# Investigating Shape Variation Using Generalized Procrustes Analysis and Machine Learning
###### Abstract  
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 80% of the true population clusters relying on the convolutional autoencoder are significantly different to the remaining clusters. Similarly, 60% 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 16% 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. generalized procrustes analysis; machine learning; convolutional autoencoder; Gaussian process latent variable models +
Footnote †: journal: Applied Sociology  
0000-0001-9993-3300]M.W. their relative position and distance are measured [3]. These manually placed landmarks provide some standardizations and automation of morphometrics analysis [4]. Their application to the field of fish biology has been especially successful because, due to their bilateral symmetry, it is possible to capture biologically significant traits in a two-dimensional image [5; 6; 7; 8]. Nevertheless, placing landmarks in pictures can be quite labor-intensive and it requires prior biological knowledge (e.g., [4]). In this context, machine learning models can solve some of these limitations. Since the publication of Alexnet [9] and its successors (e.g., VGG16 [10] or ResNet [11]), convolutional neuronal networks (CNNs) became a standard model for computer vision tasks. In contrast to landmark-based approaches where scientists carefully place the landmarks on images, CNNs learn to extract features in order to fulfil a user-defined task. CNNs are frequently implemented to solve object recognition or object detection applications. In fish biology, these models were successfully used for fish recognition [12; 13; 14; 15; 16; 17]. Nevertheless, convolutional neuronal networks are black boxes and are hard to interpret [18]. Their behavior needs to be investigated after model training relying on prediction samples [19; 20; 21; 22]. The latent explanatory factors learned by the CNN, which were previously discussed to be the key factor for reliable machine learning models [23], still cannot be unveiled. This means that biological factors contributing to the results of a neuronal network-based model cannot be extracted and analyzed. This is a strong shortcoming in contrast to landmark-based analysis, where the landmarks can be interpreted in a biological manner.