## 3 Results
### Application of the \(\delta\) and IR Cluster Patterns to New Data  
To classify new roads according to the already determined clusters, it is necessary to find which cluster centroid is the closest to the new acoustic data. As an alternative, supervised machine-learning algorithms can be used and, among them, the k-nearest neighbors (k-NN) is the most common. Let us consider a road not included in the dataset used for determining the clusters (original data), with known \(\delta\) and IR hourly values (new data). The k-NN algorithm searches for the k-nearest original data, in Euclidean distance, closer to the new data, and the classification is decided by majority vote. If there are ties for the kth nearest vector, all candidates are included in the vote. Unfortunately, this procedure most often cannot be applied because the acoustic data for the road are unknown. Thus, it is necessary to look for an alternative classifier, hopefully linked to a specific feature of the road and/or to the corresponding traffic flow. Figure 6: Differences between the hourly values of the cluster patterns and the measured values in terms of root mean square (RMSE) (**a**,**b**) and percentage of error \(\varepsilon\) of being within an interval width (**c**,**d**). In noise monitoring surveys, to save time and reduce costs, stratified samplings of urban road traffic noise based on some attributes (i.e., road categorization) are commonly used. Their features and performances have been already analyzed, for instance, in [29; 30]. Traffic flow (q), that is, the number of vehicles passing a point per unit of time (24 h, 1 h, and so on), can be a potential parameter for such a linkage because it represents information (observed or estimated by transport models) usually available for urban roads and used for their categorization in noise studies [31]. In a previous paper [32], the decimal logarithm of the day-time (06:00-22:00) total traffic flow, hereinafter \"x\", has been proposed as a \"non-acoustic\" parameter to be applied to assign cluster membership. This choice was preferred to the 24-h traffic flow because of the observed large uncertainty of the night flow calculated by the traffic model [32]. Indeed, further investigations [33; 34] have shown that there are significant differences between the traffic flow data provided by the model and those measured. This points to the need for more accurate data and, on this issue, there is an increasing interest to obtain real traffic flow data, for instance, through methodologies based on video processing and object detection tools [35], or on travel time data obtained by Google Application Programming Interface (API) and Big Data treatment [36]. Figure 7a shows the histograms of the data (bin width of x = 0.1) according to their cluster membership. It can be seen that, for 12 out of 26 bins (46.2%), there is an overlap between the two distributions. In order to figure out a threshold value to discriminate the cluster membership, the procedure to determine an analytical representation of the distribution functions in each cluster, as described in [37; 38], was applied. The probability distributions for the two clusters P(x) can be obtained from the analytical fit of the cumulative distribution I(x) according to the following relationship:  
\[\text{P(x)}=\text{ln}(10)\cdot\text{f}^{\prime}(\text{x})\cdot\text{I(x)} \tag{8}\]  
where f(x) is a 3 rd order polynomial, f(x) is the derivative of f(x), and I(x) is the cumulative distributions of x. The fit functions f1 and f2 for P(x) obtained for the two clusters are as follows:  
\[\text{f}_{1}(\text{x})=0.129-1.931\text{x}+0.664x^{2}-0.057\text{x}^{3} \tag{9}\]  
\[\text{f}_{2}(\text{x})=-1.0499-0.835\text{x}+0.444\text{x}^{2}-0.046\text{x}^{3} \tag{10}\]  
They are plotted in Figure 7b for the two distributions and show the \"probability\" that a road with a given \"x\" belongs to clusters 1 (blue curve) and 2 (red curve), respectively.