## 4 Neural Analysis  
### SOM Method  
The analysis of the extracted features was carried out using the SOM neural network [43]. The use of the SOM in this type of application is motivated by its ability to determine the intrinsic structure of the data and at the same time to test the efficiency of the proposed parameterization strategy. In future developments, we plan to create a supervised automatic system for the real-time classification of the two types of tremors using the parameterization tested with the SOM. The SOM algorithm has been applied successfully in the field of seismology and volcanology for clustering problems [31; 33; 35; 36; 38; 39; 44; 45; 46; 47; 48]. Being unsupervised, it can be applied in all cases where there is no priori information on the data as it will use similarity measures to discover their hidden structures and group them. Furthermore, as a visualization technique, the SOM realizes a non-linear projection of the data in a map that preserves their topological and metric characteristics and which, being generally two-dimensional, allows an easy interpretation of the results. The SOM learning is competitive and cooperative: for each input presented to the network the winning node (competitive aspect) is identified, i.e., the one whose prototype is most similar to the input in terms of Euclidean distance; after that, the weights of the winning node and its topological neighbors (cooperative aspect) are updated (mathematical details in [49]). In this way, not only the winner but also its whole neighborhood is moved closer to the input pattern. The updating rule uses a decreasing neighborhood function of the distance between two nodes on the map grid, usually the Gaussian neighborhood function. The neighborhood function determines how strongly the nodes are connected to each other; this defines the region of influence that an input sample has on the SOM map. The process is iterated until the final map is obtained in which topologically near nodes contain similar inputs, generally. The architecture of an SOM network presents two layers, one of the input neurons and one of the output neurons. Each input unit is connected to all nodes of the output layer and each of them has an associated prototype vector or weight vector, whose dimension is  
Figure 5: The plot of the feature vectors (34 spectral parameters + 18 waveform characteristics = 52 coefficients for each 1 min signal segment) of three hours of signal (from 21:00 UTC to midnight) of fumarolic tremors extracted from 1 min signal segments recorded from 21:00 UTC to midnight recorded on 1 December 2018 with SDEs (**a**) and 15 November 2018 without SDEs (**b**). In each plot, 180 feature vectors are represented with red solid lines for tremors with SDEs (**a**) and with solid blue lines for tremors without SDEs (**b**). The stacking of the curves (black dots on the black lines) is also shown to underline the difference between the encoding of the two types of tremor. equal to that of the input vector. A neighborhood relation that defines the map typology or structure connects adjacent nodes. In our application, we use a local hexagonal structure and a global toroid shape for the map, which is visualized as a sheet for simplifying the representation of clusters. Our map has a size of 4 \(\times\) 3 = 12 nodes. The optimal number of nodes to use for the map cannot be established a priori because it depends on the type of application and how detailed the generated clusters must be. We have conducted several tests, varying the size of the map, and we have seen that the chosen size achieves good data clustering. The yellow hexagons identify non-empty nodes and their size corresponds to the number of input vectors that fall into each of them (data density). The gray hexagons between the yellow ones show the Euclidean distances between the nodes according to a gray scale: black or darker gray indicates a clear separation between the nodes, while white or light gray indicates similar nodes. Empty nodes are also colored using the same gray scale.