## 2 Materials and Methods
### Identification Methods
#### 2.3.3 Feature Classification
Figure 5 shows the distribution of the mean identification accuracies \(\mu\) obtained in our experiments. As mentioned, the value of \(d^{\prime}\) is the input feature dimension for the six tested multi-classification methods. The two bars, with and without shading background centered at the same horizontal ordinate label, were generated with the same value of \(d^{\prime}\). With respect to the same value of \(d^{\prime}\), the altitude difference between the two bars with and without shading background represents the difference between the accuracies obtained with the training and test sets. Figure 4: Distributions of the principal components output by PCA. Points in the same color were generated with samples of the same perfume type. (**a**) PC1 and PC2 when the output feature dimension of PCA is set as 2 (\(d^{\prime}=2\)); (**b**) PC1, PC2, and PC3 when the output feature dimension of PCA is set as 3 (\(d^{\prime}=3\)). From the mean identification accuracies results shown in Figure 5, at least three conclusions can be drawn as follows:

1. The feature dimension \(d^{\prime}\) has an obvious impact on the mean identification accuracies \(\mu\) for all the six classification methods. When \(d^{\prime}<9\), all six tested methods achieved gradually increasing identification accuracies as the value of \(d^{\prime}\) escalated. In particular, as the value of \(d^{\prime}\) increased in the range 3 \(<d^{\prime}<15\), XGBoost achieved gradually increasing mean identification accuracies. This phenomenon suggests that a not-too-small feature dimension is necessary to provide sufficient information for further classification. However, when the value of \(d^{\prime}\) exceeded a certain threshold, which differed for the different methods, increasing the feature dimension can barely improve, and sometimes can even deteriorate, the mean identification accuracies. Figure 5: The mean identification accuracies \(\mu\) obtained by the six tested classification methods when the output feature dimension of PCA is set as different numbers. Bars with and without shading pattern indicate the mean accuracies obtained with the test and training sets, respectively. When the feature dimension was unnecessarily high, much redundant and unhelpful information would be incorporated, which increased the complexity of the learned model. Thus, it is important to determine an optimal value of \(d^{\prime}\) for each method to meet the demands of identification accuracy and computational burden. For example, according to the results in Figure 5, the optimal value of \(d^{\prime}\) for XGBoost was 15, since the mean identification accuracies obtained by XGBoost were to some extent stable when the value of \(d^{\prime}\) exceeded 15. 2. With respect to the same feature dimension, the mean accuracies obtained with the test sets were notably lower than those obtained with the training sets for RF, SAMME, and GBDT. These differences indicate that RF, SAMME, and GBDT were affected by the over-fitting problem when used for EN-based PI. In contrast, NN, SVM, and XGBoost obtained the same mean accuracies on the training and test sets when the feature dimension was fixed at the same value. The fact that XGBoost avoided the overfitting problem was mainly attributable to the regularization term \(\Omega\)(\(f_{m}\)) in the loss function shown in Equation (1), which penalized the model complexities during the model learning processes. A highly complex statistical model usually contains terms tailored to the training set, which have a negative influence on its prediction performance on other datasets, including the test set. 3. Last, but not least, XGBoost achieved the highest mean accuracy in our experiments. When the value of \(d^{\prime}\) exceeded 13, the mean accuracies obtained by XGBoost were generally higher than those obtained by the other tested methods. For clarification, Table 3 lists the highest mean accuracies on the test sets and the corresponding feature dimensions of the tested methods.