Low Dimensional Manifold

Low-dimensional manifold learning aims to uncover the underlying low-dimensional structure within high-dimensional data, assuming that complex datasets often reside near or on lower-dimensional manifolds embedded in their ambient space. Current research focuses on developing robust algorithms, such as those based on Ollivier-Ricci curvature, diffusion models, and graph neural networks, to effectively learn and represent these manifolds, often improving downstream tasks like classification, registration, and anomaly detection. This field is significant because it allows for efficient analysis and modeling of high-dimensional data, impacting diverse areas including image processing, single-cell genomics, and the development of more efficient machine learning models.