# Investigating Shape Variation Using Generalized Procrustes Analysis and Machine Learning
## 4 Discussion  
This study investigated the quality of extracted GPA scaled coordinates in contrast to machine learning-based features. The quality was measured by the differentiability of the known population locations. To obtain comparable latent structures, the consensus clustering method was extended by a probabilistic interpretation as well as a hypothesis test. Manually placed landmarks were extracted from image datasets obtained in Ethiopia and Uganda. These landmarks were processed using GPA. The results were statistically investigated. We observed significant relation of the GPA scaled coordinates to the population locations. Furthermore, a significant relation of the locations to the Procrustes distance was obtained. Relying on the visualization of the GPA coordinates (see Figure 6), as well as the Spearman's rank correlation tests, we concluded that the landmark-based approach results in a interpretable reduction of the image data with significant correlation to the populations location. Nevertheless, the GPA-scaled coordinate visualizations and hypotheses tests do not quantify the discriminability of the populations unveiled by the GPA approach. Furthermore, the multivariate analysis showed overlapping population distribution in the PCA and ICA reduced GPA coordinates. The proposed pCA was able to unveil significant differences for three out of six locations in Ethiopia. One of nineteen locations was found to be significantly different from the other locations in Uganda. Ref. [24] obtained similar results for supervised Nile tilapia location classification using biologically interpretable GP-LVM features as well as GPA-scaled coordinates. Their results, enhanced by the latent structure investigation of this study show, that classic landmark based-approaches are limited in terms of information discovery. Regardless, the landmark-based approaches outperform the autonomous deep learning counterparts in terms of biological explainability. The machine learning-based approaches were investigated with visualization methods and major focus on biological uninformative image regions was removed. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Abbr.** & **GPA** & **GP-LVM** & **cAE** \\ \hline \multirow{4}{*}{**GPA**} & Chamo & Cham & & & \(\times\) \\  & Hawassa & Hawa & \(\times\) & & \(\times\) \\  & Koka & Koka & & \(\times\) & \(\times\) \\  & Langano & Lang & \(\times\) & \(\times\) & \(\times\) \\  & Tana & Tana & & \(\times\) & \(\times\) \\  & Ziway & Ziwa & \(\times\) & \(\times\) & \(\times\) \\ \hline \multirow{4}{*}{**GPA**} & [PERSON] & ViKak & & & \(\times\) \\  & [PERSON] & ViM & & \(\times\) & \(\times\) \\  & [PERSON] & ViG & & \(\times\) & \(\times\) \\  & [PERSON] & ViSB & \(\times\) & & \\  & [PERSON] & ViKam & & \(\times\) & \\  & [PERSON] & AlN & & \(\times\) & \(\times\) \\  & [PERSON] & AlK & & & \(\times\) \\  & [PERSON] & [PERSON] & & \(\times\) & \(\times\) \\  & Kazinga Channel Katungulu & KaC & & \(\times\) & \(\times\) \\  & [PERSON] & EdK & & \(\times\) & \(\times\) \\  & [PERSON] & EdR & & & \(\times\) \\  & [PERSON] & KyK & & \(\times\) & \(\times\) \\  & [PERSON] & [PERSON] & & & \\  & [PERSON] & [PERSON] & & & \(\times\) \\  & [PERSON] & [PERSON] & & & \\  & [PERSON] & Ka & & \(\times\) & \(\times\) \\  & Bangena Farm & BF & & \(\times\) & \(\times\) \\  & Sindi Farm & SF & & & \\  & Rwitabingi Farm & RF & & \(\times\) & \(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of results obtained with generalized procrustes analysis (GPA), Gaussian process latent variable models (GP-LVM) as well as deep convolutional autoencoder (cAE). The significantly different locations are indicated with a cross (\(\times\)). In contrast to the manually placed landmarks of the GPA, the GP-LVM learns a latent representation of the specimen images. After training, the model reproduces the image content including background information such as specimen mounting material.