# Analysing Urban Traffic Patterns with Neural Networks and COVID-19 Response Data
## 3 Methodology and Data
### Methodology of the Study
#### 3.2.2 Methodology of Modelling--Artificial Neural Networks  
The concept of artificial neural networks, one of the most commonly used tools in machine learning, was developed at the beginning of the 1950s, but it gained more attention from researchers only in the last decades due to a significant increase in computer technologies. The authors aimed to imitate the learning process in a biological neural network, which consists of approximately 86 billion neurons interconnected by more than \(10^{14}\) synaptic connections. Neurons are designed for transmitting, processing, and storing information, with information being transmitted between neurons via electrical signals. The basic parts of a neuron are the cell body and two types of processes: dendrites and axons. Dendrites are short processes representing the signal input site into the neuron's cell body. The place where a signal is transmitted from one neuron to another is called a synapse. In a synapse, the signal can be amplified (excitation) or weakened (inhibition) before entering the cell body. All incoming signals from surrounding neurons are aggregated in the cell body, creating the neuron's internal potential. If this potential exceeds a certain threshold, the neuron generates an output signal, which exits the neuron through a single output process called an axon. The so-called Hebbian rule is utilised in the learning process of artificial neural networks. Put simply, the input neuron's activity leads to the neuron's activity on the output side. The essence of the learning process is the formation of connections, thus creating so-called memory traces. The forgetting process is represented by the interruption of synaptic connections that could excite the neuron. In the mathematical model of an artificial neuron, this rule is reflected in synaptic weights (\(w\)), which control the influence of input on excitation (positive weight values) or inhibition (negative weight values) of the neuron. Adjusting these weights during learning is crucial for achieving good results in artificial neural networks. The mathematical model of the most commonly used artificial neuron is depicted in the following figure (Figure 7). Several types of formal models of artificial neurons exist, but the most commonly used one is the perceptron, designed by [PERSON] in 1958 [53; 54]. The essence of the perceptron is the computation of the artificial neuron's internal potential, which is given as the weighted sum of inputs. This potential is further processed by an activation function, typically one of the S-shaped curves. The most commonly used is a sigmoid function, given by the following equation:\[f(x)=\frac{1}{1+e^{-x}}.\]  
However, the perceptron can only be used to solve linearly separable problems. The solution involves using multiple perceptrons arranged into several layers for more complex tasks. The learning process then takes place in the so-called hidden layers. Thus, the network contains one or more layers of neurons that are neither input nor output. Multi-layer perceptron networks (MLPs) are the most widely used type of artificial neural networks in predictive analysis. These networks can tackle more complex problems by utilising each hidden layer to extract features and recognise patterns, enabling them to effectively perform intricate classification or regression tasks. MLP networks are, therefore, suitable for solving any problem whose essence is predicting the values of the modelled (output) variable. However, it is important to set or search for the correct topology of this network. Specifically, this involves setting the number of hidden (computational) layers and the (maximum) number of neurons in them, as well as choosing a suitable activation function, which can be the sigmoid mentioned above but also other functions such as the hyperbolic tangent or the ReLU function. The goal is effective learning of the neural network on the training dataset, especially its good generalisation ability, i.e., its use of data outside the training dataset.