Learning gradients on manifolds

Details Learning gradients on manifolds Learning gradients on manifolds

2010-02-23

arxiv.org/abs/1002.4283v1

Bernoulli 2010, Vol. 16, No. 1, 181-207

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ206 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ206

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on manifolds for dimension reduction for high-dimensional data with few observations. We obtain generalization error bounds for the gradient estimates and show that the convergence rate depends on the intrinsic dimension of the manifold and not on the dimension of the ambient space. We illustrate the efficacy of this approach empirically on simulated and real data and compare the method to other dimension reduction procedures.

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