Social Media Mining: An Introduction

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CUUS2079-07 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:17

198 Information Diffusion in Social Media

50 100 150

t

A(t)

0 200 250 300

0

20

40

60

80

100

Figure 7.7. External-Influence Model forP=100 andα= 0 .01.

Internal-Influence Model

In the internal-influence model, adoption depends on how many have

adopted the innovation in the current time step.^4 In social media there

is internal influence when a group of friends join a site due to peer pressure.

Think of a group of individuals where the likelihood of joining a social net-

working site increases as more group members join the site. The internal

influence model can be described as follows:

dA(t)

dt

=βA(t)[P−A(t)]. (7.23)

PURE Since the diffusion rate in this model depends onβA(t), it is called thepure

IMITATION

MODEL

imitationmodel. The solution to this model is defined as

A(t)=

P

1 +P−A 0 A^0 e−βP(t−t^0 )

, (7.24)

whereA(t=t 0 )=A 0. TheA(t) function is shown in Figure7.8.

Mixed-Influence Model

As discussed, the mixed influence model is situated in between the internal-

and external-influence models. The mixed-influence model is defined as

dA(t)

dt

=(α+βA(t))[P−A(t)]. (7.25)