# Spherical Tree-Structured SOM and Its Application to Hierarchical Clustering
## 3 Results
### Data Clustering Utilizing the Tree Structure of the S-TS-SOM  
The S-TS-SOM proposed in this paper has a structure in which the number of nodes increases from the inner to outer layers. Therefore, we believe that by checking the results for each layer, we can obtain results with different data classification granularity. We consider that the layers closer to the inner layer have a smaller number of nodes, so the data are more roughly classified. Moreover, the layers closer to the outer layer have a larger number of nodes, so the data are more finely classified. In this section, we check the results of each layer of the S-TS-SOM to determine if the adjustment of the number of clusters is successful.  
We used the Zoo dataset of UCI as the experimental data [19]. The Zoo dataset is composed of 101 species of animals, where each animal has 17 attributes. We used 16 attributes as the input and excluded the \"type\" attribute. Therefore, each animal was treated as a vector with 16 elements. Because the \"legs\" attribute is not a Boolean value, we used the value divided by the maximum value in the \"legs\" attribute as the input. The \"type\" attribute classifies each animal into an animal type using a number from one to seven. We set the number of layers of the S-TS-SOM to L = 2 and the number of updates for each layer to 100. Figure 9 shows the results. In Section 3.1, we presented only the outermost layer of the S-TS-SOM. However, the other layers are also shown in Figure 9, and the labels are color-coded according to the \"type\" attribute. In Figure 9, the top row shows the front of the map, and the bottom row shows the back of the map. We plotted the data placed on the same winner node in the same direction as seen from the center of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**(I) S-T S-SOM**} & \multicolumn{4}{c}{**(2) S-SOM**} & \multicolumn{4}{c}{**(I)/(2)**} \\ \hline \
\begin{tabular}{c} **Number of** \\ **Outermost** \\ **Nodes** \\ \end{tabular} &
\begin{tabular}{c} **Number** \\ **of Search** \\ **Nodes** \\ \end{tabular} & **Purity** & **NMI** & **Time (s)** & **Purity** & **NMI** & **Time (s)** & **Purity** & **NMI** & **Time (s)** \\ \hline
80 & \(24\times 101\) & 0.761 & 0.481 & 215.13 & \(80\times 101\) & 0.787 & 0.508 & 235.07 & 0.967 & 0.948 & 0.915 \\
320 & \(28\times 101\) & 0.822 & 0.443 & 409.06 & \(320\times 101\) & 0.823 & 0.449 & 941.17 & 0.998 & 0.986 & 0.435 \\
1280 & \(32\times 101\) & 0.864 & 0.409 & 789.74 & \(1280\times 101\) & 0.844 & 0.401 & 3678.23 & 1.024 & 1.020 & 0.215 \\
5120 & \(36\times 101\) & 0.895 & 0.381 & 2011.44 & \(5120\times 101\) & 0.858 & 0.365 & 16,560.32 & 1.043 & 1.046 & 0.121 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance of the S-TS-SOM and S-SOM.  
the sphere. If only one data point was placed at a node in a layer other than the outermost layer, the branch growth was stopped for the sake of visibility.  
In the results of Figure 9, in the 0 th layer, the clusters are roughly formed according to each \"type\" attribute. As the number of layers increases, we can see that the clusters branch into smaller clusters. Note that some data have stopped branching because the input values are the same. Table 1 shows the groups of data with the same input value. From this experiment, we confirmed that the S-TS-SOM can extract the granularity of clustering on the tree structure by checking each layer after the data were learned.