## 5 Experimental Study
### Modelling Results
#### 5.2.1 Rheumatoid Arthritis Results
For each algorithm, the most important parameters varied as follows: the number of trees for random forest, the number of neighbors and the weighting function of the importance of neighbors for k-nearest neighbors, pruned or unpruned versions for C4.5 decision trees, and the kernel type for support vector machines. The results obtained are presented in three variants: on the entire training set, to highlight the ability of a model to learn the data, and with a 10-fold cross-validation and the leave-one-out approach, to highlight the generalization capability of the learned model. The first analysis directly considered all the records in the training set. This analysis was the baseline for comparing results. Given that some patients have only one record and others have a larger, variable number of records, the training instances were not all independent. Table 7 presents the results obtained with this approach. The text in bold represents the best result. Next, only the latest, most recent records for each patient were considered. In this way, it is ensured that the training data were independent because each patient had an equal weight in the development of the model. Table 8 presents the results obtained in this case, with kNN method proving the best result. One can see that the results are worse than those in Table 7, especially for the cross-validation procedure, because redundant patient information is removed. Therefore, the dataset was augmented to increase the number of instances in class 1. The new instances resulted from slightly perturbing the values for age and the difference between the beginning and end of therapy, while keeping the value for the class the same. Table 10 presents the results of the precision and recall analysis with the augmented dataset. One can notice much improvement compared to the case of Table 9, especially the random forest model, which succeeds in finding a good balance between the two classes and the final F1 score, combining precision and recall to be the best model compared to the other studied models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classification Method**} & \multirow{2}{*}{**Accuracy on the Training Set**} & \multicolumn{2}{c}{**Accuracy for Cross-Validation**} & \multirow{2}{*}{**Accuracy for Leave-One-Out**} \\ \hline Random forest, & & & \\
100 trees & 100\% & 80\% & 80\% \\ \hline Random forest, & & & \\
1000 trees & 100\% & 81.7391\% & 82.6087\% \\ \hline NN & 100\% & 80\% & 79.1304\% \\ \hline
**kNN**, & & & \\
**k = 20, w = 1/d** & & & \\ \hline kNN, & & & \\ k = 100, w = 1/d & & & \\ \hline C4.5, & & & \\ Pruned & 80\% & 80\% & 80\% \\ \hline C4.5, & & & \\ Unpruned & 92.1739\% & 77.3913\% & 74.7826\% \\ \hline SVM, & & & \\ Puk kernel & 85.2174\% & 78.2609\% & 78.2609\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification results for all records in the dataset. In Table 9, one can see that all methods fail to capture the patterns related to class 1, except for random forest, which manages to handle class 1 to a small extent. Another analysis referred to the evolution of the positive patients, for which the QuantiFERON indicator was initially 0 and, at one point, became 1. For these patients, a new class was included in the model, called \"P\". In this case, we wanted to highlight a symbolic model for this medical situation. Beyond the numerical results, the aim was to provide medical staff with some explanations for the conditions that could change the health of patients in the sense mentioned above. Table 11 shows the results obtained with the NNGE (non-nested generalized exemplars) algorithm, which is based on the instance-based learning paradigm, but determines generalized specimens, i.e., hyper-rectangles in the problem space, consisting of a set of individual instances that belong to the same class and cannot contain instances of a different class. These hyper-rectangles can be interpreted as rules.