Hyperspherical Representation Learning of Axial Data via Axial VAEs with Watson Distribution

In recent years, axial data, where observations are treated as axes of direction, has gained prominence in a range of complex tasks, including gene expression data clustering, blind speech separation, and depth image analysis. However, prevailing methods for axial data modeling mainly rely on shallow probabilistic models, which often overlook the hidden and hierarchical dependencies in the latent space. These methods also require a separate, human-engineered feature extractor to obtain features from raw axial data for downstream tasks. This work introduces a novel framework, Axial Variational Autoencoders (AVAEs), for modeling and representation learning of axial data by leveraging a deep generative model, the variational autoencoder (VAE). Unlike existing approaches, our method can autonomously learn more expressive representations from axial data by designing a VAE that uses the Watson distribution as the latent prior. Furthermore, we introduce a tailored reparameterization technique to support stable training. We validate the effectiveness of our model through experiments on simulated axial datasets and a real-world application.