## 2 Neural Network Approach  
Before mentioning artificial neural networks (ANN), biological neurons should be discussed. Neurons in our brains are connected to each other through synapses, while signals are transmitted between neurons through each neuron cell bonds. The signals are carried to the neurons to which the synapses are bound, and when the sum of these signals exceeds a certain level or activation level, the neuron outputs and transmits to the other neurons with synapses. It is known that there are 100 billion of neurons in our brain. Each of these neurons makes around a thousand connections with each other. These complex connections enable us to achieve many functions such as thinking, linking events, and recording memories.  
During the last half century, researchers have been to put forward a mathematical model inspired by the human brain and its features. This model, which is called an artificial neural network, is built on multiple input lines, a connected neuron, and a single output system connected to the same neuron. In the illustration given in Figure 1, each input line has a value called a weight. This weight value is multiplied by the input value and the value of that line is found. All inputs are multiplied by the weights in the line they are located on and by the neuron to which they are connected, and the threshold value is added. The total value is found and passed through the activation function. Finally, the result is the output value of the neuron.  
The simple formulas of this structure are given below; in these formulas, \(i\) input and \(w\) weight are multiplied with each other, and the obtained results for each input and weight are added together to obtain the value of \(s\) output. For the Jth neuron,  
\[\mathbf{sum_{j}}=\sum\mathbf{input_{i}*weight_{ij}} \tag{1}\]  
\[\mathbf{output_{j}}=\mathbf{f_{sigmoid}}\left(\mathbf{sum_{j}}+\mathbf{ threshold_{j}}\right). \tag{2}\]  
With this sum value (1), the threshold value is added and the output of the neuron is obtained. When this value is passed through the activation function, then the value of that neuron will transmit to other neurons. In this study, the sigmoid function was selected as the activation function.  
When a young child learns to read and write, he or she generally must be educated in a class. The child must repeat the letter A several times to learn how to write it. This repetition occurs under the supervision of the teacher and feedback is given to the student about his/her mistakes. The same process could be applied to artificial neural networks. The data to be used in artificial neural networks are compared with the response of the network. As a result of this comparison, the obtained value is the error value. This error value should be close to zero. After the calculation of each error value, the weight values should be updated. This process continues until the error approaches zero. Neurons are traced backwards and their weights are updated according to the error rates. In Figure 1, the inputs are multiplied by the weights and transferred by neurons. The obtained result is compared to the target values and weights are adjusted again. With zero resets, learning is achieved and the training of the network is completed.  
The formulas used to update the weights with the back propagation algorithm of the network are given below:  
\[\mathbf{weight_{ij}}=\mathbf{weight_{ij}^{\prime}}+\mathbf{Learning\ rate\ error_{j}*input_{i}} \tag{3}\]  
\[\mathbf{error_{j}}=\mathbf{output_{j}*\left(1-output_{j}\right)*\left(target _{j}-output_{j}\right)}. \tag{4}\]  
The information taught to artificial neural networks is stored in the weight values of the connections of the network. Since the weight values are spread over the entire network, the memory of the network is also called distributed memory.