1. Preface -People’s daily routines are typically coupled with routines across other temporal scales -E.g., going out on the town with friends on Saturday nights, or spending time with family during the December holidays. -So are animals (daily and seasonal cycle) 2. Purpose: present a methodology-- “eigenbehaviors” to quantify these universal patterns in the behavior of individuals and communities within a social network. -Eigenbehaviors- the principal components of an individual’s behavioral dataset. For full information, please refer to the original paper: http://realitycommons.media.mit.edu/pdfs/eigenbehaviors.pdf

1. Presenter: Jane Hsieh
2018.09.09

2. Introduction

3. Introduction
• Preface
• People’s daily routines are typically coupled with routines across
other temporal scales
• E.g., going out on the town with friends on Saturday nights, or
spending time with family during the December holidays.
• So are animals (daily and seasonal cycle)
• Purpose: present a new methodology-- “eigenbehaviors” to
quantify these universal patterns in the behavior of individuals and
communities within a social network.
• Eigenbehaviors- the principal components of an individual’s behavioral
dataset.

4. Materials and methods

5. Materials
• Data source
• “Reality Mining”
• representing the behavior of 100 subjects at MIT during the 2004–2005 academic year
(Eagle and Pentland 2006).
• Data collection
• collected using 100 Nokia 6600 smart phone
• Information 1: call logs, Bluetooth devices in proximity, cell tower IDs,
application usage, phone status (such as charging and idle).
• Information 2: subjects’ location, proximity, communication, and device
usage behavior.
• This paper focuses on “Temporal location data”

6. Materials
• Sample
• N=100
• Groups of subjects:
1. Sloan business school students
2. Media Lab incoming students
3. Media Lab senior students
4. MIT staff

7. Methods
• Characterize person I by
• B(x,y) : D x 24
• D: total number of
sample days
• D=113 here
• n: # of labels/
behaviors
• {Home, Elsewhere,
Work, No Signal, Off}.
• generated from
conditioned Hidden
Markov Model

8. Methods
• For data analysis
• B -> B’
• B’: matrix of binary values
• D x H
• H=24*n
• Γi: row i of B’
• represents an individual’s
behavior over day i

9. Methods
• Rationale:
• Due to the similar structure in most people’s lives, days are not distributed
randomly though this large space (𝑅 𝐻).
• Thus daily behaviors can be described by a low dimensional ‘behavior space’.
• Behavior space
• A subset of vectors of dimension H that can best characterize the distribution
of behaviors and are referred to as the primary eigenbehaviors.

10. Materials and methods
(+)work/ (-)travel (+)weekend/ (-)weekday In locations with poor phone
reception.• E.g., of Subject 4
Most
likely
Less
likely

11. Results

12. Eigenbehaviors for Individuals
• Average behavior of the individual
• Deviation (Hx1)
• Covariance matrix of Φ𝑖 (H x H)
• By PCA
• Eigenvectors: 𝑢𝑖, 𝑖 = 1, … , 𝐻 (orthonormal)
• Eigenvalues: 𝜆𝑖, 𝑖 = 1, … , 𝐻
• Eigenbehaviors: the vectors with the highest eigenvalues
D
D
D

13. Eigenbehaviors for Individuals
• An individual’s days can be projected with differing levels of accuracy.

14. • Figure 4
• 6 eigenvectors enough
• senior lab students exhibit
more behavioral regularity than
their business school
counterparts
6
.90
.96
Eigenbehaviors for Social Networks

15. Eigenbehaviors for Social Networks
• Applied to develop predictions
of an individual’s subsequent
behavior (12:00~24:00).
• Each subject => a behavior space
using
• 6 primary eigenbehaviors
• weights generated from the first
12 hrs (00:00~12:00) of a subject’s
day.
• Through the linear combination of
these weights and the subject’s
primary eigenbehaviors, a 12-
element vector is created
containing one of three location
states (home, work, elsewhere

16. Eigenbehaviors for Social Networks
• Given particular behaviors
associated with each affiliation
• Similarly, we can
1. identify the eigenbehaviors of
particular communities within the
social network
2. and project individuals onto this
behavior space.
• Can then be used to infer the
individual’s affiliation
• Measured by the Euclidean distance
between the individual and the
principal components of the
community’s behavior space

17. Eigenbehaviors for Social Networks
• Algorithm is the same as before, except
• B: with each row corresponding to the average behavior of a particular
individual in the community.
• -> B’: M x H (M: number of actors/members in the community)
• It generates eigenbehaviors of the community as a whole.

18. Eigenbehaviors for Social Networks
• Mean behaviors for each group, Ψj

19. Results: Eigenbehaviors for Social Networks
• Top 3 eigenbehaviors [𝑢1
𝑗
, 𝑢2
𝑗
, 𝑢3
𝑗
] of each group.
coffee
break
2
courses
lunch
overwork

20. Eigenbehaviors for Social Networks
• When a community’s behavior space is created, it becomes possible
to determine the similarity of the members
• By identifying how accurately their behavior can be approximated by the
community’s primary eigenbehaviors.
• An individuals behavior (Γ) can be projected onto the j community’s
behavior space through the following transformation:
• k=1,…,H;
• Reconstruction weights :
• Given j community has m’ primary eigenbehaviors )
(scalar)

21. Eigenbehaviors for Social Networks
• The vector Ω, can be used to determine which person k the individual
is most similar to in a particular community, j
• Similarity (using Euclidean distance):
• Ω 𝑘
𝑗
: reconstruction weights for the kth person in community j.
• This method can also be applied to data from a single individual to
determine which days are most like the ongoing one.

22. Eigenbehaviors for Social Networks

23. Eigenbehaviors for Social Networks
• Also possible to determine how much an individual fits in with the
community
• 𝜖: as the difference between the individuals projection onto the behavior
space of a community and the individuals original behavior.
• mean adjusted behavior Φ 𝑗 = Γ − Ψ 𝑗 ;
• A

24. Eigenbehaviors for Social Networks
• When determining the affiliation of an individual, there can be 4 possible outcomes
Community Company None
Insider 1 2
Outsider 3 4

25. Eigenbehaviors for Social Networks
• This technique enables us to
aggregate multimodel datasets.
• a community can have >1 behavior
spaces
• each behavioral space is generated
by a set of primary eigenbehaviors.
• e.g, of behavior spaces: Bluetooth,
location, phone usage
• For affiliation classification
• By determining every subject’s
distance to each of behavior
spaces.

26. • Interesting characteristic from
Figure 11
• Probability of friendship ↑ as
distance ↓
Eigenbehaviors for Social Networks

27. Discussion

28. Discussion
1. Using the behavior space generated from an individual’s six primary
eigenbehaviors, we have shown we can generate a 12-h chunk of
data with 79% accuracy.
2. Behavioral data of such magnitude will require fundamentally new
techniques for analysis.
3. Eigendecompositions are useful because they provide a low-
dimensional characterization of complex phenomena
• the first few eigenvectors typically account for a very large percentage of the
overall variance

29. Discussion
4. Eigendecomposition will allow us to characterize an individual
quickly
5. Application:
1) predict individual behavior in the near future
2) match a person to similar individuals.
3) provides us with a representation of the behavior characteristic of a
community as a whole
4) enables us to estimate the probability of a tie within the larger social
network of the population.