4 Artificial Neural networks

\label{artificial-neural-networks}
An artificial neural network (ANN) is a soft computing technique that can be widely used to process the information [13-14]. It is inspired through biological nervous systems, such as the working mechanism of brain. It is represented in terms of weighted directed graphs in which nodes act as artificial neurons and directed edges between neurons defined weights. It can be divided into two categories-feed-forward and recurrent networks. The feed-forward networks are static, whereas, recurrent networks are dynamic systems. That is, they produce only one set of output values rather than a sequence of values from a given input. The Feed-forward networks are memory-less and independent of the previous network state. When a new input pattern is presented, the neuron outputs are computed. Because of the feedback paths, the inputs to each neuron are then modified, which leads the network to enter a new state. In literature, it is found that the multilayer neural networks (MLNNs) have been successfully implemented in decision support systems for disease diagnosis systems [27-28]. In Multi-layer perceptron (MLP), [29-32] multiple layers of neurons are present, but the minimum lays are three i.e. input layer, one hidden layer, and an output layer which is responsible to generate results. It is also observed that the back-propagation (BP) algorithm [10] is widely used to train the network. Apart from the input layer, every neuron in the other layers acts as a computational element with a nonlinear activation function. The principle of the neural network is that when data are available at the input layer, the network neurons run calculations in the consecutive layers until an output value is obtained at each of the output neurons. The output of neural network specifies the appropriate class for the input data. Each neuron in the input and hidden layers is connected to all other neurons of the next layer by some weight values. The neurons of hidden layers are responsible to compute the weighted sums of their inputs and add a threshold. Fig. 2: shows the structure of multilayer perceptron using an input layer, hidden layer and output layer. The input layer represents the attributes of datasets, working of hidden layer represents the attributes of datasets which are not linearly separated and output layer provides the desired results. A threshold node is also added in input layer which specifies the weight function. The resulting sums are used to obtain the activity of the neurons by applying a sigmoid activation function. This process is defined as follows:
\begin{equation} p_{j}=\sum_{i=1}^{n}{w_{j,i}x_{i}+\theta_{j},\ \ \ \ m_{j}=f_{j}(p_{j})}\nonumber \\ \end{equation}
Where pj is the linear combination of inputs x1,x2, . . . ,xn, and the threshold \(\theta_{j}\), wji is the connection weight between the input xi and the neuron j, and fj is the activation function of the jth neuron, and mj is the output. The sigmoid function is a common choice of activation function. It is defined as
\begin{equation} f\left(t\right)=\frac{1}{1+e^{-t}}\nonumber \\ \end{equation}
To train the MLP, the back propagation learning method has been used [32] which is a gradient descent method for the adaptation of the weights. All the weight vectors (w) are initialized with small random values from a pseudorandom sequence generator.However, this process can take too many steps to train the network, and the adjusted weights are computed at each step. To overcome the above mentioned problems, a particle swarm optimization based approach is utilized to compute the optimal value of the weight and threshold functions,because PSO havethe capability to determine weight parallel and finding the optimal solutions.
Figure 2: Three layer feed forward neural network: one input, one hidden layer and one output layer for predicting Dengue disease