Generation without the residual model

For each group in the sequence of pathlet models, we can sample a new pathlet using equation 5.6 as described in section 5.3.2. The generated trajectory is then the concatenation of the generated pathlets. Note that for each generated pathlet, the timings used to reconstruct the pathlet are added to the timing at the end of the previous pathlet, so that the difference of time between the first point of a pathlet and the last point of the previous pathlet is the same as the difference of time between two consecutive points within a pathlet. This is needed to ensure a continuous representation of the timings through the whole generated trajectory.

Figure 7.6 shows generated trajectories for sequences of pathlet models extracted from trajectories T1, T2 and T3 with the normalised cut algorithm. Figure 7.7 shows generated trajectories for sequences of pathlet models extracted from trajectories T1, T2 and T3 with the greedy algorithm.

**Figure 7.6:** Trajectories generated with the normalised cut algorithm and the dynamic time warping algorithm.
[Generated from trajectory T1] $\includegraphics[height=40mm,keepaspectratio]{trajs/2c_lgt_dtw_woc.eps}$ [Generated from trajectory T2] $\includegraphics[height=40mm,keepaspectratio]{trajs/walter_lgt_dtw_woc.eps}$ [Generated from trajectory T3] $\includegraphics[height=40mm,keepaspectratio]{trajs/non_lgt_dtw_woc.eps}$

**Figure 7.7:** Trajectories generated with the greedy algorithm.
[Generated from trajectory T1] $\includegraphics[height=40mm,keepaspectratio]{trajs/2c_lgt_greedy_woc.eps}$ [Generated from trajectory T2] $\includegraphics[height=40mm,keepaspectratio]{trajs/walter_lgt_greedy_woc.eps}$ [Generated from trajectory T3] $\includegraphics[height=40mm,keepaspectratio]{trajs/non_lgt_greedy_woc.eps}$

One can notice some jumps in the generated trajectories, especially on figure 7.6. Since the points are linked by lines on figures 7.6 and 7.7, those jumps correspond to straight lines. Some of those jumps (the larger ones) correspond to problems of prediction of the VLMM. Generating a wrong pathlet state sequence generates a discontinuous trajectory since the ends of pathlets do not match.

We can see that the VLMM has more trouble modelling the sequence of pathlet models when we use the normalised cut algorithm and the dynamic time warping than when we use the greedy algorithm. This is due to the fact that the well formed pathlet groups extracted with the greedy algorithm give a more structured sequence of pathlet models, for structured trajectories. Outliers appearing in the pathlet groups extracted with the normalised cut algorithm tend to give less structured pathlet model sequences. If an outlier is modelled in a pathlet model, it generates an unlikely temporal relationship with the other pathlet models. A VLMM being trained on an unlikely sequence of pathlet models has more chance of selecting unsuitable pathlet models.