data
27 senior high-school students
Data collected for 5 months: Sep’10 – Feb’11 (only considered
105 days with data)
We used the bluetooth data and build a graph G
• Each user is a node in G
• There is a link between two users if they have been in
proximity for more than 60 min a day. (preanalysos)
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Indicator

11. Experiment settings
Homophily conditions: Two users are expected to be
connected if they have more than f friends in common
We have discretize the 105 days of data into W periods of
lenght L, so that
𝑊 ∗ 𝐿 = 105
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Indicator

12. Experiment settings
Homophily conditions: Two users are expected to be
connected if they have more than f friends in common
We have discretize the 105 days of data into W periods of
lenght L, so that
𝑊 ∗ 𝐿 = 105
Several experiments, such as:
• Experiment A: W=15, f=2
• Experiment B: W=5, f=3
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System parameters

13. Results & Observations
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Figure 2. Aff and Hom indicator
values reported for Experiment A.
Figure 3. Aff and Hom indicator
values reported for Experiment B.

14. Conclusions & Future Work
We propose an homophily indicator that overcomes the
weaknesses of others proposed in the literature. It is easier to
understand and interpret, potentially useful in existing
context-aware systems.
Future work includes
• the extension of the indicator to account for time periods,
• the development of model driven solutions based for
context inference based on our Hom indicator.
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Indicator
Alejandro Rivero
alejandro.rivero@tut.fi