Investigating Shape Variation Using Generalized Procrustes Analysis and Machine Learning

The biological investigation of a population’s shape diversity using digital images is typically reliant on geometrical morphometrics, which is an approach based on user-defined landmarks. In contrast to this traditional approach, the progress in deep learning has led to numerous applications ranging from specimen identification to object detection. Typically, these models tend to become black boxes, which limits the usage of recent deep learning models for biological applications. However, the progress in explainable artificial intelligence tries to overcome this limitation. This study compares the explanatory power of unsupervised machine learning models to traditional landmark-based approaches for population structure investigation. We apply convolutional autoencoders as well as Gaussian process latent variable models to two Nile tilapia datasets to investigate the latent structure using consensus clustering. The explanatory factors of the machine learning models were extracted and compared to generalized Procrustes analysis. Hypotheses based on the Bayes factor are formulated to test the unambiguity of population diversity unveiled by the machine learning models. The findings show that it is possible to obtain biologically meaningful results relying on unsupervised machine learning. Furthermore we show that the machine learning models unveil latent structures close to the true population clusters. We found that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>80</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the true population clusters relying on the convolutional autoencoder are significantly different to the remaining clusters. Similarly, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>60</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the true population clusters relying on the Gaussian process latent variable model are significantly different. We conclude that the machine learning models outperform generalized Procrustes analysis, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>16</mn><mo>%</mo></mrow></semantics></math></inline-formula> of the population cluster was found to be significantly different. However, the applied machine learning models still have limited biological explainability. We recommend further in-depth investigations to unveil the explanatory factors in the used model.