# Machine Learning Algorithms: An Experimental Evaluation for Decision Support Systems
## 4 Materials and Methods
### Evaluation Metrics  
The predictive performance of the supervised techniques was assessed by the metrics _Accuracy_ in Equation (2), _Precision_ in Equation (3), _Recall_ in Equation (4), _F1-Score_ in Equation (5) and ROC-AUC-Score, where ROC stands for Receiver Characteristic Operator and AUC for Area Under the Curve. _TP_, _TN_, _FP_ and _FN_ stand for true positive, true negative, false positive and false negative, respectively. A true positive is an outcome wherein the model correctly predicts the positive class. Similarly, a true negative is an outcome where the model correctly predicts the negative class. A false positive is an outcome where the model incorrectly predicts the positive class. Similarly, a false negative is an outcome wherein the model incorrectly predicts the negative class. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{2}\]  
\[Precision=\frac{TP}{TP+FP} \tag{3}\]  
\[Recall=\frac{TP}{TP+FN} \tag{4}\]  
\[F1-Score=\frac{2\times Recall\times Precision}{Recall+Precision} \tag{5}\]  
Regarding the ROC-AUC-Score, ROC is a probability curve and AUC represents the degree or measure of separability. It expresses the extent to which the model is capable of distinguishing between classes. A higher AUC is positively correlated with the better performance of the model's prediction of zero classes as zero and one classes as one. For clustering unsupervised techniques, the predictive performance was assessed by the metrics Silhouette Score, Homogeneity Score, Completeness Score, V Measure Score, Adjusted Rand Score and Adjusted Mutual Info Score. _Silhouette_ Score, presented in Equation (6), is calculated using the mean intra-cluster distance (\(a\)) and the mean nearest-cluster distance (\(b\)) for each sample. It has values between \(-1\) and \(1\), where the value \(0\) indicates overlapping clusters, and negative values indicate that the instance was assigned to the wrong cluster and the best values as close as possible to \(1\). \[Silhouette=\frac{(b-a)}{\text{max}(a,\ b)} \tag{6}\]  
_Homogeneity_ Score, shown in Equation (7), is useful to check whether the clustering algorithm meets an important requirement: a cluster should only contain samples belonging to the same class. Figure 10: Correlation of features from the human resource dataset with the label left after applying the ANOVA model. to a single class. It has values between 0 and 1, where 1 means that there is a perfect homogeneous classification. \[Homogeneity=1-\frac{H\Big{(}Y_{true}\Big{|}Y_{pred}\Big{)}}{H(Y_{true})} \tag{7}\]  
_Completeness_ Score, shown in Equation (8), has the purpose of checking whether all the data points that are members of a given class are elements of the same cluster. This varies between 0 and 1, where 1 means that all members of a class belong to the same cluster. \[Completeness=1-\frac{H\Big{(}Y_{pred}\Big{|}Y_{true}\Big{)}}{H\Big{(}Y_{pred} \Big{)}} \tag{8}\]  
_V Measure_ Score, shown in Equation (9), is the harmonic mean between homogeneity and completeness, varying between 0 and 1, with values of 1 meaning that there is a perfect homogeneous and complete classification. Beta is the ratio of weight attributed to homogeneity versus completeness. \[V\text{ }Measure=\frac{(1+beta)\times homogeneity\times completness}{beta\times homogeneity \times completeness} \tag{9}\]  
_Adjusted Rand Score_, shown in Equation (10), is used to determine whether two cluster results are similar to each other. In formula (10), \(RI\) stands for the Rand index, which calculates the similarity between two cluster results by taking all the points identified within the same cluster. It can have values between \(-1\) and 1, where values close to 0 mean a random classification and values closer to 1 mean the best classification. \[Adjusted\text{ }Rand\text{ }Score=\frac{RI-Expected\_RI}{\max(RI)-Expected\_RI} \tag{10}\]  
_Adjusted Mutual Info Score_, shown in Equation (11), is an adjustment of the Mutual Information (\(MI\)) score to account for chance.