# Contributing towards Representative PM Data Coverage by Utilizing Artificial Neural Networks
## 2 Materials and Methods
### Methodology  
Initially, as mentioned above, the AGP station was selected as a target station for which all the steps of the methodology were performed. This station had high percentages of data availability (>90%) for both pollutants and for all three years (2016-2018), which was important for the evaluation of the results. Accordingly, yearly averaged, maximum and minimum concentrations for PM\({}_{10}\) and PM\({}_{2.5}\) were calculated in AGP. These descriptive statistics are helpful during the discussion of the results and act as an initial description of the 2016-2018 PM conditions for this specific location. The selected machine learning scheme which was used in this study is an FFNN model designed for spatial point interpolation. According to [PERSON] et al., this type of architecture can effectively simulate the relationship between input and output to various degrees of accuracy, based on several parameters that are part of the networks structure (Figure 3) [55]. The FFNN is a multilayer perceptron and the information flow follows one direction, advancing from the input to the output without looping [56]. The equation through which the output of a neuron can be calculated is the following:  
\[y=f\left(\sum_{i=1}^{M}x_{i}w_{i}+b\right) \tag{1}\]  
where \(f\) is the activation function, \(x_{i}\) the inputs, \(w_{i}\) the synaptic weights and \(b\) the bias. The synaptic weights are the internal connections among the neurons of the network (Figure 3), and through adjustments of their values, the strength of the connections is modified [57]. The PM\({}_{10}\) and PM\({}_{2.5}\) concentrations were estimated by using AGP as a target station and the remaining stations' concentrations as inputs. The number of input stations is different for each pollutant (eight and five for PM\({}_{10}\) and PM\({}_{2.5}\), respectively). Three stations for PM\({}_{10}\) are not available for PM\({}_{2.5}\) due to limited data, and they were excluded. Additionally, the daily temperature and wind speed values at AGP were used as predictors in the model. Four different models were developed in order to compare their performance. For the first model, the predictors were only the data of the input stations. For the second, third and fourth model, the number of predictors/inputs increased by adding the temperature values, the wind speed values and both wind speed and temperature values, respectively. In all  
Figure 2: Monthly averaged concentrations for PM\({}_{10}\) and PM\({}_{2.5}\) ((**a,b**) respectively) and for the three-year time period (2016–2018) at AGP target station. four models, the output was the AGP PM concentrations. Eventually, eight models were created in total (four for PM\({}_{10}\) and four for PM\({}_{2.5}\)). The aim of this additive process was to investigate how much the meteorological parameters affect the accuracy of the estimations. Initially, the datasets (PM\({}_{10}\), PM\({}_{2.5}\), Temperature and Wind Speed) were randomly divided into the training (70%), validation (15%) and test (15%) subsets. While the pollutants and meteorological data points for these datasets where randomly selected from the 2016-2018 time period, they were common for all inputs of each individual network development. When the network used a data point for a random hour from a monitoring station, the same hour was selected for the remaining stations. This procedure was followed so as to retain the daily variability and avoid mixing seasons and even days due to the short-term fluctuations of the PM concentrations. The next step involved the selection of the optimum number of neurons in the hidden layer. The FFNN consists of three layers, the input, hidden and output layers [58]. The number of neurons in the input and output layers is completely determined by the inputs and outputs. The hidden layer size is an important part of the network architecture. In order to select the optimum architecture, the criterion that was followed was the minimization of the Mean Absolute Error (MAE) on the validation subset [59].