## 3 Results  
### Determination of Clusters and Patterns of Hourly Values of \(\delta\) and IR  
The clustering algorithms ranking based on their performance as determined by all the validation measures showed that the best solution was the k-means agglomeration algorithm, a centroid-based clustering, and a division into two clusters. The obtained partition into two groups corresponds to the minimal discrimination among the data, and this low discrimination enables an easier association of new data with the determined clusters. Table 2 reports the distribution of the sites in each road type and cluster, compared also with the distribution obtained by the DIANA algorithm applied earlier to the hourly IR values only [8]. The two classifications are rather similar as they overlap for 93.3%, that is, 93.3% of all sites are classified in the same category by both clustering algorithms and the percentage of disagreement is 6.7% of pairs. Cluster 2, with the largest number of sites, includes the majority of \"F\" road types (local roads with low traffic flow), whereas cluster 1 includes the majority of sites in the remaining roads.  
The multidimensional scaling (MDS) applied to the data provided the bi-dimensional plot given in Figure 2, where the two clusters obtained by k-means look satisfactorily separated.  
Figure 3 reports, for each cluster, the 24-h pattern of the hourly median values (thick lines) \(\pm\) the median absolute deviation (MAD, grey area) for both \(\delta\) and IR, as well as the observed time pattern  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multirow{2}{*}{**Clustering**} & \multicolumn{2}{c}{**k-Means**} & \multicolumn{2}{c}{**DIANA [8]**} \\  & & \multicolumn{2}{c}{**(Accounting for \(\delta\) and IR)**} & \multicolumn{2}{c}{**(Accounting for IR)**} \\ \hline  & **Cluster** & **1** & **2** & **1** & **2** \\ \hline  & **N. of sites (\%)** & 40 (44.4) & 50 (55.6) & 34 (37.8) & 56 (62.2) \\ \hline  & A (motorway) & 2 (100) & 0 (100) & 2 (100) & 0 (0) \\ \cline{2-5}
**Road Type** & D (thoroughfare roads) & 4 (57.1) & 3 (42.9) & 4 (57.1) & 3 (42.9) \\ \cline{2-5}  & E (urban district roads) & 20 (70.0) & 9 (30.0) & 16 (55.2) & 13 (44.8) \\ \cline{2-5}  & F (urban local roads) & 14 (26.9) & 38 (73.1) & 12 (23.1) & 40 (76.9) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Distribution of the 90 sites in the two clusters and type of road; percentage values are between (). IR, intermittency ratio.  
Figure 2: Bi-dimensional plot of the two clusters obtained by k-means. Dimension 1 and 2 explain 37.8% and 13.7% of the variance, respectively. The rectangular frames highlight the two sites with the greatest distance (dissimilarity) between them in the bi-dimensional plot.  
(thin lines) for each of the sites included in the cluster. The patterns show that, in the night period (22:00-06:00), the IR values are the highest for both clusters because of the presence of noise events clearly emerging above the background noise, which is lower than that observed during the day-time. The hourly IR values for cluster 2 are higher than those for cluster 1 because the traffic flow for the sites belonging to cluster 2 is lower (mainly local roads) than that for the sites belonging to cluster 1. Figure 4 shows the straight comparison between the time patterns for the two clusters. The largest differences between the two clusters are observed during the night-time for \(\delta\) and between 10:00 and 16:00 for IR. Thus, these periods are the most suitable to discriminate between the two clusters.  
Figure 4: Comparison of the time patterns of \(\delta\) and IR parameters for the two clusters obtained by k-means. Thick lines represent hourly median values and shaded areas correspond to \(\pm\) MAD.  
Figure 3: Time patterns of \(\delta\) and intermittency ratio (IR) parameters for the two clusters obtained by k-means (median values represented by thick lines and grey areas corresponding to \(\pm\) median absolute deviation (MAD)) and actual values at each site (thin lines).