## 7 Discussion
### Relevance of the Used Features  
We aim to further analyze the \(NowDeepN\) approach by determining the relevance of the features used in the training process. More precisely, our goal is to examine if the radar products' values from a neighborhood of a certain location at time \(t\) are suitable for predicting the products' values at time \(t+1\), for the same location. The analysis from this section is conducted for answering question RQ3.  
For determining the significance of the features, we are comparing the results of \(NowDeepN\) using the original set of features with those obtained by applying \(NowDeepN\) after the prior application of a feature extraction step. Two feature extractors will be applied on the original set of features, for reducing the dimensionality of the input data.  
Figure 11: Predicted data, using the model trained on uncleaned data, for product \(R01\) (reflectivity at the lowest elevation angle, measured in dBZ with values ranging form 0 to 70) at 14:37:22 UTC.  
1. A sparse denoising AE is applied on the original data using a dimensionality of 250 for the hidden state. The AE's latent space representation (i.e., the result of the encoding part) will be further used (as a lower-dimensional representation of the input data) by \(NowDeepN\) for the prediction task. For the AE implementation we have used the following model: 7 hidden layers, 3 hidden layers for encoding (1000, 750, 500 neurons respectively), 250 neurons on the encoding layer and 3 hidden layers for decoding (500, 750, 1000 neurons respectively), all of these layers using the ReLU activation function, with the exception of the encoding layer, which used the linear activation function; the output size is equal to the input size (2197 neurons), with the linear activation function; using mean squared error loss and the Adam optimizer; the network was trained for 30 epochs using a batch of 1024 instances.
2. The PCA algorithm is applied for a linear dimensionality reduction of the input data into a 250 dimensional space. For PCA we have used the existing scikit-learn Python implementation of the algorithm using 250 principal components and the default values for the other parameters [52].  
Table 3 depicts the results obtained applying \(NowDeepN\) with a previous feature extraction step (AE/PCA). Comparing the results with those obtained without applying a feature extraction step (Table 1) we observe an improvement in the predictive performance of \(NowDeepN\) achieved without a prior feature extraction step. The last column from the table illustrate the improvement obtained by \(NowDeepN\) on the original data (computed as the difference between the measure on the original and on the reduced data divided to the value obtained on the reduced data).  
The results depicted in the last column from Table 3 empirically demonstrate that the features (i.e., the radar products' values from a neighborhood of a certain location at time \(t\)) used in training \(NowDeepN\) are relevant for predicting the radar products' values at time \(t+1\), for the same location. The relevance of the features is validated by the fact that a dimensionality reduction technique (AE/PCA) applied prior to the classification using \(NowDeepN\) does not improve the learning performance. The last column from Table 3 also reveals that AEs preserve better than PCA the characteristics of the data when reducing its dimensionality, which is expectable as AEs perform a non-linear mapping whilst PCA a linear one.