# Typhoon Track Prediction Based on Deep Learning
## 2 Materials and Methodology
### Typhoon Dataset
#### 2.1.2 Missing Filling  
Due to the long chronological span of the typhoon best track data set in the South China Sea, the data were mostly kept by manual handwriting due to the limited technical level in the early days, which easily caused data missing due to improper data storage. Before the 1970s, the satellite technology was not widely used, and the types of data recorded by various national observatories inevitably fluctuated, resulting in some missing data. The missing data will adversely affect the results of the subsequent model, so we need to deal with the missing data.  
The direct deletion method is the most common and easy-to-implement method for handling missing values, but considering that multiple predictors have more or less some missing values, the direct deletion method is not used for missing processing. In addition, because these missing data also need to consider the correlation between the before and after data, they cannot be filled using the mean, plural, etc. At the same time, because the ordinary fitting method fits a function that only. In contrast, the regression equation constructed by the interpolation method will ensure that the values of all known data samples are passed, which is more stable and has guaranteed convergence. Therefore, in this paper, we choose to fill in the missing data using cubic spline interpolation.  
First, the variables containing missing values in the data set were screened, and four categories of predictors, WIND, PRES, ROCI, and EYE, were found to have missing values. Subsequently, the typhoons with missing values were eliminated category by category, and four different sets of samples without missing values were obtained and normalized separately, and detailed formulas of normalization are shown in Equations (1)-(3).  
\[\mu_{d}=\frac{\sum\limits_{i=1}^{n}x_{i}}{n} \tag{1}\]  
\[\sigma_{d}^{2}=\frac{\sum\limits_{i=1}^{n}(x_{i}-\mu_{d})}{n} \tag{2}\]  
\[\hat{x}_{i}=\frac{x_{i}-\mu_{d}}{\sqrt{\sigma_{d}^{2}}} \tag{3}\]  
where \(\mu\) denotes the mean of the predictors, \(\sigma^{2}\) denotes the variance of the predictors, \(\hat{x}_{i}\) denotes the normalized data values of the predictors, \(x_{i}\) denotes the data values of the predictors, and \(n\) denotes the sample set size.  
Then the missing rate was set for the sample set, the predicted values were obtained using three times spline interpolation, and the effect of data filling was evaluated by calculating the root mean square error between the predicted and observed values and the error results are shown in Table 2. The formula for calculating the root-mean-square error is shown in Equation (4).  
\[RMSE=\sqrt{\frac{1}{\hat{n}}\sum\limits_{i=1}^{n}\left|r_{i}-e_{i}\right|^{2}} \quad i=1,2,\cdots,n \tag{4}\]  
where \(n\) indicates the total number of missing values, and \(r_{i}\) and \(e_{i}\) indicate the true and filled values of the \(i\)th missing value, respectively. a smaller value of \(RMSE\) represents a smaller average error between the filled and true values and higher filling accuracy [25].  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Meteorological Variables** & **WIND** & **PRES** & **ROCI** & **EYE** \\ \hline _RMSE_ & 0.035081 & 0.03641 & 0.03694 & 0.03589 \\ \hline \end{tabular}
\end{table}
Table 2: Error evaluation results for missing fill.  
By observing Table 2, we can find that the \(RMSE\) of all four variables reached the level of 0.01, which is fair. Finally, the four predictors in the original dataset were filled with missingness one by one using three times spline interpolation.