Unknown Manifold

Unknown manifold research focuses on analyzing and modeling data distributed on low-dimensional structures embedded within high-dimensional spaces, without prior knowledge of the manifold's geometry. Current efforts concentrate on developing deep generative models, such as diffusion models and generative adversarial networks, and algorithms like projected subgradient methods, that effectively learn from and operate on this data without explicit manifold learning steps. This research is crucial for improving the performance of machine learning algorithms on complex, real-world datasets and has implications for diverse fields including robotics, network analysis, and signal processing.