## 5 Supervised Classification of Clients
### Execution of State-of-the-Art Algorithms  
For this, we tested several state-of-the-art classifiers able to deal with mixed an incomplete data. The classifiers were Nearest Neighbor (NN) [58], Naive Bayes (NB) [59], C4.5 [60], Repeated Incremental Pruning to Produce Error Reduction (RIPPER) [61], Voting Algorithm (ALVOT) [62], Assisted Classification for Imbalance Data (ACID) [63], Extended Gamma (EG) [64; 65] and Naive Associative Classifier (NAC) [8; 66]. The parameter values of the compared classifiers are given at Table 2 and were selected according to the suggestions founded in the corresponding papers. We used Knowledge Extraction based on Evolutionary Learning (KEEL) environment [67] to test the C4.5 and RIPPER classifiers, and EPIC environment [68; 69] for the remaining ones. Figure 4: Distribution of clients per cluster. There are a large number of classifiers pertaining to the supervised paradigm in the state of the art. Among the most famous we can mention Bayesian classifiers, decision trees, vector support machines and neural networks (including deep learning). However, all these classifiers are only useful for PATTERNS WITH NUMERICAL FEATURERES. If in the patterns there are categorical features, or mixed or lack of information (missing values), these classifiers totally lose their usefulness. That is when the eight classifiers as shown in Table 2 becomes important, which are adopted as benchmark for comparison, given the obvious advantages it exhibits. The positive effects on the overall results are obvious. All the parameter values of the eight classifiers compared are included in Table 2, and the performance in Table 3. The parameters of the proposed classifier are specified immediately after Table 4. That is the totality of parameters that are used in the manuscript. No more parameters are required than specified. In all cases, we have respected the suggestions of the authors of each of the compared classifiers. We do not experiment with other values because that IS NOT THE OBJECTIVE of our paper. In addition, we believe that this experimentation is not necessary, because authors typically publish the BEST VALUES of the parameters of their classifiers; and those values we have used for comparisons. We used the same partitions of the dataset in all the computational algorithms that were applied. Due to the imbalance of the data, with an imbalance ratio IR = 9, the 5 \(\times\) 2 cross validation was used, where the data set is divided five times, in two parts each time. The three main methods of model validation are Hold-out, k-fold cross-validation, and Leave-one-out. However, for unbalanced datasets the 5 \(\times\) 2 cross validation is recom \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Balanced Accuracy** & **Averaged F1** & **Training Time 1** & **Testing Time 1** \\ \hline ACID & 0.5316 & 0.5104 & 0.4922 & 0.0020 \\ ALVOT & 0.6968 & 0.6502 & 2.4162 & 0.4711 \\ C4.5 & 0.4027 & 0.4006 & 0.0658 & 0.0002 \\ EG & 0.5125 & 0.4772 & 0.6778 & 0.0020 \\ NAC & **0.7181** & **0.6747** & 5.3552 & **0.0001** \\ NB & 0.6783 & 0.6549 & 3.1702 & 0.0020 \\ NN (k = 1) & 0.6837 & 0.6606 & **0.0003** & 0.0020 \\ NN (k = 3) & 0.6252 & 0.6113 & **0.0003** & 0.0020 \\ RIPPER & 0.3437 & 0.3721 & 0.0593 & **0.0001** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of the compared classifiers. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameters** \\ \hline ACID & Np = 25, It = 1000, \(\varepsilon\) = 0.1, Dissimilarity: HEOM \\  & SSS: Typical testors, \(\Gamma_{\Omega_{i}}(o,\,y)=\rho_{i}*\theta_{y}*\theta(o,y,\Omega_{i})\), \\  & \(\Gamma_{\Omega_{i}}^{j}(o)=\frac{\sum_{\omega\in\Gamma_{i}}\Gamma_{\Omega_{i}}(o,y)}{|K_{j}|}\), \(\Gamma_{j}(o)=\frac{\sum_{\Omega_{i}\in\Gamma_{i}^{j}}(o,y)}{|S|}\), Decision rule: class \\  & with maximum \(\Gamma_{j}(o)\), Similarity: 1/HEOM \\  & & \\  & & \\  & & \\  & & \\  & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values suggested by the authors of the compared classifiers.