# Temporal Convolutional Neural Network for the Classification of Satellite Image Time Series
## 3 Material and Methods
### Data Preparation
#### 3.3.3 Feature Normalization  
In remote sensing, the input time series are generally standardized by subtracting the mean and dividing by the standard deviation for each feature where each time stamp is considered as a separate feature. This standardization, named \(z\)-normalization of each band at each date in the following, ensures that the variation in the features is not dominated by a single feature that has a high dynamic rank. However, this transforms the general trend of the series.  
In machine learning, the input data are generally \(z\)-normalized by subtracting the mean and divided by the standard deviation for each time series [67]. This \(z\)-normalization of each time series has been introduced to be able to compare time series that have similar trends, but different scaling and shifting [68]. However, it leads to a loss of the meaning of the magnitude, whereas magnitude is crucial for vegetation mapping, e.g., corn will have higher NDVI values than other summer crops.  
To overcome both limitations of the common normalization methods, we use a min-max normalization per feature across all images. The traditional min-max normalization performs a subtraction of the minimum, then a division by the range, i.e., the maximum minus the minimum [69]. As this normalization is highly sensitive to extreme values, we propose to use 2% (or 98%) percentile rather than the minimum (or the maximum) value. For each feature, both percentile values are extracted from all the time-stamp values. In the following, this normalization is named global feature min/max normalization.  
Figure 7 displays four NDVI temporal profiles (top left)--rapeseed, corn, deciduous and water--for the three types of normalization: \(z\)-normalization of each time series, \(z\)-normalization of each band at each date, global feature min/max normalization (2-98%). \(Z\)-normalization of each time series (top right) produces highly transformed temporal profiles, and loses the relative vertical positioning of the spectra. Similarly, \(z\)-normalization of each band at each date (bottom left) also  
\begin{table}
\begin{tabular}{r c c c c} \hline \hline \multirow{2}{*}{**Temporal Sampling**} & \multicolumn{2}{c}{**NDVI**} & **SB** & **SB-NDVI-NDWI-IB** \\ \cline{2-5}  & & \(\mathbf{D=1}\) & \(\mathbf{D=3}\) & \(\mathbf{D=6}\) \\ \hline
**original** & \(T=46\) & 46 & 138 & 276 \\
**2 days** & \(T=149\) & 149 & 447 & 894 \\ \hline \hline \end{tabular} SB: Spectral Bands, NDVI: Normalized Difference Vegetation Index, NDWI: Normalized Difference Water Index, IB: Brilliance Index.  
\end{table}
Table 2: Number of features (\(D\times T\)) for the studied dataset with \(T\) the length of the time series, and \(D\) the number of spectral features.  
modifies the meaning of the amplitude. For instance, the normalized rapeseed profile looks flat during the growing season (between day of year 35 and 75), although the NDVI increases during this period (indicating a growth of the plant). Finally, global feature min/max normalization (2-98%) (bottom right) is the only one that does not change the shape of the temporal profiles, while ensuring that most of the values are within \([-1,1]\).