## 3 Results and Discussion
### Classification of Granulation Levels  
#### 3.3.1 Discriminant Analysis of Models in Five Granulation Levels  
Based on the visible and near-infrared transmittance spectroscopy and chemometrics, the LDA [56], PCA-SVM, and PCA-GRNN models were used to classify samples into five granulation levels. By discriminant analysis of the samples, the confusion matrices of the three models could be calculated, as shown in Table 4, and these data could be utilized to calculate _TP_, _TN_, _FP_, and _FN_. In the confusion matrix, the \(ARM\) of each model represents the ratio as the sum of samples on the main diagonal to the total number of samples. According to the prediction set of samples (Table 4), the \(ARM\) values of LDA, PCA-SVM, and PCA-GRNN were 87.5%, 95.5%, and 95.5%, respectively, as calculated by Equation (12). Based on _TP_, _TN_, _FP_, and _FN_, predictive performance measures (\(CA\), \(CS\), and _CSP_) could be derived from Equations (13) to (15). Table 5 presents the predictive performances of the three models for five granulation levels for samples in the prediction set. Compared to PCA-SVM and PCA-GRNN, LDA had lower values of \(CA\), \(CS\), and _CSP_ for Class C. Therefore, the predictive performance was higher for PCA-SVM and PCA-GRNN compared to LDA for discriminant analysis of the five granulation levels. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Method**} & \multirow{3}{*}{**N**} & \multicolumn{6}{c}{**Calibration**} & \multicolumn{6}{c}{**Prediction**} \\ \cline{3-14}  & & \multicolumn{3}{c}{**Actual**} & \multicolumn{3}{c}{**Predicted Class**} & \multirow{3}{*}{**N**} & \multicolumn{3}{c}{**Actual**} & \multicolumn{3}{c}{**Predicted Class**} \\ \cline{3-14}  & & & **Class** & & **A** & **B** & **C** & **D** & **E** & & **Class** & **A** & **B** & **C** & **D** & **E** \\ \hline \multirow{6}{*}{LDA} & 131 & A & 83 & 48 & 0 & 0 & 0 & 15 & A & 11 & 4 & 0 & 0 & 0 \\ \cline{2-14}  & 101 & B & 12 & 89 & 0 & 0 & 0 & 65 & B & 7 & 58 & 0 & 0 & 0 \\ \cline{2-14}  & 41 & C & 0 & 3 & 38 & 0 & 0 & 35 & C & 0 & 0 & 35 & 0 & 0 \\ \cline{2-14}  & 70 & D & 0 & 0 & 2 & 63 & 5 & 50 & D & 0 & 0 & 0 & 45 & 5 \\ \cline{2-14}  & 57 & E & 0 & 0 & 3 & 17 & 37 & 35 & E & 0 & 0 & 0 & 9 & 26 \\ \hline \multirow{6}{*}{PCA-SVM} & 114 & A & 104 & 10 & 0 & 0 & 0 & 32 & A & 32 & 2 & 0 & 0 & 0 \\ \cline{2-14}  & 131 & B & 6 & 125 & 0 & 0 & 0 & 35 & B & 1 & 34 & 0 & 0 & 0 \\ \cline{2-14}  & 21 & C & 0 & 0 & 16 & 0 & 5 & 55 & C & 0 & 0 & 52 & 0 & 3 \\ \cline{2-14}  & 94 & D & 0 & 0 & 0 & 88 & 6 & 26 & D & 0 & 0 & 0 & 25 & 1 \\ \cline{2-14}  & 40 & E & 0 & 0 & 3 & 4 & 33 & 52 & E & 0 & 0 & 2 & 2 & 48 \\ \hline \multirow{6}{*}{PCA-GRNN} & 99 & A & 90 & 5 & 4 & 0 & 0 & 47 & A & 44 & 1 & 2 & 0 & 0 \\ \cline{2-14}  & 111 & B & 3 & 106 & 0 & 2 & 0 & 55 & B & 1 & 54 & 0 & 2 & 0 \\ \cline{1-1} \cline{2-14}  & 50 & C & 4 & 0 & 46 & 0 & 0 & 26 & C & 2 & 0 & 24 & 0 & 0 \\ \cline{1-1} \cline{2-14}  & 80 & D & 0 & 0 & 0 & 71 & 9 & 40 & D & 0 & 0 & 0 & 37 & 3 \\ \cline{1-1} \cline{2-14}  & 60 & E & 0 & 0 & 0 & 8 & 52 & 32 & E & 0 & 0 & 0 & 0 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix of the samples in the models. The results from use of LDA to classify predicted samples are shown in Figure 10a. Class C obtained perfect classification. Eleven samples in Class A and Class B were mistakenly classified as other classes, so there was an intersection set between Class A and Class B. This also occurred for Class D and Class E. Excessive misjudgment of samples decreased the accuracy of sample classification except for Class C in LDA. Figure 10b shows the discriminant results of PCA-SVM for predicted samples for the five granulation levels. The predictive performance of PCA-SVM was superior to that of LDA, indicating more samples were accurately classified. For example, Class A and Class B together had only three samples incorrectly classified in the PCA-SVM model, which is obviously less than the number classified by LDA.