## 2 Materials and Methods
### Identification Methods
#### 2.3.3 Feature Classification
\begin{table}
\begin{tabular}{c l l l} \hline \hline  & \multicolumn{1}{c}{**Notation**} & \multicolumn{1}{c}{**Range**} & \multicolumn{1}{c}{**Meaning**} \\ \hline \multirow{6}{*}{RF} & \(M\) & [50, 100,..., 250] & Total number of tree learners \\  & \(sd\) & \{0.1, 0.2,..., 1\} & The number of samples drawn to train each \\  & \(ud\) & \{1, 2,..., 10\} & Upper limit of the tree learner depth \\  & \(mln\) & \{2, 3,..., 10\} & Upper limit of sample numbers in a single leaf node \\  & \(mss\) & \{2, 3,..., 10\} & Minimum number of samples required to split a node \\ \hline \multirow{3}{*}{SAMME} & \(M\) & \{50, 100,..., 250\} & Total number of tree learners \\  & \(\eta\) & \{0.1, 0.2,..., 1\} & Learning rate used in the weight update \\  & \(ud\) & \{1, 2,..., 10\} & Upper limit of the tree learner depth \\ \hline \multirow{6}{*}{GBDT} & \(M\) & \{50, 100,..., 250\} & Total number of tree learners \\  & \(\eta\) & \{0.1, 0.2,..., 1\} & Learning rate used in the prediction update \\  & \(ud\) & \{1, 2,..., 10\} & Upper limit of the tree learner depth \\  & \(ss\) & \{0.5, 0.6,..., 1\} & Proportion of sample used for fitting each tree learner \\  & \(mid\) & \{0.5, 1,..., 5\} & Minimum impurity decrease required to split a node \\ \hline \multirow{6}{*}{XGBoost} & \(M\) & \{50, 100,..., 250\} & Total number of tree learners \\  & \(\eta\) & \{0.1, 0.2,..., 1\} & Learning rate used in the prediction update \\  & \(ud\) & \{1, 2,..., 10\} & Upper limit of the tree learner depth \\  & \(ss\) & \{0.5, 0.6,..., 1\} & Proportion of samples used for fitting each \\  & \(mcw\) & \{3, 4,..., 7\} & Integer learner \\ \hline \multirow{6}{*}{NN} & \(hls\) & \{400, 500, 600, 700\} & Number of neurons in the first hidden layer \\  & \(act\) & \{’relu’, 'logistic’, 'tanh’, 'identity’\} & Activation function for the hidden layer \\  & \(slv\) & \{’lbfgs’,'sgd’, 'adam’\} & Solver for weight optimization \\ \hline \multirow{3}{*}{SVM} & \(deg\) & \{0.5, 1, 1.5, 2\} & Degree of the polynomial kernel function \\  & \(C\) & \{1e3, 1e4, 2e4, 1e5\} & Penalty inversely proportional to \\ \cline{1-1}  & & & regularization strength \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ranges of main tunable hyper-parameters of the tested methods. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{1}{c}{**Highest**\(\mu\)} & \(\mathbf{d^{\prime}}\) \\ \hline RF & 94.17\% & 17 \\ \hline SAMME & 95\% & 23 \\ \hline GBDT & 88.33\% & 13 \\ \hline NN & 92.5\% & 13 \\ \hline SVM & 92.5\% & 7 \\ \hline XGBoost & 97.5\% & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The highest mean identification accuracies \(\mu\) obtained on the test sets with the six classification methods, and the corresponding feature dimensions \(d^{\prime}\). perfume samples was calculated as the identification accuracy. For example, if \(n^{\prime}\) perfume instances are correctly identified, the identification accuracy is \(n^{\prime}/n\). ### Identification Accuracy Comparison

The feature dimension reduction results obtained by PCA are shown in Figure 4. Each point in Figure 4 represents an individual sampling instance. A total of 120 points were plotted in each subfigure of Figure 4, since the perfumes were sampled 120 times. The point color stands for the corresponding perfume type, which means points in the same color were generated with the same perfume. In both subfigures of Figure 4, points in different colors are mixed with each other. It is hard to find a decision boundary to discriminate the sampling instances corresponding to different perfumes. The mixing of points in different colors reveals that the perfume samples cannot be identified using PCA alone. Moreover, when the output feature dimension of PCA is set as two or three, the output features contain little distinctive information about the perfume type, which poses difficulties for further classification. It is necessary to evaluate the influence of output feature dimension of PCA (\(d^{\prime}\)) on the further classification performance.