# Estimating Road Segments Using Kernelized Averaging of GPS Trajectories
## 5 Conclusions  
We have described a procedure for cleaning noisy sets of GPS trajectories corresponding to road segments. This procedure includes, in the first stage, an oversampling of the trajectories, prior to the calculation of a centroid or the search for a medoid, which composes the second stage of the procedure. It also includes, as a third stage, the detection and suppression of potential outliers, which improves on average the HC-SIM measure for almost all centroid based methods. A down-sampling finalizes the procedure to produce centroid/medoid estimates whose lengths match the average length of the input trajectories.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Rank** & **Train** & **Test** & **Length** & **Points** & **Time** \\ \hline A & 68.5\% & 62.2\% & 99\% & 9882\% & 30 min \\ B & 67.1\% & 62.0\% & 99\% & 89\% & seconds \\ C & 70.4\% & 61.8\% & 101\% & 83\% & seconds \\ D & 68.0\% & 61.8\% & 99\% & 83\% & seconds \\ E & 68.3\% & 61.7\% & 99\% & 145\% & 30 min \\ F & 66.6\% & 61.5\% & 100\% & 70\% & seconds \\ G & 67.4\% & 61.2\% & 100\% & 107\% & 10 min \\ H & 66.6\% & 61.2\% & 102\% & 205\% & seconds \\ I & 68.1\% & 60.9\% & 99\% & 67\% & seconds \\ DTW Medoid & 57.3\% & 55.3\% & 98\% & 169\% & 1 h \\ CellNet & 64.7\% & 61.2\% & 96.3\% & 144\% & seconds \\ \hline \hline \end{tabular}
\end{table}
Table 2: Challenge results as produced by the organizers: ranking of the competing methods according to the HC-SIM measure (in %). The iTEKA method corresponds to methods A and E.  
Figure 8: Elapsed processing time as the size of the re-sampled trajectories, \(T\), varies (\(T\in\{50,100,200,300\}\)).  
The experiment allowed comparomg time elastic and Euclidean averaging approaches with more straightforward medoid approaches.  
Our experimentation showed that: (i) centroid based methods outperform medoid based methods; (ii) the outlier detection and removal step improves on average the HC-SIM of final centroid estimation, but not the HC-SIM of the medoid selection; and (iii) over-sampling seems to also be a valuable step.  
With the limited training data, it cannot be guaranteed that the comparative results presented here are effectively significant. However, it clearly emerged from our experimentation that centroid-based approaches outperform medoid-based approaches. Furthermore, the algorithmic complexity is clearly in favor to centroid-based approaches, since it is linear with the size of the sets of trajectories that are processed, whereas it is quadratic for medoid-based approaches.  
As a perspective, to improve the HC-SIM quality of the cleaned trajectory estimation, one should consider the optimization of the meta parameters (\(T\) and \(\tau\) essentially, as \(\
u\) or \(\gamma\) may be considered as a function of \(T\)) on each segment of road (instead on the whole set of segments), according to its topology. In that line of improvement, one should try first to clusterize the GPS datasets according to the segment shapes, and then optimize for each cluster the meta parameters.  
This research received no external funding.  
The author declares no conflict of interests.