## 2 Materials and Methods
### Image Classification Using DBN Model  
In this study, the DBN model is exploited for land cover classification. Deep Belief Network (DBN) is a probabilistic generalization mechanism that has multiple hidden layers [21]. Through updating the weights amongst neurons and training the network, the whole network is capable of recovering input dataset by the maximum probability. The DBN is made up of two networks. A number of Restricted Boltzmann machine (RBMs) are superimposed at the bottom of the network, and the RBM of every layer alter the variable \(\theta\), such that the feature of the sampling data is transmitted to the hidden layer through the maximum probability, and later the extracted feature values are considered as an input of the succeeding RBM. The data are extracted layer-wise through several RBMs, and lastly, higher-level data feature values are attained. Along with the DBN is a BPNN entity classifier. Now, a label set is attached to the topmost layer. Simultaneously, the high-level eigenvalue extracted by several RBMs is considered the input of BPNN for supervised learning. Now, the network adjusts the parameter value between different networks based on the BP and, lastly, constructs the DBN. Figure 2 showcases the framework of DBN. DBN is composed of stacked RBM that is learned layer-wise via unsupervised greedy method. Assume the initial weight, train the initial RBM and utilize the output as an input to following layer. The output of lowermost RBM is frequently applied as an input of uppermost RBM. In this circumstance, assume that the neuron of the hidden layer h and visible layer v of RBM use binary numbers within \([0,1]\). Assume \((v,h)\), the energy function can be determined:  
\[E(v,\ h|\theta)=-\sum_{i=1}^{m}\sum_{j=1}^{n}v_{i}\omega_{ij}h_{j}-\sum_{i=1}^{ m}a_{i}v_{i}-\sum_{j=1}^{n}b_{j}h_{j} \tag{7}\]  
From the expression, \(a_{j}\) and \(b_{j}\) denotes the deviation parameter of the i-th visible unit and jth hidden unit correspondingly, where m, n represents the maximum possible range of visible and hidden layers; \(\omega_{ij}\) indicates the connection weight; \(\{a_{j},\ \omega_{ij},\ b_{j}\}\) shows the parameters \(\theta\) of RBM. \[P(v,\ h|\theta)=\frac{1}{Z_{\theta}}-e^{-E(v,h|\theta)} \tag{8}\]  
\[Z_{\theta}=\sum_{v}\sum_{h}e^{-E(v,h|\theta)} \tag{9}\]  
Now \(Z_{\theta}\) represent the regularization factor. Figure 2: Framework of DBN. RBM has two-layer NN such as h and v hidden and visual layers. The unsupervised learning capability of RBM has gained popularity; [PERSON] 2002 introduced contrast divergence (CD) algorithm, a fast-learning mechanism for RBM. The conditional probability is based on the principles of Bayesian formula:  
\[p\big{(}h_{j}=1|v\big{)} =\sigma\Bigg{(}b_{j}+\sum_{i}\omega_{ij}v_{i}\Bigg{)} \tag{10}\] \[p(v_{i}=1|h) =\sigma\Bigg{(}a_{i}+\sum_{i}\omega_{ij}h_{j}\Bigg{)} \tag{11}\]  
where \(\sigma\)(x) shows the logistic function. \[\sigma\)(x) =\frac{1}{1+e^{-x}} \tag{12}\]  
[PERSON] introduced CD algorithm to calculate the updated formula of every parameter. Especially initialization of the visible layer based on the initial input sample; then, evaluate the equation of conditional probability and the conditional probability of hidden neurons based on value of visible layer; last, Gibbs sampling is utilized for extracting a sample by the computed probability. \[W_{ij}=E\big{(}\big{\langle}V_{i}h_{j}\big{\rangle}_{data}-\big{\langle}V_{i}h_ {j}\big{\rangle}_{recon}\big{)} \tag{13}\]  
\[a_{i}=E(\left\langle V_{i}\right\rangle_{data}-\big{\langle}V_{i}\big{\rangle} _{recon}) \tag{14}\]  
\[b_{j}=E\big{(}\left\langle h_{j}\right\rangle_{data}-\big{\langle}h_{j}\big{ \rangle}_{recon}\big{)} \tag{15}\]  
Now, \(\epsilon\) represents the learning rate, \(\langle\cdot\rangle_{-}\)data and \(\langle\cdot\rangle_{-}\)recon is the mathematical expectation of the data itself and after model reconstruction, correspondingly. With that condition, appropriate weight was attained, and the same technique was used until the entire weight of RBM was rehabilitated.