## 4 Conclusions  
In this study, the measurement of 11 quality indicators of 200 peaches was completed within 48 h. Quality indicator data were normalized, and outliers were excluded. A BP neural network was constructed in MATLAB to predict the firmness of fresh peaches from their dielectric properties, and the overall fitting ratio of the predicted values and the observed values was 86.9%. PCA results indicated that the cumulative variance explained by the first five principal components was 85%, indicating that the first five components captured most of the information from the 11 original indicators. Based on k-means clustering of normalized data from 11 indicators, 190 peaches were divided to five clusters, containing 24.7%, 19%, 14.2%, 21.6%, and 20.5% of the samples, respectively. The average comprehensive score was calculated for each cluster; fresh peach quality of cluster 1 was the best, and fresh peach quality of cluster 4 was the worst. Poor correspondence between the comprehensive scores and the percentage of red surface area demonstrated that red surface area is not a good basis for picking fresh peaches for consumers. This study establishes that dielectric properties can be used to predict the firmness of fresh peaches, and it describes an evaluation and grading model based on multiple indicators. The model provides a scientific, objective, and feasible way of studying and classifying the quality of fresh peaches. It provides a reference for the proposed evaluation of quality in other foods and a technical guarantee of food safety to protect the rights of the consumer. This research provides a technical basis for the detection of dielectric properties related to fruit quality, which will be an important focus of future studies. Based on this research, more convenient and effective fruit quality detection methods will be developed, providing technical support for post-harvest evaluation and classification of fruits in future work. [PERSON] and [PERSON] designed the research (conceptualization). [PERSON], [PERSON], and [PERSON] were responsible for the performance of the investigation, acquisition of data, and analysis and interpretation of the results. [PERSON] and [PERSON] were responsible for the original draft preparation. [PERSON] and [PERSON] acquired funding. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Cluster**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** \\ \hline Z\({}_{\text{X1}}\) & 0.227 & 0.756 & \(-\)0.715 & \(-\)0.883 & 0.362 \\ Z\({}_{\text{X2}}\) & 0.773 & 0.408 & \(-\)0.650 & \(-\)0.972 & 0.360 \\ Z\({}_{\text{X3}}\) & 0.401 & 0.237 & \(-\)0.283 & \(-\)0.098 & \(-\)0.267 \\ Z\({}_{\text{X4}}\) & \(-\)0.645 & \(-\)0.346 & 0.550 & 10.039 & \(-\)0.550 \\ Z\({}_{\text{X5}}\) & 0.947 & \(-\)0.724 & 0.812 & \(-\)0.834 & \(-\)0.317 \\ Z\({}_{\text{X6}}\) & \(-\)0.358 & 0.586 & 0.677 & \(-\)0.056 & \(-\)0.346 \\ Z\({}_{\text{X7}}\) & 1.068 & \(-\)0.724 & 0.942 & \(-\)0.918 & \(-\)0.373 \\ Z\({}_{\text{X8}}\) & \(-\)0.993 & 0.918 & \(-\)1.103 & 0.793 & 0.301 \\ Z\({}_{\text{X9}}\) & \(-\)0.310 & 0.668 & 0.316 & \(-\)0.066 & \(-\)0.370 \\ Z\({}_{\text{X10}}\) & \(-\)0.149 & \(-\)0.116 & \(-\)0.548 & \(-\)0.002 & 0.914 \\ Z\({}_{\text{X11}}\) & \(-\)0.127 & 0.472 & 0.688 & \(-\)0.041 & \(-\)0.976 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Final cluster center results for 190 peaches by k-means clustering analysis.