Barrett's Esophagus (BE) is the only precursor known to Esophageal Adenocarcinoma (EAC), a type of esophageal cancer with poor prognosis upon diagnosis. Therefore, diagnosing BE is crucial in preventing and treating esophageal cancer. While supervised machine learning supports BE diagnosis, high interobserver variability in histopathological training data limits these methods. Unsupervised representation learning via Variational Autoencoders (VAEs) shows promise, as they map input data to a lower-dimensional manifold with only useful features, characterizing BE progression for improved downstream tasks and insights. However, the VAE's Euclidean latent space distorts point relationships, hindering disease progression modeling. Geometric VAEs provide additional geometric structure to the latent space, with RHVAE assuming a Riemannian manifold and $\mathcal{S}$-VAE a hyperspherical manifold. Our study shows that $\mathcal{S}$-VAE outperforms vanilla VAE with better reconstruction losses, representation classification accuracies, and higher-quality generated images and interpolations in lower-dimensional settings. By disentangling rotation information from the latent space, we improve results further using a group-based architecture. Additionally, we take initial steps towards $\mathcal{S}$-AE, a novel autoencoder model generating qualitative images without a variational framework, but retaining benefits of autoencoders such as stability and reconstruction quality.

翻译：巴雷特食管（BE）是食管腺癌（EAC）已知的唯一癌前病变，此类食管癌确诊后预后极差。因此，BE诊断对食管癌的预防与治疗至关重要。尽管有监督机器学习可辅助BE诊断，但组织病理训练数据中存在的显著观察者间变异限制了这些方法的效果。基于变分自编码器（VAE）的无监督表征学习展现出潜力——该类方法将输入数据映射至仅保留有效特征的低维流形，从而刻画BE进展特征以改进下游任务并获取洞察。然而，VAE的欧几里得潜空间会扭曲点间关系，阻碍疾病进展建模。几何VAE为潜空间赋予额外几何结构，其中RHVAE假设黎曼流形而$\mathcal{S}$-VAE假设超球面流形。本研究表明，在低维设置下$\mathcal{S}$-VAE优于普通VAE：其重建损失更低、表征分类准确率更高、生成图像与插值质量更优。通过从潜空间中解耦旋转信息，我们进一步采用基于群组的结构提升了结果。此外，我们初步探索了$\mathcal{S}$-AE这一新型自编码器模型——该模型无需变分框架即可生成定性图像，同时保留了自编码器的稳定性与重建质量优势。