## 3 The Proposed Model
### Traffic Flow Prediction Using HDBN Model  
For forecasting the traffic flow in the near future, the HDBN model is derived. DBN is a vital process from DL. Restricted Boltzmann Machine (RBM) unit is a generative stochastic artificial neural network which can learn a probability distribution over the set of inputs. It is similar to Boltzmann machines. It can be represented as the orientation of all actions and utilization of resources to accomplish effective results. The RBM improve the  
Figure 1: Overall process of proposed method. transparency and accountability, permitting intervention to complement each other and eliminate overlapping [21]. There is no linking amongst all the neural units from all the layers of RBM technique, besides, every neural unit from the visible layer (VL) was linked for every neural unit from the hidden layer (HL). Besides, the resultant of every layers of RBM was utilized as input for next layer. The bottom layer of DBN approach implements a multilayer RBM infrastructure. The greedy technique was utilized for training the instance data layer by layer. Figure 2 showcases the infrastructure of DBN. The DBN composed of multiple layers of latent variables (\"hidden units\"), with connections between the layers but not between units within each layer. The parameters attained with trained the primary layer RBM were utilized as input of secondary layer RBM, and the parameters of all the layers were attained by analogy. The trained procedure goes to unsupervised learning. The joint configuration energy of VL and HL in RBM are demonstrated as:  
\[E(\
u,\ h|\theta)=-\sum_{i=1}^{n}a_{i}v_{i}-\sum_{j=1}^{m}b_{j}h_{i}-\sum_{i=1 }^{n}\sum_{j=1}^{m}v_{i}w_{ij}h_{j} \tag{2}\]  
where \(\theta=\left\{w_{ij},a_{i},b_{j}\right\}\), it can be linking weighted value amongst visible unit \(i\) and hidden unit \(j\), \(a_{i}\) refers the internal bias of VL neurons, and \(b_{j}\) can be HLs. If the parameter \(\theta\) is set, dependent upon the energy function, the joint probability distribution of VL and HL are attained in Equation (3) and linking it with Equation (4) as follows:  
\[P(\
u,\ h|\theta)=\frac{e^{-E(\
u,h|\theta)}}{Z^{\theta}} \tag{3}\]  
\[Z^{\theta}=\sum_{v,h}e^{-E(\
u,h|\theta)} \tag{4}\]  
If the state of VL \(\
u\) is identified, the activation probability of _jth_ neural unit of HL \(h\) is obtained:  
\[P\left(h_{j}=1\big{|}\
u,\ \theta\right)=\sigma\Bigg{(}b_{j}+\sum_{i}v_{i}w_{ij} \Bigg{)} \tag{5}\]  
Figure 2: Structure of DBN. If the HL state \(h\) can be recognized, the activation probability of \(ith\) neural unit of VL \(\
u\) is reached:  
\[P(v_{i}=1|h,\;\theta)=\sigma\Bigg{(}a_{i}+\sum_{i}h_{i}w_{ij}\Bigg{)} \tag{6}\]  
In which, \(\sigma(x)=\frac{1}{1+\text{exp}\;(-x)}\) refers the activation function, termed the sigmoid function. Every neuron is defining their state value as one or zero has probability \(P\). For the unsupervised learning method, the drive of trained RBM can be obtaining the parameter method that is offered by log-likelihood function as:  
\[L(\theta)=\sum_{n=1}^{N}ln(\
u^{n},h) \tag{7}\]  
\[\theta=argmax\chi L(\theta)=argmax\chi\sum_{n=1}^{N}ln(\
u^{n},h) \tag{8}\]  
The HDBN model is presented by the use of DBN with an adaptive learning step approach to enhance the convergence rate. Training of the DBN model is difficult, especially in terms of training numerous RBMs. So, proper learning data requires fixing, which is essential to train the DBN model, by the use of contrastive divergence. A comparatively high learning rate results in unbalanced training procedure and low learning rate leads to a poor convergence rate. For addressing this issue, the HDBN model is derived using adaptive learning step (ALS) for computing effectual learning rate. The step size is modified based on the sign changes.