## 2 Preliminaries
### High Degree F-Transform
As well as for the white wine quality training set, the size of the data points in the transformed training set is reduced from eleven to five. Table 5 shows the Accuracy, Precision, Recall, and F1-score measures computed on the training and test sets executing the five classification methods. The results of the tests applied on the red wine quality dataset confirm that the best performances are obtained executing the F\({}^{1}\)-transform classification method The F\({}^{1}\)-transform method improves the classification accuracy of MFC by about 5% on both training and test sets. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Phase** & **Method** & **Accuracy** & **Precision** & **Recall** & **F1-Score** \\ \hline \multirow{4}{*}{Training} & SVM & 0.75 & 0.77 & 0.74 & 0.75 \\  & RF & 0.73 & 0.76 & 0.71 & 0.73 \\ \cline{1-1}  & ANN & 0.78 & 0.79 & 0.77 & 0.78 \\ \cline{1-1}  & MFC & 0.76 & 0.77 & 0.75 & 0.76 \\ \cline{1-1}  & F\({}^{1}\)-transform & 0.83 & 0.82 & 0.83 & 0.82 \\ \hline \multirow{4}{*}{Test} & SVM & 0.74 & 0.75 & 0.74 & 0.74 \\ \cline{1-1}  & RF & 0.73 & 0.74 & 0.71 & 0.72 \\ \cline{1-1}  & ANN & 0.77 & 0.80 & 0.77 & 0.79 \\ \cline{1-1}  & MFC & 0.76 & 0.76 & 0.74 & 0.76 \\ \cline{1-1}  & F\({}^{1}\)-transform & 0.82 & 0.81 & 0.82 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: White wine dataset: Classification performance comparison. Figure 4: Scree plot obtained for the red wine quality training set; the orange line shows the elbow point. The F1-transform method improves the classification accuracy obtained by executing ANN by about 4% on the training set and 3% on the test set; it improves the one obtained by executing MFC by about 7% on the training set and 5% on the test set. ### Adult Classification Dataset

The Adult dataset contains information extracted from the United States census bureau database, which includes information on residents of various states to determine whether a citizen earns more or less than 50K USD per year. The training set contains 32,561 unambiguous data points; the data points are vectors formed by fourteen input features, four continuous and ten categorical. The test set contains 16,282 unambiguous data points. Table 6 shows the description of each feature. The output class feature, called class, assumes two values, depending on whether the person makes over 50K or under 50K USD a year. The dataset is unbalanced, where over 75% of the data points are classified with an annual income under 50K USD. To execute F1-transform, all the categorical features were transformed into integers assigning to each term in the list of values an integer starting from 1 to the number of unique values. PCA is executed in order to reduce the number of features. Figure 5 shows the scree plot and the elbow point set to 2.5. The first nine components are selected and the input features are reduced from fourteen to nine. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Feature Name** & **Description** & **Type of Field** \\ \hline age & Age & Continuous \\ workclass & Work class & List \\ fnlwgt & Survey weight & Continuous \\ education & Education & List \\ education-num & Education number & Continuous \\ marital status & Marital status & List \\ occupation & Occupation & List \\ relationship & Type of relationship & List \\ race & Race & List \\ sex & Gender & List: (Female, Male) \\ capital-game & Capital-game & Continuous \\ capital-loss & Capital-loss & Continuous \\ hours-per-week & Hours of work per week & Continuous \\ native-country & Native country & List: \\ class & Annual income & List: (\textless{<=50 K, <50 K}) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Adult dataset: Description of the features.