## 5 Experimental Results and Discussion
### Experimental Settings  
In this section, we examine the settings of the final network architecture. The basic Pixel R-CNN model, shown in Figure 3, is the result of a careful design aimed at obtaining the best performance in terms of accuracy and computational cost. Indeed, the final model is a lightweight model with 30,936 trainable parameters (less than 1 MB), fast and more accurate than the existing state-of-the-art solutions. With the suggested approach, we employed only an RNN layer with 32 output units for each peephole LSTM cell randomly turned off, with a probability \(p=0.2\), by a Dropout regularization operation. For all experiments, peephole LSTM has shown an improvement in overall accuracy around 0.8% over standard LSTM cells. Then, Time Distributed Dense transforms \(Y_{(lstm)}^{(i)}\) in a \(9\times 9\) square matrix that feed a stack of two CNN layers with a number of features \(n_{1}=16\) and \(n_{2}=32\), respectively. The first layer as a filter size of \(f_{1}=3\) and the second one \(f_{2}=7\) producing a one-dimensional output array. Finally, a fully connected layer with SoftMax activation function maps \(Y_{(corr2)}^{(i)}\) to the probability of the \(K=15\) different classes. Except for the final layer, we adopted ReLU as activation functions. To find the best training hyperparameters for the optimizer, we used 10% of the training set to perform a random search evaluation, with few epochs, in order to select the most promising parameters. Then,  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Class** & **Pixels** & **Percentage** \\ \hline Tomatoes & 3020 & 3.20\% \\ Artificials & 9343 & 10.14\% \\ Trees & 7384 & 8.01\% \\ Rye & 4382 & 4.75\% \\ Wheat & 12,826 & 13.92\% \\ Soya & 5836 & 6.33\% \\ Apple & 849 & 0.92\% \\ Peer & 495 & 0.53\% \\ Temp Grass & 1744 & 1.89\% \\ Water & 2451 & 2.66\% \\ Lucerne & 17,942 & 19.47\% \\ Durum Wheat & 1188 & 1.28\% \\ Vineyard & 6110 & 6.63\% \\ Barley & 2549 & 2.76\% \\ Maize & 15,997 & 17.37\% \\
**Total** & 92,116 & 100\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Land cover types contribution in the reference data.  
after this first preliminary phase, the analysis has been focused only on the value of the most promising hyperparameter, fine-tuning them with a grid search strategy.  
Figure 10: Pareto chart of the explained variance as a function of the number of components.  
Figure 9: Visual representation of the data points projected in the tri-dimensional space using PCA. The three principal components took into account preserve 64.5% of the original data set variance.  
So, for the AMSGrad optimizer, we set \(\beta_{1}=0.86\), \(\beta_{2}=0.98\), and \(\epsilon=10^{-9}\). Finally, as previously introduced, with a preliminary procedure, we linearly increased the learning rate of \(\eta\) while observing the value of the loss function to estimate the initial value of this important hyperparameter. In conclusion, we fed our model with more than 62,000 samples for 150 epochs with a batch size of 128 while cyclically varying the learning rate value with a cosine aneling strategy. All tests have been carried out with the TensorFlow framework on a workstation with 64 GB RAM, Intel Core i7-9700K CPU, and an Nvidia 2080 Ti GPU.