# A Cognitive Model for Technology Adoption
## 3 Methodology
\"Mobile broadband subscription per 100 population\" is one of the WEF indicators that could be considered a measure and benchmark for technology acceptance and adoption in different countries. The Pearson correlation coefficient \(r(X,Y)\) is calculated as in Equation (2) where \(X=(x_{1}\), \(x_{2}\),..., \(x_{130})\) is a typical attribute in the set of all 169 attributes of 130 countries, and \(Y=(y_{1}\), \(y_{2}\),..., \(y_{130})\) is the \"Mobile broadband subscription per 100 population\" attribute of all 130 countries. \(\overline{X}\) and \(\overline{Y}\) are the means of the values of the x-variable and y-variable, respectively. \[r(X,Y)=\frac{\sum(x_{i}-\overline{X})(y_{i}-\overline{Y})}{\sqrt{\sum(x_{i}- \overline{X})^{2}\sum(y_{i}-\overline{Y})^{2}}} \tag{2}\]  
After doing this correlation analysis, attributes with an absolute correlation score of less than 0.2 with the Mobile broadband subscription attribute or an absolute correlation of greater than 0.95 with other attributes but Mobile broadband subscription were removed from the list, and finally, 137 attributes left for the countries clustering, scoring, and model training purposes. The correlation score of each attribute is used to weigh the attributes before using them as input to our machine-learning algorithm. A machine learning clustering technique that optimizes the K-means objective function was applied to these weighted features. All 130 countries were grouped into 3 clusters based on their new technology adoption capabilities. These three groups are labeled as (fast, average, and slow) in technology adoption, and the number of countries that fall in each group is 28, 57, and 45, respectively. After this clustering step, a score is calculated for each country in the clusters, which is the sum of all the weighted features. Finally, the countries in each cluster are ranked based on this final score. The list of some countries in each cluster and their scores are presented in Table 3.  
_Discussion._ In the machine learning step, after the attribute selection process based on correlation analysis, the remaining 137 attributes were used as input features for the machine learning algorithm. It is important to note that the correlation score of each attribute was used to weigh the attributes before using them as input to the machine learning algorithm. This means that attributes with a higher correlation score would have a higher weight in the model, and vice versa. The clustering technique used in this study was K-means clustering, which is an unsupervised learning algorithm that partitions data points into K clusters based on their similarity. In this case, K was set to 3 to group countries based on their technology adoption capabilities. K-means clustering was chosen as it is a commonly used technique for clustering analysis and is suitable for large datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Country** & **Adoption Speed** & **Cluster** & **Score** \\ \hline
1 & Singapore & Fast & 0 & 111.6559803 \\
2 & Switzerland & Fast & 0 & 104.4918966 \\
3 & United States & Fast & 0 & 101.4976655 \\
4 & Netherlands & Fast & 0 & 96.44233507 \\
5 & Finland & Fast & 0 & 95.98025303 \\
6 & Spain & Average & 1 & 43.82418314 \\
7 & Portugal & Average & 1 & 40.71621859 \\
8 & Slovenia & Average & 1 & 37.04722678 \\
9 & Czech Republic & Average & 1 & 36.92720008 \\
10 & Lithuania & Average & 1 & 35.76320354 \\
11 & Botswana & Slow & 2 & \(-\)17.68696894 \\
12 & Kenya & Slow & 2 & \(-\)19.30727184 \\
13 & Rwanda & Slow & 2 & \(-\)19.33175194 \\
14 & Tajikistan & Slow & 2 & \(-\)25.03134229 \\
15 & Ghana & Slow & 2 & \(-\)25.41625821 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: List of some countries, their clusters, and scores. To optimize the K-means objective function, an appropriate value of K was chosen that resulted in the most meaningful and interpretable clusters.