# Investigating Shape Variation Using Generalized Procrustes Analysis and Machine Learning
## 3 Experimental Results
### Latent Structure Investigation Relying on pCA  
The pCA result for GPA for both datasets is summarized in in the pCA matrix as well as the Bayes factor plot in Figure 13.  
The results show that minor individual population location structure was identified to be different. Three out of six locations in Ethiopia (Hawassa, Langano and Ziway) and one out of nineteen locations in Uganda (Victoria Sango Bay) were identified to be significantly different. We emphasize that the pCA matrix visualization may lead to incomprehensible results in the Bayes factor analysis due to the brightness. The Bayes factor investigation is based on the comparison of the intra-location similarity. Thus this value decreases, even if minor obvious relations were measured in the remaining locations. The results obtained by the B-GP-LVM are visualized in Figure 14.  
Figure 13: Visualization of the results obtained by pCA and the Bayes factor hypothesis test relying on GPA. Both pCA matrices show minor visible structure. Three of six locations of Ethiopia were found to be significantly different to the remaining populations. Similarly, one out of nineteen locations were identified to be significantly different in Uganda’s locations. (**a**) pCA and Bayes factor results for Ethiopia relying on GPA scaling. (**b**) pCA and Bayes factor results for Uganda relying on GPA scaling. The KyB population label in the pCA matrix was removed due to readability. The pCA matrix for Ethiopia appears to be noisy. However, the individual probability values of the intra population locations exceed the probability values of inter population locations. This led to four out of six populations in Ethiopia which were significantly different to the other populations. Different to the GPA, lake Tana appears to be significantly different to the remaining locations. This significant difference and distinctiveness of the Lake Tana population has also been reported at molecular genetic level [28; 29]. The pCA matrix for Uganda shows visible structure for the individual locations. The different locations in the same water bodies (e.g., the lake Victoria locations) are visible. However, similarities of these water bodies (e.g., Albert or Victoria) are visible as well. Eleven out of nineteen of Uganda's population locations significantly differed from the remaining locations. Finally, the results for cAE are summarized in the visualizations in the Figure 15.  
Figure 14: Visualization of the results obtained by pCA and the Bayes factor hypothesis test relying on GP-LVM. Both pCA matrices show visible structure. Four of six locations in Ethiopia were found to be significantly different to the remaining locations. Eleven out of nineteen locations were identified to be significantly different in Uganda’s locations. (**a**) pCA and Bayes factor results for Ethiopia relying on GP-LVM. (**b**) pCA and Bayes factor results for Uganda relying on GP-LVM. The KyB population label in the pCA matrix was removed due to readability. In both pCA matrices, the majority of locations can be clearly distinguished. All locations of Ethiopia were found to be significantly different to the remaining locations. Fourteen of nineteen locations in Uganda differed significantly. However, again the locations of Lake Viktoria did show similarities. We summarize our findings of the proposed approach in Table 3, where the population's locations (which were observed to be significantly different) are marked with a cross (\(\times\)). We observed that for all applied methods the locations Langano and Ziway significantly differed from the remaining populations in Ethiopia. Furthermore, the location Victoria Sango Bay in Uganda was observed to be significantly different, only relying on GPA scaled landmarks. The locations Kyoga Bukungu, Mulehe Musezero as well as the Sindi Farm in Uganda were never observed to be significantly different to the remaining locations. Figure 15: Visualization of the results obtained by pCA and the Bayes factor hypothesis test relying on cAE.