## 6 Experiments
### Results
#### 6.4.2 Batch Spectral Clustering Results  
For comparative purposes, we consider a batch spectral clustering algorithm [11] as benchmark. It is worth highlighting that this batch spectral clustering algorithm has complete information about all the descriptors from the beginning of the process, and can calculate all the mutual similitudes to perform the clustering process. Therefore, it constitutes a powerful benchmark to compare the relative performance of our proposal. To use this batch technique, the number of clusters has to be set initially and all the images must be available, for this reason it is not a good option to create maps incrementally, as the robot explores new areas. Figures 11 and 12 show the results after using a batch spectral clustering method and either HOG or gist descriptors respectively. These figures represent average silhouette versus number of clusters. Figure 11 shows the average silhouette when the HOG descriptor is used. This figure shows that the average silhouette decreases when the number of clusters continuously increases. The results obtained with the INNOVA dataset show that the silhouette is between 0.1 and 0.3; in particular if we observe the result with 6 clusters (which lead to the maximum silhouette with the proposed method) silhouette is 0.13 while with the proposed method is 0.3973. In the case of the Saarbrucken dataset, while the silhouette obtained with batch spectral clustering is between 0.1 and 0.3, the results with proposed incremental method are between \(-0.4\) and 0.3. Observing the result with 16 clusters  
Figure 11: Average silhouette after batch spectral clustering process using HOG versus number of clusters. Figure 12: Average silhouette after batch spectral clustering process using gist versus number of clusters. (which led to the best silhouette with the proposed method) we note this is about 0.15 as opposed to 0.2756 with the proposed algorithm. Finally, regarding the Freiburg dataset, while the results using batch spectral clustering are between 0.1 and 0.25, results using the incremental method are among \(-0.5\) and \(-0.15\). The maximum value of silhouette of the proposed method is equal to \(-0.1526\) with 30 clusters, while the batch clustering method provides a silhouette of 0.13 with the same number of clusters. Additionally, Figure 12 show the silhouette when the gist descriptor is used. In this case, the results are less similar to the results obtained with the proposed method. Again, the higher the number of clusters is, the lower the silhouette values are. The best silhouette obtained with gist and the INNOVA dataset is 0.2556 with 6 nodes, the batch clustering method leads to a silhouette equal to 0.38 with the same number of nodes. With the Saarbrucken dataset, silhouette results with a high number of clusters are around 0.25 and 0.4 with the batch method and 0.1262 (19 clusters) with the proposed method. Finally, the results output by the batch clustering method on Freiburg show a silhouette between 0.1 and 0.25 but using the proposed incremental clustering process the maximum silhouette is \(-0.1449\), obtained with 34 clusters. With 34 clusters the silhouette obtained with batch clustering is 0.15. The results of this comparative evaluation between the proposed method and the benchmark algorithm are summarized in Table 3. This table includes the maximum silhouette obtained with the proposed method, and the silhouette obtained with the batch spectral clustering with the same number of clusters. It is necessary to highlight the fact that the proposed method provides better results with HOG in the Innova and Saarbrucken datasets. It is especially relevant, considering that the proposed method permits building the map as the robot explores the environment (i.e., it works with incomplete visual information) but the batch clustering needs to have all the images captured before running the algorithm. The results with the Freiburg dataset are less conclusive, due to the features of this dataset, commented previously.