Figure 5.10: Fitness values for di erent parameter values A and B, when pedestrian trajectories are simulated with the social-force model and the force speci - cation in Eq. (5.5). The darker the shade is, the better the tness, for the corresponding combination of A and B values. Next, let us look at the resulting parameter values for the best performing model speci cation, which is the Elliptical II speci cation with a variable parameter N and a variable . The resulting parameter values of our three datasets are put after each other in matrix P , where each row corresponds to a pedestrian and each column corresponds to a parameter. The covariance C = cov(P ) is computed and in order to analyze how di erent parameters correlate with each other, we compute the correlation coe cient R(i; j) which measures how well parameter i correlates with parameter j. It is de ned via the covariance C as p C(i; j) R(i; j) = (5.14) : C(i; i)C(j; j) The correlation coe cient spans from perfect correlation R(i; j) = 1 (rows i and j di er only by a scaling constant) via zero correlation R(i; j) = 0 (C(i; j) = 0) to perfect de-correlation R(i; j) = 1, which means that columns i and j are orthogonal. The resulting correlation coe cients R(i; j) are in Tab. 5.4 with exceptional values highlighted in boldface. We see for example that parameter A correlates strongly 91
Figure 5.10: Fitness values for di erent parameter values A and B, when pedestrian trajectories are simulated with the social-force model and the force speci - cation in Eq. (5.5). The darker the shade is, the better the tness, for the corresponding combination of A and B values. Next, let us look at the resulting parameter values for the best performing model speci cation, which is the Elliptical II speci cation with a variable parameter N and a variable . The resulting parameter values of our three datasets are put after each other in matrix P , where each row corresponds to a pedestrian and each column corresponds to a parameter. The covariance C = cov(P ) is computed and in order to analyze how di erent parameters correlate with each other, we compute the correlation coe cient R(i; j) which measures how well parameter i correlates with parameter j. It is de ned via the covariance C as p R(i; j) = C(i; j) (5.14) : C(i; i)C(j; j) The correlation coe cient spans from perfect correlation R(i; j) = 1 (rows i and j di er only by a scaling constant) via zero correlation R(i; j) = 0 (C(i; j) = 0) to perfect de-correlation R(i; j) = 1, which means that columns i and j are orthogonal. The resulting correlation coe cients R(i; j) are in Tab. 5.4 with exceptional values highlighted in boldface. We see for example that parameter A correlates strongly 91
Data-Driven_Modeling_of_Pedestrian_Crowds.docx