# Advancing Taxonomy with Machine Learning: A Hybrid Ensemble for Species and Genus Classification
## 3 Materials and Methods
### Dataset with Simulated Undescribed Species
Notice that, before the sum rule, the scores of each approach are normalized to mean 0 and standard deviation 1. In the tests reported in the following Tables 2 and 3, we suppose that an oracle divides the animals between those with known species and those only with known genera. In the final test, reported in Figure 6, we adopt a robust protocol in which all animals are classified at the species level, using a rejection threshold; those not classified in any species are classified at the genus level: this test is similar to a real application of this kind of problem. While accuracy provides an overall measure of the model's performance, it does not fully capture the nuances of classification performance, especially for imbalanced datasets. Therefore, we will extend the evaluation metrics to include Precision and Recall for comparing our proposed ensemble with the baseline SVM. Precision (PR) and Recall (RE) are defined as follows:

Figure 2:5

Figure 2:6

where \(TP\) = true positives; \(FP\) = false positives; and \(FN\) = false negatives. In Table 7, we report PR and RE for comparing our proposed ensemble with SVM\({}_{f}\), when it is available, or SMV\({}_{O}\). This test provides further confirmation of the effectiveness of the proposed ensemble compared to the SVM ensemble. This is significant, as SVM remains one of the most widely used classifiers in both the academic literature and practical applications. \begin{table}
\begin{tabular}{l c} \hline \hline
**Unseen** & **Genus** \\ \hline SVM\({}_{D}\) & 23.85 \\ \hline SVM\({}_{O}\) & 32.75 \\ \hline SVM\({}_{N}\) & 46.82 \\ \hline SVM\({}_{f}\) & 47.70 \\ \hline DWT\({}_{O}\) & 30.38 \\ \hline DWT\({}_{N}\) & 28.25 \\ \hline DWT\({}_{f}\) & 42.73 \\ \hline DWT\({}_{f}\) + SVM\({}_{f}\) & 48.15 \\ \hline eDNA & 33.36 \\ \hline
**Proposed** & **48.56** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Accuracy of different methods on the Unseen Dataset, Section 3.2. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Badirli** & **Species** & **Genus** \\ \hline Bad & 98.21 & 81.95 \\ \hline Bad\({}_{D}\) & 98.65 & 71.85 \\ \hline
[45] & 99.47 & 83.22 \\ \hline SVM\({}_{D}\) & 99.20 & 80.23 \\ \hline SVM\({}_{O}\) & 99.22 & 81.26 \\ \hline DWT\({}_{O}\) & 99.17 & 76.57 \\ \hline DWT\({}_{O}\) + SVM\({}_{O}\) & 99.40 & 81.92 \\ \hline eDNA & 98.74 & 87.20 \\ \hline
**Proposed** & **99.47** & **87.74** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy of different methods on the Badirli Dataset. \begin{table}
\begin{tabular}{l c c} \hline \hline
**New Insects** & **Species** & **Genus** \\ \hline
[45] & 99.05 & 84.02 \\ \hline SVM\({}_{D}\) & **99.16** & 79.07 \\ \hline SVM\({}_{O}\) & 98.21 & 82.01 \\ \hline SVM\({}_{N}\) & 98.05 & 65.05 \\ \hline SVM\({}_{f}\) & 99.00 & 83.67 \\ \hline DWT\({}_{O}\) & 98.83 & 75.08 \\ \hline DWT\({}_{N}\) & 98.54 & 82.98 \\ \hline DWT\({}_{f}\) & 99.12 & 83.85 \\ \hline DWT\({}_{f}\) + SVM\({}_{f}\) & 99.15 & 85.51 \\ \hline eDNA & 98.48 & 88.49 \\ \hline Proposed & 98.99 & **91.35** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy of different methods on the New Insects Dataset, Section 3.1. The following conclusions can be obtained considering the tables reported in this section:

* In each dataset, one of the methods tested in this paper gets the new SOTA, and ensemble is proposed as the best method among the tested approaches. In general, the conclusions are different whether we use the large datasets or the two small ones (i.e., Beetle and Fish); this is, logically, because of the size of the training set, a more important factor for neural networks than SVM. * Interestingly, between SVM and DWT, there is no winner; in some cases, SVM does better, in others DWT. However, their fusion allows both methods to improve. Performance is similar in the three large datasets, while in Beetle and Fish, which are much smaller in size, SVM performs much better than DWT; it is assumed that this is due to the fact that DWT is based on neural networks, which require a larger training set size than SVM.