Social Media Mining: An Introduction

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

232 Influence and Homophily

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Figure 8.5. Linear Threshold Model (LTM) Simulation. The values attached to nodes

denote thresholdsθi, and the values on the edges represent weightswi,j.

Assuming discrete time steps, we can formulate the size of the influenced

population|P(t)|:

|P(t)|=

∑

u∈P(t)

I(u,t−tu). (8.33)

Figure8.6shows how the model performs. Individualsu,v, andware

activated at time stepstu,tv, andtw, respectively. At timet, the total number

of influenced individuals is a summation of influence functionsIu,Iv, andIw

at time stepst−tu,t−tv, andt−tw, respectively. Our goal is to estimate

I(., .) given activation times and the number of influenced individuals at all

times. A simple approach is to utilize a probability distribution to estimate

I function. For instance, we can employ the power-law distribution to

estimate influence. In this case,I(u,t)=cu(t−tu)−αu, where we estimate