## 5 Experiments
### Creating Compact Maps through Clustering
#### 5.2.1 Clustering in the Quorum V Environment  
Figure 6 shows the results of the two clustering methods using FS as the descriptor depending on the parameter \(k_{1}\). Figure 7 shows the results using HOG depending on the parameter \(k_{2}\). Figure 8 shows the results using _gist_ depending on the parameter \(k_{3}\) and with \(n_{masks}=16\). These figures present the graphs that determine the goodness of each configuration to carry out the mapping task through clustering. The three figures show the moment of inertia and average silhouettes vs. the number of clusters. In all cases, the range of the vertical axis is the same, for comparison purposes. Furthermore, Figure 9 shows the computing time necessary to cluster the environment through the two clustering methods.  
Regarding the parameters used to measure the compactness of the maps, the lower the moment of inertia and the higher the silhouettes are, the more compact the map is. Generally, Method 1 (spectral clustering) produces the best results. Method 2 (SOM) does not improve these results. As for the use of the global appearance descriptor with the spectral clustering method, FS is not capable of creating reliable clusters. As for HOG, the moment of inertia and silhouettes depend considerably on the value of \(k_{2}\). When \(k_{2}\) is low, the results are poor, but when \(k_{2}>8\), the moment of inertia, as well as the silhouettes improve significantly. At last, regarding the _gist_ descriptor, low values of \(k_{3}\) produce low silhouettes and high moments of inertia, and high values of this parameter imply better results.  
As for the computation time required to carry out the clustering through the two methods, the SOM method presents the highest values. The computing time required for the clustering process through the FS descriptor is the highest, whereas the time through HOG or _gist_ is lower, and the fastest one would be determined by the value of either \(k_{2}\) or \(k_{3}\).  
Figure 6: Results of the two clustering methods: average moment of inertia, average silhouette of points, and average silhouette of descriptors vs. number of clusters, when using FS in the Quorum V environment. SOM, Self-Organizing Maps.  
Figure 7: Results of the two clustering methods: average moment of inertia, average silhouette of points, and average silhouette of descriptors vs. number of clusters, when using HOG in the Quorum V environment.  
As expected, the more components the descriptor has, the more time is required. In Section 5.3, the trade-off descriptor size-localization accuracy will be studied.  
Therefore, in the case of HOG, a value of \(k_{2}=32\) or \(k_{2}=64\) could be a good choice to achieve a compromise between compactness and computing time, and in the case of _gist_, an intermediate value of \(k_{3}\) could be also a good choice for the same purpose. The FS descriptor presents, in general, the worst results: the moment of inertia is higher, and the silhouettes are lower, in general. Hence, the best clustering results are obtained through the use of the spectral clustering method and the use of HOG (for a configuration of \(k_{2}=[32,64]\)) or _gist_ (for a configuration of \(k_{3}=[16,32]\) and \(n_{masks}=16\)) as the global appearance descriptor. Figure 10 shows a bird's eye view of the clusters obtained with spectral clustering and gistwith \(k_{3}=32\) and \(n_{masks}=16\).