# An Empirical Recommendation Framework to Support Location-Based Services +
## 5 Experimental Results and Evaluation
### Evaluation of Our Proposed Mechanism  
Once our proposed system is developed, it is necessary to evaluate the accuracy of the system. For the similarity calculation we also considered the Pearson coefficient given in Formula (3) alongside with the Cosine similarity.  
\[r_{x,y}=\frac{N\sum x_{i}y_{i}-\sum x_{i}\sum y_{i}}{\sqrt{(N\sum x_{i}^{2}-( \sum x_{i})^{2})(N\sum y_{i}^{2}-(\sum y_{i})^{2})}} \tag{3}\]  
To measure the best similarity score we compared this two well-known correlation co-efficient formula and plot it into a graph. Figure 7 represents a graph where we compared each user profile with 50 other users using these two correlation. It can be seen that the cosine coefficient gives more effective scores than the Pearson coefficient to find the top-k similar user.  
To demonstrate the results of our system outcome, the three accuracy measurement parameter is used. The first parameter of the measurement is known as the Precision rate in Formula (4).  
\[precision=\frac{t_{p}}{t_{p}+f_{p}} \tag{4}\]  
Here, the variable \(t_{p}\) defines the number of true suggestions and \(f_{p}\) defines the number of suggestions that are false to the user. A higher precision rate means our results are useful. The next measure rate recall is given below.  
\[recall=\frac{t_{p}}{t_{p}+f_{n}} \tag{5}\]  
Figure 7: Comparison between Cosine and Pearson similarity.  
From Formula (5), \(f_{n}\) defines the number of instances when the system fails to suggest a POI place. Higher recall value means our system outcomes are complete. The last parameter is _F-measure_ and the formula is given here.  
\[\textit{F-measure}=2*\frac{\textit{precision}*\textit{recall}}{\textit{ precision}+\textit{recall}} \tag{6}\]  
_F-measure_ is the weighted Harmonic Mean of _precision_ and _recall_ value. Higher the _F-measure_ value higher the accuracy of the system. We have divided our total dataset equally into five group 20%, 40%, 60%, 80%, and 100%, to measure the accuracy metrics. Then we tested our system into two steps. The first one is for the single user. We selected 50 users and measured the performance metrics. Table 9 represents the _precision_, _recall_, and _F-measure_ value of our system with the increasing number of dataset.  
From the table we can see that _F-measure_ value increases with the amount of data where the average value of _F-measure_, _precision_, and _recall_ is measured as 0.962, 0.969, and 0.955, respectively. Figure 8 shows the accuracy graph for the recommendations.  
Now for the second step of evaluation, we considered 10 different groups and measured all the metrics. Table 10 shows the resultant values where we get almost similar result as for the single user.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quantity of Dataset** & **F-measure** & **Recall** & **Precision** \\ \hline
20\% & 0.973 & 0.968 & 0.979 \\
40\% & 0.970 & 0.965 & 0.976 \\
60\% & 0.965 & 0.959 & 0.971 \\
80\% & 0.957 & 0.948 & 0.966 \\
100\% & 0.942 & 0.933 & 0.952 \\ Avg. & 0.962 & 0.955 & 0.969 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Measure of Accuracy for the single user.  
Figure 8: Performance metrics for the single user.  
Figure 9 shows the accuracy graph on the recommendations for the groups.