## 5 Results
### Classification Results
#### 5.3.1 Radial Feed  
For the classification of radial feed into five equidistant steps from \(-0.02\) mm to \(0.02\) mm, the values of the accuracy of the different classification methods with different feature combinations are shown in Table 5.  
For the classification of the radial feed, the SVM is best suited with the highest accuracy of \(0.9\), which works with five features of the raw signal determined by MANOVA and the WPT with \(15\) coefficients. The learning data set and the predicted output variables of the best two of these five features can be seen in Figure 11, as well as the confusion matrix of the SVM on the right. The plot of the best two of the five features used only gives an impression of the separability of the different classes, but not of the class boundaries in the five-dimensional space. The confusion matrix is a method to assess the quality of a classification model in machine learning. It visualize the number of predictions that were correct or incorrect. The numbers entered in the main diagonal correspond to the number  
Figure 10: STFT spectra at different radial feeds and a tool tumble of \(0\) μm.  
of correctly classified test data. The color scale (from blue to red) represents the proportion of correctly and incorrectly classified data.  
From the confusion matrix, it can be seen that misclassifications are only assigned to adjacent levels of radial feed, but not to levels further away. The reason for this can be the overlapping of the different classes in the multidimensional feature space, whereby no clear separation plane can be found. Consequently, misclassifications occur in the border area.  
The other features selected using MANOVA are also able to correctly classify at least 83% of the validation data when using an SVM. The KNN method, on the other hand, is poorly suited for predicting radial feed, especially in combination with feature selection using ANOVA and the rank correlation coefficient, since only low accuracy values are achieved. The features of the raw signal selected by ANOVA and the DWT also provide low accuracy values for the classification with the KNN method as well as when using an SVM.  
Figure 11: Best two features and confusion matrix of SVM for radial-feed classification (feature selection: MANOVA, features from raw signal and WPT with 15 coefficients).  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Feature Selection** & \begin{tabular}{l} **Number of** \\ **Features** \\ \end{tabular} & \begin{tabular}{l} **Accuracy** \\ **Bayes** \\ \end{tabular} & \
\begin{tabular}{l} **Accuracy** \\ **SVM** \\ \end{tabular} &
\begin{tabular}{l} **Accuracy** \\ **KNN** \\ \end{tabular} \\ \hline MANOVA RS + STFT & \(1\) & 0.60 & 0.53 & 0.55 \\ \hline MANOVA RS + CWT & \(1\) & 0.60 & 0.67 & 0.62 \\ \hline MANOVA RS + DWT & \(1\) & 0.68 & 0.69 & 0.62 \\ \hline MANOVA RS + WPT with 15 coeff. & \(1\) & 0.83 & 0.88 & 0.83 \\ \hline MANOVA RS + WPT with 128 coeff. & \(1\) & 0.83 & 0.83 & 0.85 \\ \hline ANOVA + r\({}_{\text{s}}\) RS + STFT & \(60\) & 1.00 & 1.00 & 1.00 \\ \hline ANOVA + r\({}_{\text{s}}\) RS + CWT & \(60\) & 1.00 & 1.00 & 1.00 \\ \hline ANOVA + r\({}_{\text{s}}\) RS + DWT & \(60\) & 0.97 & 1.00 & 1.00 \\ \hline ANOVA + r\({}_{\text{s}}\) RS + WPT with 15 coeff. & \(60\) & 0.70 & 1.00 & 0.97 \\ \hline ANOVA + r\({}_{\text{s}}\) RS + WPT with 128 coeff. & \(60\) & 0.98 & 1.00 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Evaluations of the classification models for the classification of radial feed.