## 3 User Influence and User Activity
### User Influence  
User influence represents the amount of impact that a certain user has. The amount of impact here can be defined as the degree of influence that causes the change in other users' behaviors. To analyze the level of influence, four different factors were considered. These major factors are shown below in Figure 1, as the number of generated useful information on a certain category, expertness, interest, and compliments that were given by other users. The rationale for these four factors of user influence are as follows. First, an influential user is one who usually provides useful information to others in a specific category. For example, an influential user may write some message on a board and many other users may give many positive votes to the message. Second, an influential user is one who is generally acknowledged as an expert in the social network community with an \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attribute** & **Meaning** & **Example Data** \\ \hline type & type info (ex.user) & “type”: “user” \\ \hline user\_id & assigned id for user & “user\_id”: “4 ducDxDMiRJ[]bc2 CmuziAg” \\ \hline name & name of user & “name”: “[PERSON]” \\ \hline review\_count & Total number of reviews from a certain user & “review\_count”: 19 \\ \hline average\_stars & average stars from a certain user & “average\_stars”: 4.2999999999998 \\ \hline votes & votes from other users & “votes”: [“funny”: 1, “useful”: 0, “cool”: 0] \\ \hline friends & id of user’s friend & “friends”: [“Cg4 CUfhhK4 mXKo1 RYhVow”, \\  & & “sHGpxxBcP59 Tzd69 fnj\_A”.] \\ \hline elite & the year when a certain user got “elite” & “elite”: [2008, 2009, 2010, 2011] \\ \hline  & & \\ \hline  & & \\ \hline  & & \\ \hline  & & \\ \end{tabular}
\end{table} 
Table 1: User object in the Yelp data. exceptional and formal status. An example is being selected as an elite class user or leader of the community. Third, an influential user is one who receives a lot of attention and interest from other users and has large number of followers or subscribers. For example, an influential user may have a lot of fans or subscribers of published content. Fourth, an influential user is one who usually gets positive compliments from others. For instance, the influential user may receive many messages containing many positive comments from other users. The _Influence_ (\(P\), \(C\)) that formulates the user \(P\)'s influence over category \(C\) is measured by the sum of the weights of four different factor variables, as shown in Equation (1). \[Influence(Pn,\ Ci)=\alpha_{1}\beta_{1}\frac{N\Big{(}Reviews_{ positive_{C_{i}}}\Big{)}}{N\Big{(}Reviews_{all_{C_{i}}}\Big{)}}+\alpha_{2}\beta_{2}Wexpert+ \alpha_{3}\beta_{3}Winterest+\ \alpha_{4}\beta_{4}Wcompliments \tag{1}\]  
In this formula, the four components each have two kinds of configurable parameters, \(\alpha\) and \(\beta\), which are multiplied with the components. The \(\alpha\) is a parameter that is used to assign different weights to the components so that the different application requirements can emphasize on specific components. If the same value for \(\alpha\) is given to all four components, the components are considered as of equivalent importance. The \(\beta\) is a parameter that is used to normalize the component values so that the ranges of the component values may be adjusted to be in identical or similar ranges of values. The \(\beta\) for each component could be the inverse value of the maximum of the component value to make the components fit into the range of 0 to 1. For example, if the maximum value of the third component is 1000, then \(\beta_{3}\) may be assigned 0.001. If the \(\beta\) are all assigned as 1, no normalization is done, and the various component ranges will affect the outcome. In this formula, the first component measures the amount of useful information regarding category \(Ci\) that is generated by the user \(Pt\).