Non Linear Manifold

Nonlinear manifold learning aims to uncover the underlying low-dimensional structure within high-dimensional data, often assuming data points lie near a curved, lower-dimensional surface. Current research focuses on developing algorithms that effectively identify and represent this structure, including methods leveraging graph-based approaches (e.g., Ollivier-Ricci curvature), neural networks (e.g., autoencoders, generative adversarial networks), and manifold-constrained optimization techniques. These advancements have significant implications for various fields, improving performance in tasks such as image quality assessment, human pose estimation, and federated learning by enabling more efficient and robust data representation and analysis.