# DR-Transformer: A Multi-Features Fusion Framework for Tropical Cyclones Intensity Estimation
## 4 Experiment
### Analysis of the Loss  
To demonstrate the effectiveness of our DC loss, we further compare it with several deep metric learning (DML) methods. We reproduced N-pair loss and log-ratio loss with dense sampling, and we optimized all the losses under the same experimental conditions as described in Section IV but without the transformer. We use Saffir-Simpson Hurricane Wind Scale (SSHWS) along with intensity categorization for tropical storm and tropical depression as tropical cyclone intensity categories. We report the RMSE and MAE of each category and the results are shown in Table 2.  
As we can see, our DC + RI loss is superior to other methods. Npair loss and cross-entropy loss show comparable results on RMSE but our loss is better than theirs. Comparing with log-ratio loss, we improved RMSE from 10.21 to 8.88 (shown in Table 1), which means the N-tuplet-based training strategy of our DC loss is better with regard to discrimination. In terms of results of each category, our method performs better with a large intensity, such as categories H4, H3, H2, and TS. In particular, our method yielded an RMSE of 12.35 in category H3, with the second-best being circa 2.83 knots higher.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Approach** & **Temporal** & **Rmse (kt)** \\ \hline
1 & FASI [31] & - & 12.70 \\
2 & Improved DAV-T [32] & - & 12.70 \\
3 & TI index [33] & - & 9.34 \\
4 & [PERSON] (2016) [34] & - & 12.01 \\
5 & [PERSON] (2017) [35] & - & 10.00 \\
6 & [PERSON] (2018) [2] & - & 10.18 \\ \hline
7 & CNN-TC [3] & - & 10.18 \\
8 & Cross-entropy & - & 10.36 \\
9 & Npair [14] & - & 10.75 \\
10 & log-ratio [16] & - & 10.21 \\
11 & **Ours** (DC + RI) & - & 8.88 \\ \hline
12 & ADT [28] & smooth & 11.79 \\
13 & AMSU [29] & smooth & 14.10 \\
14 & SATCON [30] & smooth & 9.21 \\
15 & CNN-TC(S) [4] & smooth & 8.39 \\ \hline
16 & Ours (DR + smooth) & smooth & 9.16 \\
17 & Ours (DR + LSTM) & LSTM & 8.67 \\
18 & **Ours** (DR + transformer) & transformer & **7.76** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Tropical cyclone estimation results compared with other methods. Bold numbers denote the best results. The second column represents the different ways we handled temporal data.  
As mentioned before, our DC loss can make the difference between samples in the embedding space proportional to that in the label space. In this embedding space, even if misclassified, it will be classified into neighboring classes. Therefore, we visualized the results of log-ratio loss, repair loss, cross-entropy loss, and ours (DC + RI). We used scatter plots which are shown in Figure 4. The horizontal axis represents the groundtruth and the vertical axis represents predicted intensity. The blue line from bottom left to top right represents the best prediction. The grey, orange, and red crosses in the figure represent the errors within 10 knots, between 10 and 20 knots, and greater than 20 knots, respectively. Compared with other methods, in our method, there are fewer samples having an error of more than 20 m, and most of the samples have an error of less than 10 m.