Thus, here we propose a novel and computationally efficient image denoising method that is capable of producing an accurate output.
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research.
Herein, we propose a framework for nonlinear dimensionality reduction that generates a manifold in terms of smooth geodesics that is designed to treat problems in which manifold measurements are either sparse or corrupted by noise.
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure.
Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates.
In a topological sense, we describe these changes as switching between low-dimensional embedding manifolds underlying a group of evolving agents.