## 4 Structure of the Networks and Input Features  
We apply several FFNNs to investigate the influence of interaction range (the distances with the neighbors) on pedestrian speed. These networks are fed with various input features for training. We analyze the results using cross-validation to control eventual prediction overfitting and to determine the optimal complexity of the networks in terms of layer and neuron numbers [28]. In this technique, we resample the dataset by randomly dividing the total dataset to 80% for training (i.e., UX experiments: 12,715 observations) and 20% for testing (i.e., UX experiments: 3178 observations). Furthermore, multiple iterations are applied following the bootstrap resampling technique to evaluate the error estimate precision and be able to determine whether an error difference is statistically significant [29,30] (see Figure 3). Randomly subsampling the training and testing datasets \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment** & **Factor** & **No. of Samples** & **Mean** & **SD** & **N** \\ \hline \multirow{4}{*}{UX} & Subject PD * speed (m/s) & & 0.219 & 0.111 & \\  & Subject PD headway (m) & & 0.595 & 0.11 & \\  & Predecessor PD headway (m) & & 0.608 & 0.124 & \\  & Follower PD headway (m) & & 0.588 & 0.109 & \\ \hline \multirow{4}{*}{UF} & Subject PD speed (m/s) & & 0.615 & 0.102 & \\  & Subject PD headway (m) & & 0.711 & 0.104 & \\  & Predecessor PD headway (m) & & 0.731 & 0.111 & \\  & Follower PD headway (m) & & 0.712 & 0.120 & \\ \hline \multirow{4}{*}{UM} & Subject PD speed (m/s) & & 0.660 & 0.095 & \\  & Subject PD headway (m) & & 0.694 & 0.136 & \\  & Predecessor PD headway (m) & & 0.689 & 0.121 & \\  & Follower PD headway (m) & & 0.706 & 0.143 & \\ \hline \multirow{4}{*}{UX} & Subject PD speed (m/s) & & 0.500 & 0.104 & \\  & Subject PD headway (m) & & 0.717 & 0.119 & \\  & Predecessor PD headway (m) & & 0.693 & 0.128 & \\ \cline{1-1}  & Follower PD headway (m) & & 0.704 & 0.126 & \\ \hline \hline \end{tabular}  
* PD is the abbreviation for ”pedestrian”.  
\end{table} 
Table 1: This table shows the descriptive statistics (number of pedestrians (N), mean, and standard deviation) for the Palestine dataset [26]. The second column contains the inputs and output that are used for the proposed FFNNs. Figure 2: The trajectories over time for a sample of UX experiments. allows us to obtain a distribution of the errors instead of a point estimate. The estimation is finally performed using the average of bootstrap subsamples error, whereas the precision of estimation is evaluated using the bootstrap confidence interval represented as a boxplot. To quantify the error between the predicted and real values of the speed, we use the mean squared error (MSE) loss function:  
\[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}\left(Y_{i}-\hat{Y}_{i}\right)^{2}, \tag{6}\]  
where \(n\) is the number of observations, \(Y\) is the vector of real speed values, and \(\hat{Y}\) is the vector of predicted values. The developed networks are trained using the Adam optimizer [31], with a learning rate of \(lr=0.003\). During the training phase, the hyperparameters, namely the number of hidden layers and the number of hidden neurons, are tuned to reach a robust model. In addition, the back-propagation algorithm [32] is used for training FFNNs by updating the weights' values. We fit the model using different epoch sizes and a batch size of 10, which in most cases is sufficient to verify the progress of learning. Moreover, the Sigmoid activation function is applied for all layers in the different versions of the developed algorithm. Finally, to build a prototype for the proposed prediction model, the Keras framework [33] is utilized. Different versions of the proposed FFNN are employed, varying in the number of input features fed into the input layer. These inputs indicate the movement characteristics of pedestrians walking in a single-file experimental setup. In the analysis, we focus on different combinations of the following headway distances as inputs:  
1.