Riemannian manifold learning for nonlinear dimensionality reduction

Authors:
Tony Lin;Hongbin Zha;Sang Uk Lee
Affiliations:
National Laboratory on Machine Perception, Peking University, Beijing, China;National Laboratory on Machine Perception, Peking University, Beijing, China;School of Electrical Engineering, Seoul National University, Seoul, Korea
Venue:
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Year:
2006

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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 Riemannian manifold learning (RML). A Riemannian manifold can be constructed 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.