# A Predictive Vehicle Ride Sharing Recommendation System for Smart Cities Commuting
## 4 Discussion  
### Discussion on the Results  
The results are based on certain decision of adopted experimental parameters. Such a decision is rational according to common sense for the proposed model and experimental setup. Specifically, the experiments assess the efficiency of prediction accuracy, \(a\), and \(map@N\), based on calculated based on 10-fold cross validation for 1000 iterations run on a user population of \(U=100\) users for \(d=7\) days per week, in a total period of \(w\in[1,8]\) weeks, and dataset size of 2958 instances containing spatial GPS coordinates. It is experimentally found that the optimal value for historic window size is \(m=6\). This value means that the proposed model is able to converge to an efficient value of prediction accuracy, \(a\), assessing the last \(m=6\) GPS locations of the users' movement. A lower value of \(m\) means that the system cannot reach a mature decision since the number of historic locations are few, thus, it is not able to infer a certain user movement pattern. Instead, in case \(m\) has a higher value the system also cannot achieve an efficient value since it is not able to capture certain user movement behavior from different GPS places but rather merges them inelegantly.  
Having settled to a certain value of historic window size \(m=6\) it is observed how prediction accuracy, \(a\), increments through the adopted experimental setup and converges to a certain value of \(a=0.9168\) after \(w=4\) week of the system evaluation. Actually, the prediction accuracy starts from values near to zero since in the beginning of the evaluation phase there is not enough knowledge to assess the system's effectiveness. However, as time passes more data are gathered and forming a much richer knowledge base. This knowledge base follows an incremental way of maturity till the value of \(w=4\) week. After this value there is no need to train the system since it is already intelligent to assess certain user movement. By forcing the system to be trained more than \(w=4\) week might result in the unfortunate state of overfitting which would deteriorate the efficiency of the system.  
Previous experiments evaluated the prediction accuracy, \(a\), of the system with regards to the efficiency that it adopts new instances in order to perform better predictions of the next future location, where the user is going to visit during her daily trip. However, prediction evaluation metrics are not able to assess the effectiveness of the recommendation results, which is the precision of the recommended users proposed by the adopted system. To evaluate the precision of the system, it incorporated the MAP@N, \(map@N\), recommendation evaluation metric. This metric defines the optimal number of recommended users the system returns to the pivot user who invokes the proposed system. MAP@N achieves optimal value \(map@N=~{}0.8234\) for \(N=5\) recommended users, which means that for less recommended users the pivot user cannot find a match to ride share a certain commute, while for more recommended users the pivot user does not variate her behavior. This stability of the pivot user behavior after \(N=5\) recommended users explains why the system converges to a certain \(map@N=~{}0.8234\) value.