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• W2112148214 abstract "We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sample data into locally linear low-dimensional patches, merge these patches into a single low-dimensional coordinate system, and compute forward and reverse mappings between the sample and coordinate spaces. The objective functions are convex and their solutions are given in closed form." @default.
• W2112148214 created "2016-06-24" @default.
• W2112148214 creator A5013617347 @default.
• W2112148214 date "2002-01-01" @default.
• W2112148214 modified "2023-10-18" @default.
• W2112148214 title "Charting a Manifold" @default.
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