# Deep Belief Networks (DBN) with IoT-Based Alzheimer's Disease Detection and Classification
## 3 Proposed System
### Deep Belief Network  
A Deep Belief Network (DBN) is a type of generative model that utilizes multiple processing layers to capture complex structures and abstractions in data. It consists of a series of individually trained Restricted Boltzmann Machines (RBMs) stacked on top of each other. The RBMs in a DBN are trained in an unsupervised manner, where the training process begins with an unsupervised stage. In a DBN, there are typically two processing layers in each of the RBMs, referred to as the \"visible\" layer and the \"hidden\" layer. The visible layer represents the observable entities or features of the data, while the hidden layer captures latent or hidden representations. The units within the same layer of an RBM do not have direct connections to each other. Instead, the interconnectedness between layers allows for the construction and reconstruction processes. The training of a DBN involves iteratively training each RBM in a layer-wise manner. The first RBM is trained using the visible layer as input, and its hidden layer activations become the visible layer for the next RBM. This process continues until all RBMs are trained. This layer-wise pretraining helps to fix problems that can occur when the network is initially set up with untrained, arbitrary connection weights. Using unsupervised learning techniques, generative stochastic neural networks can be learned from probability models. The RBM's network has two distinct processing levels, labelled \"visible\" and \"hidden\" in Figure 4. The units within the same layer have no connection to one another, but the construction and reconstruction processes are made possible by the interconnectedness of these layers. A large quantity of observable entities \((v_{1},v_{2},\ldots v_{i})\) make up the network's visible layer (\(v\)), which is trained on the unlabeled pattern structures fed into it, and a large number of unseen entities \(\left(h_{1},h_{2},\ldots h_{j}\right)\) Unseen nodes in the network have binary values, receive information from the seen nodes, and are able to reconstruct the patterns (\(h\)). All the obvious nodes talk to all the obvious nodes as a symmetric two-way matrix of weight \((S_{ij})\), in addition to the biases \((b_{i})\) and \((a_{j})\) that are already there. \[R(v,h)=\sum_{i\in vis}\frac{(v_{i}-b_{i})^{2}}{2\lambda_{i}^{2}}-\sum_{j\in hid }a_{j}h_{j}-\sum_{ij}\frac{v_{i}}{\lambda_{i}}h_{j}S_{ij} \tag{1}\]  
where \(\lambda\) represents the dispersion of the Gaussian noise in the \(i\)th visible dimension. The learning process may become more challenging if both the exposed and concealed units are Gaussians. The standard deviations of the assumed noise levels are used to calculate the coefficients of the quadratic \"containment\" terms that keep the activities within reasonable bounds. The energy function then takes the form (2). \[R(v,h)=\sum_{i\in vis}\frac{(v_{i}-b_{i})^{2}}{2\lambda_{i}^{2}}+\sum_{j\in hid }\frac{\left(h_{j}-a_{j}\right)^{2}}{2\lambda_{i}^{2}}-\sum_{ij}\frac{v_{i}h_ {j}}{\lambda_{i}\lambda_{j}}S_{ij} \tag{2}\]  
Data in the training set was used for guesses about the probabilities of the hidden units and to represent those predictions graphically (3). \[M(h_{j}=1)=l(a_{j}+\sum_{i}v_{i}w_{ij}) \tag{3}\]With just a sample of \(h\), we can reconstruct the invisible variable \(v^{\prime}\) at the visible level. Next, we collect a fresh set of \(h^{\prime}\) hidden activations (as shown in Step 4 of the Gibbs algorithm). \[M(v_{i}=1)=l\big{(}b_{i}+\sum h_{j}s_{ij}\big{)} \tag{4}\]  
The result of multiplying \(v^{\prime}\) by \(h^{\prime}\) from the outside was the key to this solution (negative phase). Proposed Amendments to the Law of the Weight Matrix (5)  
\[\Delta Sij\ =\ \eta\big{(}(v_{i}\bullet hj)_{data}\ -\ \big{(}v^{\prime}_{i} \bullet h^{\prime}j\big{)}_{model}\big{)} \tag{5}\]  
where learner speed \(\eta\) is assumed. Make the changes to \(b_{i}\) and \(h_{i}\) in Equations (6) and (7), where (\(\bullet\)) is a logistic activation function, respectively.