## 3 Results  
In this section, the classification results are presented. A support vector machine (SVM) with a linear kernel is trained in a \"leave one patient out\" manner. The three types of features are tested, i.e., the reduced bands, the subtractions features, or the divisions' features. It is to note that two hyperparameters can be tuned: the number of features retained in the feature selection step \(k\) and the regularization parameter \(c\) that controls the balance between misclassification rate and the size of the margin. A lower value of \(c\) leads to a better misclassification rate but also a smaller margin, thus being less robust to over-fitting. In this section, data acquired by the two cameras are processed separately. The Table 2 presents the results obtained with the VIS camera and Table 3, the one obtained with the NIR camera. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Healthy** & **Chronic** & **Intestinal** \\
**Gastritis** & **Metaplasia** \\ \hline
4 & 7 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of multispectral data according to histology. Figure 4: Acquisitions with VIS and NIR cameras. In Table 2, we observe that intestinal metaplasia is confounded with chronic gastritis. For the three types of features, the results are close to 53% of precision and 67% recall. Better results are obtained in Table 3, especially with divisions and subtractions' features. The average of the three classes is 80% for the precision and 80% for the recall. It can be seen in the confusion matrix Figure 5 that the healthy class is sometimes confounded with intestinal metaplasia and that chronic gastritis is sometimes confounded with intestinal metaplasia. This second point is more acceptable in the sense that intestinal metaplasia usually appears as little patches in the middle of chronic gastritis. Thus, a patient with intestinal metaplasia has always chronic gastritis too. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Optimal**} & \multirow{2}{*}{**Class**} & \multirow{2}{*}{**Precision**} & \multirow{2}{*}{**Recall**} & \multirow{2}{*}{**F1-Score**} \\  & \multicolumn{1}{c}{**Hyperparameter**} & & & & \\ \hline Reduced & c = 0.0001 & Healthy & 0.98 & 1.00 & 0.99 \\ Bands & k = 1 & Chronic gastritis & 0.58 & 0.99 & 0.73 \\  & & Intestinal metaplasia & 0.00 & 0.00 & 0.00 \\  & & Average & 0.52 & 0.66 & 0.57 \\ \hline Divisions & c = 0.0001 & Healthy & 1.00 & 1.00 & 1.00 \\  & k = 1 & Chronic gastritis & 0.58 & 1.00 & 0.74 \\  & & Intestinal metaplasia & 0.00 & 0.00 & 0.00 \\  & & Average & 0.53 & 0.67 & 0.58 \\ \hline Subtractions & c = 0.0001 & Healthy & 1.00 & 1.00 & 1.00 \\  & k = 1 & Chronic gastritis & 0.58 & 1.00 & 0.74 \\  & & Intestinal metaplasia & 0.00 & 0.00 & 0.00 \\  & & Average & 0.53 & 0.67 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification results with the VIS camera. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Optimal**} & \multirow{2}{*}{**Class**} & \multirow{2}{*}{**Precision**} & \multirow{2}{*}{**Recall**} & \multirow{2}{*}{**F1-Score**} \\  & \multicolumn{1}{c}{**Hyperparameter**} & & & & \\ \hline Reduced & c = 0.001 & Healthy & 0.88 & 0.51 & 0.64 \\ Bands & k = 1 & Chronic gastritis & 0.59 & 0.94 & 0.73 \\  & & Intestinal metaplasia & 0.73 & 0.37 & 0.49 \\  & & Average & 0.73 & 0.61 & 0.62 \\ \hline Divisions & c = 0.001 & Healthy & 0.87 & 0.56 & 0.68 \\  & k = 1 & Chronic gastritis & 0.87 & 0.96 & 0.91 \\  & & Intestinal metaplasia & 0.69 & 0.78 & 0.73 \\  & & Average & 0.80 & 0.80 & 0.80 \\ \hline Subtractions & c = 0.001 & Healthy & 0.86 & 0.57 & 0.69 \\  & k = 1 & Chronic gastritis & 0.86 & 0.96 & 0.91 \\  & & Intestinal metaplasia & 0.69 & 0.76 & 0.73 \\  & & Average & 0.80 & 0.77 & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification results with the NIR camera. It is interesting to detail the classification results for each patient. Figure 6 presents the number of spectra classified in each category for each patient.