Social Media Mining: An Introduction

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CUUS2079-08 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 17:22

8.2 Influence 229

Table 8.1. Rank Correlation between Top 10%

of Influentials for Different Measures on Twitter

Measures Correlation Value

In-degree vs. retweets 0.122

In-degree vs. mentions 0.286

Retweets vs. mentions 0.638

value. Contrary to public perception, the number of followers is considered

an inaccurate measure compared to the other two. This is shown in [Cha

et al., 2010], where the authors ranked individuals on Twitter independently

based on these three measures. To see if they are correlated or redundant,

they compared ranks of individuals across three measures using rank cor- SPEARMAN’S

RANK

CORRELATION

relation measures. One such measure is the Spearman’s rank correlation

coefficient,

ρ= 1 −

6

∑n

i= 1 (m

i

1 −m

i

2 )^2

n^3 −n

, (8.30)

wheremi 1 andmi 2 are ranks of individualibased on measuresm 1 andm 2 ,

andnis the total number of users. Spearman’s rank correlation is the Pearson

correlation coefficient for ordinal variables that represent ranks (i.e., takes

values between 1...n);hence, the value is in range [−1,1]. Their findings

suggest that popular users (users with high in-degree) do not necessarily

have high ranks in terms of number of retweets or mentions. This can be

observed in Table8.1, which shows the Spearman’s correlation between the

top 10% influentials for each measure.

8.2.2 Modeling Influence

In influence modeling, our goal is to design models that can explain how

individuals influence one another. Given the nature of social media, it is

safe to assume that influence takes place among connected individuals. At

times, this network is observable (explicit networks), and at others times, it is

unobservable (implicit networks). For instance, in referral networks, where

people refer others to join an online service on social media, the network

of referrals is often observable. In contrast, people are influenced to buy

products, and in most cases, the seller has no information on who referred

the buyer, but does have approximate estimates on the number of products

sold over time. In the observable (explicit) network, we resort to threshold