## 3 Experimental Results
### Self-Organizing Maps (SOMs)  
One of the major contributions of this work is the use of Self-Organizing Maps in the spike sorting of biosignals, as this type of neural network had not been used in this type of signal. A SOM, also known as a Kohonen map [33; 34], is a type of artificial neural network used for unsupervised learning and the visualization of high-dimensional data. SOMs are particularly effective for clustering and dimensionality reduction tasks. The network consists of a grid of interconnected nodes (see Figure 13), each representing a specific region in the input data space. During training, the SOM learns to map input data points to nodes in a way that preserves the underlying data topology. Neighboring nodes on the grid respond similarly to similar input patterns, leading to a self-organized representation of the input data in a lower-dimensional space. This arrangement enables the visualization of complex data relationships and grouping of similar data points into clusters on the grid. SOMs are especially useful for exploratory data analysis, pattern recognition, and data visualization. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Spike Shape** & **Number of Spikes** \\ \hline
0 & & 59 \\ \hline
1 & & 106 \\ \hline
2 & & 38 \\ \hline
4 & & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Groups formed with hierarchical clustering (human pancreatic data). Figure 13 provides insight into the weighting of each input variable across various segments of the map. This visualization allows us to discern the significance of each variable within each node of the map. However, a more comprehensive understanding of the variable importance within the map is encapsulated in Figure A4. In this illustration, a set of contrast graphs is presented for each individual variable. These visual representations offer a clearer indication of the variables that yield the most influence when activating each neuron within the map, thereby dictating the assignment of input data to these specific nodes. Figure A4 shows the predominant impact of each variable across distinct regions of the map through the pronounced red and orange hues. Unlike the representation in Figure 13, this graph deliberately amplifies the contrast between areas with high and low values. This emphasis serves to facilitate a more intuitive grasp of the variable influence distribution within the map. Figure 13: (**a**) A 6 \(\times\) 6 map for the macaque monkey data and (**b**) a 5 \(\times\) 5 map for the human pancreatic data. Figure 14a exhibits a density graph, an illustrative visualization that facilitates the identification of regions within the map housing the highest concentration of instances. This density mapping is depicted using a color scale that conveys the prevalence of data points within each node. It is important to note that the nodes within the map themselves do not directly correspond to the formed groups. Rather, these groups emerge later through the aggregation of nodes based on common characteristics. To assemble the groups, the method involves calculating the Euclidean distance between each neuron and its neighboring nodes. Illustrated in Figure 14b, the distance graph offers a visual representation of the formed map, facilitating the subsequent formation of groups. This process entails aggregating neurons sharing a comparable distance, as nodes belonging to the same group typically exhibit proximity to each other. As previously highlighted, it is imperative to note that the nodes within the map do not inherently equate to groups. However, these nodes are structured in a manner where adjacent nodes share analogous weight vectors. Consequently, each map node operates as a precursor to a group and subsequently undergoes hierarchical grouping.