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Riemannian Manifold Learning for Nonlinear Dimensionality Reduction

2020-03-27 | |  56 |   42 |   0

Abstract

In recent years, nonlinear dimensionality reduction (NLDR) techniques have attracted much attention in visual perception and many other areas of science. We propose an efficient algorithm called Rie- mannian manifold learning (RML). A Riemannian manifold can be con- structed in the form of a simplicial complex, and thus its intrinsic dimension can be reliably estimated. Then the NLDR problem is solved by constructing Riemannian normal coordinates (RNC). Experimental results demonstrate that our algorithm can learn the data’s intrinsic geometric structure, yielding uniformly distributed and well organized low-dimensional embedding data.

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