## 3 Results and Discussion  
### Correlation Analysis of Indicators  
PCA can simplify the number of evaluation indicators while preserving most of the indicators' information. Multiple original indicators were converted into a smaller number of independent indicators, making it easier to establish a quality evaluation method for peaches. \(Z_{\text{X1}}\) to \(Z_{\text{X11}}\) represented the normalized data for each of the 11 indicators (shape index, volume, mass, density, firmness, color, \(Z\)s, \(\theta\), SSC, \(TA\), and sugar-acid ratio). Correlations between normalized indicators were calculated before PCA in SPSS (IBM ver. 25.0) and are shown in Table 1. \begin{table}
\begin{tabular}{c|c c c c c c c c c c c} \hline \multicolumn{11}{c}{**Correlation Matrix**} \\ \hline \multicolumn{1}{c}{**Correlation**} & \(Z_{\text{X3}}\) & \(Z_{\text{X2}}\) & \(Z_{\text{X3}}\) & \(Z_{\text{X4}}\) & \(Z_{\text{X3}}\) & \(Z_{\text{X6}}\) & \(Z_{\text{X7}}\) & \(Z_{\text{X8}}\) & \(Z_{\text{X9}}\) & \(Z_{\text{X10}}\) & \(Z_{\text{X11}}\) \\ \hline Shape index & \(Z_{\text{X1}}\) & 1.000 & & & & & & & & & & & \\ Volume & \(Z_{\text{X2}}\) & 0.477 & 1.000 & & & & & & & & & & \\ Mass & \(Z_{\text{X3}}\) & \(-\)0.027 & 0.486 & 1.000 & & & & & & & & & \\ Density & \(Z_{\text{X4}}\) & \(-\)0.545 & \(-\)0.869 & 0.006 & 1.000 & & & & & & & & \\ Firmness & \(Z_{\text{X5}}\) & 0.040 & 0.270 & 0.068 & \(-\)0.274 & 1.000 & & & & & & & \\ Color & \(Z_{\text{X8}}\) & \(-\)0.019 & \(-\)0.108 & 0.074 & 0.166 & \(-\)0.136 & 1.000 & & & & & \\ \(Z\)s & \(Z_{\text{X7}}\) & 0.079 & 0.250 & 0.085 & \(-\)0.235 & 0.752 & \(-\)0.092 & 1.000 & & & & \\ \(\theta\) & \(Z_{\text{X8}}\) & 0.550 & \(-\)0.217 & \(-\)0.131 & 0.173 & \(-\)0.746 & 0.035 & \(-\)0.812 & 1.000 & & & \\ SSC & \(Z_{\text{X9}}\) & 0.158 & \(-\)0.061 & 0.089 & 0.124 & \(-\)0.106 & 0.262 & \(-\)0.077 & 0.072 & 1.000 & & & \\ \(TA\) & \(Z_{\text{X10}}\) & 0.139 & 0.040 & \(-\)0.106 & \(-\)0.083 & \(-\)0.135 & \(-\)0.200 & 0.145 & 0.232 & 1.000 & & \\ Acid-sugar ratio & \(Z_{\text{X11}}\) & \(-\)0.029 & \(-\)0.092 & 0.151 & 0.194 & \(-\)0.018 & 0.287 & 0.121 & \(-\)0.073 & 0.460 & \(-\)0.744 & 1.000 \\ \hline \end{tabular}
\end{table} 
Table 1: Correlation analysis results for eleven normalized indicators measured in fresh peaches. Figure 3: Outline of data processing and analysis. From Table 1, it was obvious that the two dielectric properties (\(Z\)s and \(\theta\)) showed a strong correlation with firmness. A traditional back propagation (BP) neural network, which was multi-layered and had several hidden layers in addition to input and output layers (Figure 4), was used to explain the correlation between them [33; 34]. The original data of Zs and \(\theta\) were set as the inputs, and the firmness was set as the output for the BP neural network established in this study. In total, 190 samples were randomly assigned to training (70%), validation (15%), and test (15%) sets. The number of neurons in the fitting network's hidden layer was 10, and the Levenberg-Marquardt algorithm was chosen as the training function. The correlation coefficient between the simulated outputs and the observed values of the BP neural network could be quickly obtained with Matlab R2018b (Figure 5). Figure 4: Diagram of back propagation (BP) neural network in Matlab. Figure 5: Regression results of the BP neural network model. From Tables 2 and 3, five principal components were retained, with eigenvalues of \(e_{1}\) = 3.064, \(e_{2}\) = 2.241, \(e_{3}\) = 1.776, \(e_{4}\) = 1.206, and \(e_{5}\) = 1.058. The cumulative variance of the five principal components was 85%, which included most of the information from the 11 original indicators.