Least-squares gradients for dimension reduction (LSGDR) is a supervised dimension reduction method. 

LSGDR possesses the following features:

• The transformation matrix is efficiently estimated "in a closed form" through the eigenvalue decomposition to the expectation of the outer product of the logarithmic conditional density gradient.

• The gradients of the logarithmic conditional densities are accurately estimated by a proposed estimator called least-squares logarithmic conditional density gradients (LSLCG):

  • LSLCG directly estimates log-conditional density gradients without conditional density estimation.

  • The solutions in LSLCG are analytically computed.

  • A cross-validation method is available for tuning all parameters in LSLCG.

MATLAB implementation of LSGDR and LSLCG: LSGDR.zip

Currently, this implementation is intended for regression only. Implementation for classification will be available soon.

References

• Hiroaki Sasaki, Voot Tangkaratt and Masashi Sugiyama, "Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities", the 7th Asian Conference on Machine learning (ACML), JMLR: Workshop and Conference Proceedings, vol.xx, pp.xxx-xxx, 2015.