# Advancing Taxonomy with Machine Learning: A Hybrid Ensemble for Species and Genus Classification
## 3 Materials and Methods
### Dataset with Simulated Undescribed Species
* Similarly, also between the features proposed in [16] and those proposed in this paper, there is no clear winner; however, the fusion allows to improve the results of the \begin{table}
\begin{tabular}{l c} \hline \hline
**Fish** & **Species** \\ \hline [27] & 96.30 \\ \hline SVM\({}_{D}\) & 94.75 \\ \hline SVM\({}_{O}\) & 91.73 \\ \hline SVM\({}_{N}\) & 95.70 \\ \hline SVM\({}_{f}\) & 95.61 \\ \hline DWT\({}_{O}\) & — \\ \hline DWT\({}_{N}\) & 93.22 \\ \hline DWT\({}_{r}\) & 92.82 \\ \hline DWT\({}_{r}+\text{SVM}_{f}\) & 96.83 \\ \hline eDNA & 96.75 \\ \hline
**Proposed** & **97.03** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Accuracy of different methods on the Fish Dataset. \begin{table}
\begin{tabular}{l c} \hline \hline
**Beetle** & **Species** \\ \hline [27] & 98.10 \\ \hline [45] & 98.20 \\ \hline SVM\({}_{D}\) & 95.13 \\ \hline SVM\({}_{O}\) & 90.48 \\ \hline SVM\({}_{N}\) & 97.69 \\ \hline SVM\({}_{f}\) & 97.69 \\ \hline DWT\({}_{O}\) & — \\ \hline DWT\({}_{N}\) & 62.72 \\ \hline DWT\({}_{r}\) & 86.66 \\ \hline DWT\({}_{r}+\text{SVM}_{f}\) & 98.03 \\ \hline eDNA & 98.20 \\ \hline
**Proposed** & **98.51** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy of different methods on the Beetle Dataset. individual methods. Again, there is a difference in the results between the three large datasets and the two smaller ones (Beetle and Fish), in which the features proposed in [16] perform badly. In the final test, reported in Figure 6, we adopt a realistic protocol for the proposed dataset, i.e., the one detailed in Section 3.1, where all the insects are first classified at the species level (the species are the classes); notice that we have two trained nets, one for species and one for genera classification. Let us suppose the following:

* \(\theta_{1}(\mathbf{x})\) is the highest score (obtained using the species classification net) among the different species (i.e., classes) given a pattern \(\mathbf{x}\);
* \(\theta_{2}(\mathbf{x})\) is the second highest score (obtained using the species classification net) of that pattern;
* \(\theta(\mathbf{x})=\theta_{1}(\mathbf{x})-\theta_{2}(\mathbf{x})\). Our rejection criteria are as follows:

* If \(\theta(\mathbf{x})>\tau\), the insect is assigned to a species class; otherwise, it is assigned to a genus class (i.e., it is classified by the network trained using the genus as classes). * If a pattern belongs to a known species but is classified at the genus level, it is considered a classification error; clearly, a pattern with an unknown species is regarded as an error if classified at the species level. In Figure 6, we report the plot of the species accuracy (x-axis) versus genus accuracy (y-axis) obtained by varying the rejection threshold \(\tau\). The green line is obtained by \(\text{SVM}_{f}\), and the black line by our ensemble 'Proposed'. This test clearly shows the usefulness of the proposed ensemble versus SVM. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Approach** & **Precision** & **Recall** \\ \hline \multirow{2}{*}{Beetle} & \(\text{SVM}_{f}\) & 99.73 & 100 \\ \cline{2-4}  & Proposed & 99.81 & 100 \\ \hline \multirow{2}{*}{Fish} & \(\text{SVM}_{f}\) & 99.48 & 100 \\ \cline{2-4}  & Proposed & 99.57 & 100 \\ \hline \multirow{2}{*}{Badirli—Species} & \(\text{SVM}_{O}\) & 99.82 & 98.71 \\ \cline{2-4}  & Proposed & 99.42 & 99.14 \\ \hline \multirow{2}{*}{Badirli—Genus} & \(\text{SVM}_{O}\) & 90.16 & 85.74 \\ \cline{2-4}  & Proposed & 93.17 & 92.02 \\ \hline \multirow{2}{*}{New—Species} & \(\text{SVM}_{f}\) & 99.46 & 99.00 \\ \cline{2-4}  & Proposed & 99.38 & 98.99 \\ \hline \multirow{2}{*}{New—Genus} & \(\text{SVM}_{f}\) & 90.91 & 89.69 \\ \cline{2-4}  & Proposed & 95.90 & 95.63 \\ \hline \multirow{2}{*}{Unseen} & \(\text{SVM}_{f}\) & 57.29 & 53.91 \\ \cline{2-4}  & Proposed & 58.11 & 54.50 \\ \hline \end{tabular}
\end{table} 
Table 7: Precision–Recall performance indicator on different datasets. ## 5 Discussion

Several interesting insights can be drawn from the results presented in the previous section.