# Attention-Survival Score: A Metric to Choose Better Keywords and Improve Visibility of Information
## 3 The Attention-Survival Model
### The Attention-Survival Score  
Let \(K_{j}=\{k_{1},k_{2},\ldots,k_{n}\}\) be the set of initial candidate keywords, as defined by the user for manuscript \(j\).  
When authors search for manuscripts by entering specific inputs, we presume that only one manuscript will be extracted from each search process. Therefore, we denote the article selected as the survivor manuscript.  
Let \(C(k)\) be the community of keyword \(k\). We define community as the set of manuscripts that contains a given keyword. \(C(k)\) defines the set of articles containing the keyword \(k\); thus, they are the ones that will compete with our manuscripts to survive.  
Let \(S(k),k\in K\) be the survival score of a keyword. Given an article that contains the keyword \(k\), \(S(k)\) is the propensity of the keyword to survive, according to our basic model. We assume that our recommendation system is neutral so that the retrieval process is unbiased. In order to help readers understand our model, we did not consider values by relevance, length, cites, impact, or publication date (i.e., basic model). If we apply a biased retrieval process, then we have to redefine \(S(k),k\in K\) according to the bias applied. This situation is explained in Appendix A. Under our basic model supposition, the survival score is defined as follows:  
\[S(k)=\frac{1}{|C(k)|}\]  
We consider that an author can look for either one keyword (e.g., \(k\)) or a set of them (e.g., \(K\)). When looking for multiple keywords at the same time, the community \(C(K)\) is described as the set of manuscripts that contains every keyword in \(K\) simultaneously.  
We can compute the survival score of \(K\) as follows:  
\[S_{\cup}(K)=\frac{\sum S(k_{i})}{|K|}\]  
where \(K=\{k_{1},k_{2},\ldots,k_{n}\}\).  
Another important concept in our work is keyword attention, \(A(k)\), which is the level of interest shown by the community for a certain keyword. As discussed later in the paper, the attention of a word is a function of the number of times that word is used in a query. We derived this value using information provided by Google Trends.  
Similarly, we can compute the attention of a set of keywords as the average value of the attention scores from every keyword in the input set. This is presented as  
\[A_{\cup}(K)=\frac{\sum A(k_{i})}{|K|}\]  
We define the attention-survival score, \(AS\), as the score of a manuscript defined by \(K\) keywords. This score depends on the community and the attention of \(K\):  
\[AS_{\cup}(K)=\alpha\cdot S_{\cup}(K)+(1-\alpha)\cdot A_{\cup}(K)\]  
where \(\alpha\in[0,1],\alpha\in R\) is a weighting factor for \(S_{\cup}(K)\) and \(A_{\cup}(K)\).  
Finally, it is relevant to consider that since survival scores range from 0 to 1, the attention score will need to be normalized.  
Keyword Intersections  
Sometimes, information retrieval systems search for the intersection of each term introduced by the user instead of treating each term separately. In that case, we need to adjust our expressions. Firstly, we introduce the survival of an intersection as follows:  
\[S_{\cap}(K)=\prod S(k_{i})\]  
while the attention of an intersection is defined in the following way:  
\[A_{\cap}(K)=\prod A(k_{i})\]  
Attention scores for each keyword should be computed or extracted from a reliable data source. Finally, we can adapt the attention-survival metric previously defined as follows:  
\[AS_{\cap}(K)=\alpha\cdot S_{\cap}(K)+(1-\alpha)\cdot A_{\cap}(K)\]