Bernoulli

  • Bernoulli
  • Volume 16, Number 1 (2010), 181-207.

Learning gradients on manifolds

Sayan Mukherjee, Qiang Wu, and Ding-Xuan Zhou

Full-text: Open access

Abstract

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.

Article information

Source
Bernoulli Volume 16, Number 1 (2010), 181-207.

Dates
First available in Project Euclid: 12 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1265984708

Digital Object Identifier
doi:10.3150/09-BEJ206

Mathematical Reviews number (MathSciNet)
MR2648754

Zentralblatt MATH identifier
1200.62070

Keywords
classification feature selection manifold learning regression shrinkage estimator Tikhonov regularization

Citation

Mukherjee, Sayan; Wu, Qiang; Zhou, Ding-Xuan. Learning gradients on manifolds. Bernoulli 16 (2010), no. 1, 181--207. doi:10.3150/09-BEJ206. https://projecteuclid.org/euclid.bj/1265984708


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