## 5 Results and Analysis  
Our research aims to investigate the influence of the follower, predecessor, and second predecessor pedestrians' headway distances on the speed behavior of a pedestrian. The investigation examines the isotropic nature of the interaction behavior, considering that a pedestrian interacts not only with pedestrians in their field of vision to regulate the speed but also with the pedestrians behind. We start training and testing several FFNNs with the Palestine dataset. To estimate the importance of different input features \((DF,D,DP)\) on predicting the speed of pedestrians, we first feed each distance alone to the FFNN and then a combination of features. Seven networks with different input features are developed and validated:  
1. In the networks \(DF\), \(D\), \(DP\), we have one input feature for each network: the headway distance of the follower pedestrian, subject pedestrian, and the predecessor pedestrian, respectively. 2. In networks \((DF+D)\), \((DF+DP)\), and \((D+DP)\), we predict the speed as a function of combinations of distances in front and behind to investigate the anisotropy of the pedestrians' interaction behavior. 3. The \((all)\) network fed with the headway distances of the subject pedestrian and neighbors altogether \((DF+D+DP)\). In Figure 6, the MSE values of the algorithms are visualized for training and testing phases using UX experiments, N = 20, 24, 30 samples. As we can see, the gap between the training and testing MSE results is not wide. That means the algorithms are reliable, and there are no overfitting problems. It is also observed that the speed prediction is enhanced with increasing input features. Figure 7 shows the relative MSEs of the algorithms taking \(D\)-input network for comparison. We predict the individual speed by training the networks  
Figure 4: Illustration of pedestrians’ positions in 1D scenario, indicating the investigated headway distances. Figure 5: The structure of the feedforward neural network with two hidden layers (3, 2). for several iterations following the bootstrap approach. Considering the impact of the influential factors, we compare the networks with the same number of inputs together. In networks with one input feature, the \(D\) improves the estimation of speed by 1.5% compared to the \(DF\) algorithm. That means the distance with a pedestrian in front has a greater impact on the speed prediction than the distance with the follower pedestrian. This result was confirmed previously, as the headway distance is the main dependency in many models [35]. Moreover, the algorithm with \(DP\) increased the MSE by 13% compared to the \(D\) algorithm. This result indicates that the headway distance of the second predecessor has no significant influence on the subject pedestrian's speed. In the case of two input factors, the algorithm \((DF+D)\) improves the performance of speed prediction by 16% and 11% in comparison with the \((DF+DP)\) and \((D+DP)\) networks, respectively. Interestingly, the combination of distance with the pedestrian in front and right behind improves the speed prediction compared to the combination of headway distances in front. From observing experiment videos, we notice that the pedestrians in relatively high densities start to adjust their speed when they approach the nearest neighbors to avoid colliding. This result demonstrates that the interaction behavior is not strictly anisotropic in single-file movement, contrary to classical modeling approaches that assume that only the front distances influence the speed. Therefore, it is suggested that a dynamical model that considers both distances \(D\) and \(DF\) is likely to describe more aspects of the single-file dynamics. Finally, the \((all)\) algorithm that was fed with all headway distances as inputs improves the results by 21% compared to the \(D\) algorithm (3% compared to the \((DF+D)\) algorithm). This result indicates that with many input features, we can improve the speed estimation with percent corresponding to the impact of the inputs.