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Barrett's Esophagus (BE) is the only precursor known to EsophagealAdenocarcinoma (EAC), a type of esophageal cancer with poor prognosis upondiagnosis. Therefore, diagnosing BE is crucial in preventing and treatingesophageal cancer. While supervised machine learning supports BE diagnosis,high interobserver variability in histopathological training data limits thesemethods. Unsupervised representation learning via Variational Autoencoders(VAEs) shows promise, as they map input data to a lower-dimensional manifoldwith only useful features, characterizing BE progression for improveddownstream tasks and insights. However, the VAE's Euclidean latent spacedistorts point relationships, hindering disease progression modeling. GeometricVAEs provide additional geometric structure to the latent space, with RHVAEassuming a Riemannian manifold and $\mathcal{S}$-VAE a hyperspherical manifold.Our study shows that $\mathcal{S}$-VAE outperforms vanilla VAE with betterreconstruction losses, representation classification accuracies, andhigher-quality generated images and interpolations in lower-dimensionalsettings. By disentangling rotation information from the latent space, weimprove results further using a group-based architecture. Additionally, we takeinitial steps towards $\mathcal{S}$-AE, a novel autoencoder model generatingqualitative images without a variational framework, but retaining benefits ofautoencoders such as stability and reconstruction quality.

Geometry-Aware Latent Representation Learning for Modeling Disease Progression of Barrett's Esophagus