## 3 Results
### Machine Learning-Based Processing  
The seismic data used for training the proposed ML architectures consist of 83, 147 pre-labeled events, of which 75,133 samples are from background noise signals acquired at the four volcanoes. They represent the most consistent part of the dataset, used to train our ML models; to improve the efficacy of the ML methods, an additional 8014 samples from known events, i.e., LPs, VTs, quarry blasts, and undersea explosions, recorded by seismic sensor networks are added to the dataset. These transient events can be considered a sort of variability and heterogeneity to assess the ML-based classification performances. Let us recall that for MLP training, seismic events have been preprocessed using LPC for extracting spectral features [60, 61], as well as signal parametrization to obtain waveform information [29], so the input vector for MLP model is composed of 80 components for each signal. Instead, the raw data, i.e., 24 s windowed signals, were used to train the CNN 1D model, with no data preprocessing. Starting from the results presented in [34], two experiments have been introduced aimed at the detection and classification of the background noise signals. The first experiment was carried out on all the background noise signals. The ML methods were trained to distinguish among the noise signals at the different sources used. As reported in Table 2, four classes of signals have been considered; the dataset results are balanced, since each class is approximately composed of the same number of signals. The second experiment has the same classes reported in the first experiment, with one more composed of transients, i.e., VTs, LPs, quarry blasts, and undersea explosions [34]. This class represents a set of \"no background signals\" used to validate the ML method's capability to learn and classify noise signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Campi Flegrei** & **Vesuvio** & **Ischia** & **Colima** & **Events** \\ \hline Experiment 1 & 18,622 & 18,837 & 18,837 & - \\ \hline Experiment 2 & 18,622 & 18,837 & 18,837 & 8014 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experiment setting: class sizes associated with each background noise source. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Campi Flegrei** & **Vesuvio** & **Ischia** & **Colima** & **Events** \\ \hline Experiment 1 & 18,622 & 18,837 & 18,837 & 18,837 & - \\ \hline Experiment 2 & 18,622 & 18,837 & 18,837 & 18,837 & 8014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characterization of the frequency content of the seismic noise recorded at the Campi Flegrei, Ischia, Vesuvius, and Colima volcanoes. The interpretation of the origin of the spectral peaks is based on the works described in the _Seismological Overview_ subsection. Our goal in both experiments is to discriminate the volcano fingerprint (in the stationary phase) across the background noise also in the presence of higher energy transient events. The performance evaluation for the MLP and CNN methods are calculated considering the known metrics, namely precision (P), recall (R), F1 score (F1), and accuracy (Acc). These measures are based on the evaluation of the following parameters:  
* _tp_ (true positive): is the number of samples correctly assigned to a class. * _tn_ (true negative) is the number of samples correctly not assigned to a given class. * _fp_ (false positive) is the number of samples wrongly assigned to a class. * _fn_ (false negative) is the number of samples wrongly not assigned to a given class. More precisely, these metrics are reported in Table 3: the precision describes how precise/accurate our model is out of those predicted positives; the recall calculates how many of the actual correctly classified our model captures by labeling them as true positives. The F1 score is the weighted average of precision and recall, while the accuracy is the simplest metrics, providing a ratio of correctly classified samples to the total sample dataset.