## 3 Results and Discussion
### Identification of Penicillin Manufacturers
The classification accuracy of the RF-SVM model (\(c=60.1465\), \(g=39.7502\)) was 98.33% with the top 16 important characteristic spectral lines. Two LIBS spectra of AC3 were misclassified into AC2. Compared with LDA and SVM, the ANN classifier has higher accuracy when inputting the same number of characteristic spectral lines. When inputting the top six important characteristic spectral lines and using the RF-ANN (\(l=13\)) model, the classification accuracy reached 100%, successfully identifying different AC manufacturers. It can be seen from Figure 3b that the order of the important weights of the first six important characteristic variables is Na (588.9 nm) > Mg (279.7 nm) > Mg (279.1 nm) > Ca (393.1 nm) > C\({}_{2}\) (516.8-518.7 nm) > Mg (284.7 nm). The elements of Na and Mg came from the lubricants sodium dodecyl sulfate (C\({}_{12}\)H\({}_{25}\)SO\({}_{4}\)Na) and magnesium stearate (C\({}_{36}\)H\({}_{70}\)MgO\({}_{4}\)), respectively, in the prescription of AC [46]. The element of Ca might come from impurities or additives introduced by different manufacturers during the production process for AC. Figure 4c shows that, when inputting the top 23 important characteristic spectral lines and using RF-LDA to build the model, the classification accuracy reached 99.17%. One LIBS spectrum of ACPT3 was misclassified into ACPT1. It can also be seen from Figure 2 that the LIBS spectrum of ACPT3 is more similar to that of ACPT1 than the spectra of ACPT2 and ACPT4. The classification accuracy of the RF-SVM model (\(c=7.2070\), \(g=6.2123\)) reached 100% with the top fifteen important characteristic spectral lines. When inputting the top four important characteristic spectral lines and using the RF-ANN (\(l=10\)) model, the classification accuracy reached 100%. The LIBS spectra of four different ACPT manufacturers could be correctly classified by using the SVM and ANN models. It can be seen from Figure 3c that the order of the important weights of the first four important characteristic variables is Na (588.9 nm) > K (766.4 nm) > CN (384.8 nm-388.0 nm) > Ca (422.6 nm). The elements of Na and Ca might come from impurities or additives introduced by different manufacturers during the production process for ACPT. The element of K came from clavulanate potassium in the prescription of ACPT [47]. The molecular band of CN had two sources. The molecular structure of the ACPT sample was destroyed by the high-energy laser, producing some CN fragments. In addition, CN could also be formed by a chemical reaction between the C in the sample and the N in the atmosphere [44]. For PPT, AC and ACPT manufacturer identification, the RF-LDA model failed to reach 100% accuracy in AC and ACPT manufacturer identification; RF-SVM failed to achieve 100% accuracy in AC manufacturer identification; RF-ANN achieved 100% accuracy in the manufacturer identification of PPT, AC and ACPT. LDA is more suitable for the classification of linear data. However, the penicillin LIBS data in this study are nonlinear data. Part of the data of the penicillin LIBS spectra fall on the support vectors of SVM. Compared with that of ANN, the learning ability of SVM is insufficient. Through the repeated learning and training of known information, ANN can better adjust the connection weights of neurons, has strong robustness and fault tolerance to noise, and can fully approximate complex nonlinear relationships. Therefore, the established model is more suitable for nonlinear systems and unclear functional relationships. Overall, compared with RF-LDA and RF-SVM, RF-ANN was the most suitable model for penicillin manufacturer identification in this study.