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Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear decomposition methods, onto lower-dimensional latent manifolds, with the goal of either visualizing ...
Uniform Manifold Approximation and Projection This page was last edited on 18 December 2019, at 07:00 (UTC). Text is available under the Creative Commons ...
Nonlinear dimensionality reduction#Uniform manifold approximation and projection; Retrieved from "https: ...
Uniform manifold approximation and projection (UMAP) is a nonlinear dimensionality reduction technique. Visually, it is similar to t-SNE, but it assumes that the data is uniformly distributed on a locally connected Riemannian manifold and that the Riemannian metric is locally constant or approximately locally constant.
The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction techniques in machine learning. Many techniques of dimensional reduction make the assumption that data lies along a low-dimensional submanifold, such as manifold sculpting, manifold alignment, and manifold regularization.
There are also nonintrusive model reduction methods that learn reduced models from data without requiring knowledge about the governing equations and internals of the full, high-fidelity model. Nonintrusive methods learn a low-dimensional approximation space or manifold and the reduced operators that represent the reduced dynamics from data.
An orthogonal projection collapses some dimensions of the space it is applied to, which reduces the length of all vectors, as well as distance between vectors in the space. Under the conditions of the lemma, concentration of measure ensures there is a nonzero chance that a random orthogonal projection reduces pairwise distances between all ...
The projection filter in Hellinger/Fisher metric when implemented on a manifold / of square roots of an exponential family of densities is equivalent to the assumed density filters. [3] One should note that it is also possible to project the simpler Zakai equation for an unnormalized version of the density p. This would result in the same ...