## 3 Experimental Results
### Results and Discussion  
To examine the feature dimension reduction capability of the deep neural networks, scatter plots of the main original features and the features derived by principal component analysis (PCA), DBN and SAE are shown in Figure 6. Two of the most discriminative features, conformity coefficient and degree of polarization (DoP) of HH and VV transition/receiving combinations, as two of the most effective feature in oil spill classification [31], are plotted in Figure 6a. Scatter plots of the first two components derived by PCA are shown in Figure 6b. In this paper, taking the advantage of DBN and SAE, the dimension of polarimetric features are reduced to six, then they are put into fully connected neural network. To show these features in a scatter plot, PCA was implemented on the six features, and then the first two components are shown in Figure 6c,d. It can be observed that deep neural network algorithms effectively extracted the information from high dimensional features and improved their separability to distinguish mineral oil and none mineral samples. The classification results are shown in Table 6 statistically, some key findings and discussions are listed as follow:  
* SAE achieved the highest classification accuracy (lowest testing error) among all the algorithms on different sample sizes. DBN achieved a close performance to SAE. SAE and DBN applied in the experiment had similar structures and both of them took the advantage of greedy unsupervised layer-wise pretraining, so very similar performances were achieved. The unsupervised pretraining worked as a feature optimizer, which can reveal the latent relationship and reduction of noise in features. It helps to improve the performance of the followed supervised classification procedure. * On the small training data set, deep learning algorithms have much higher performance than neural networks. When the number of data set is reduced, the parameters of traditional NN cannot be sufficiently tuned. Based on unsupervised pretraining, deep learning algorithms such as SAE and DBN have much stronger capability to achieve the optimized solution of the learning problem. * When the number of data sample size is reduced, the classification error will increase (i.e., the accuracy is reduced). When the number of data sets reduced, the characteristics of the studied object cannot be sufficiently expressed by the limited number of data samples, so the classification performance is reduced. * On the large training data set, NN have a close performance to deep learning algorithms. With large number of training data, the parameters of NN can be sufficiently adjusted. In this experiment, the NN have a few hidden layers, the gradient of objective function could pass to the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Sizes of RBM layers & [8; 6] \\ Number of epochs when training RBM & 10 \\ Batch size when training RBM & 100 \\ Momentum for RBM & 0 \\ Learning rate alpha of RBM & 1 \\ Size of the whole network & [10; 8; 6; 2] \\ Activation function of the neural network & Sigmoid \\ Number of epochs when making fine-tuning & 100 \\ Batch size when making fine-tuning & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter settings of the deep belief network (DBN). layers in the front effectively. As the result, comparable classification performance was achieved by NN on large data set. * SVM has better performance on small sample sizes than NN. SVM is based on structural risk minimization, which has superior performance on relative small data sets. It maximizes the classification margin, which is decided by a few support vectors and could successfully avoid the risk of the \"curse of dimensionality\". However, although the SVM has several advantages, it is equivalent to a NN with one hidden layer, so on learning complicated relationships its performance is no better than the other three more complex classifiers applied in the experiment.