Nov 2007
We extend the sliced inverse regression (SIR) framework for dimension reduction using kernel models and regularization. The result is a nonlinear dimension reduction method that finds submanifolds containing the inverse regression curve rather than linear subspaces and can be applied to high-dimensional data. This is advantageous when the relevant predictor variables are concentrated on a nonlinear low dimension manifold and generalizes the SIR setting to distributions that are not elliptically symmetric with respect to predictor variables. We provide a simple algorithm for nonlinear dimension reduction. A proof of consistency of the method under weak conditions is given. Simulations as well as applications to high-dimensional data are used to illustrate the efficacy of the method.
Keywords: Dimension reduction, sliced inverse regression, kernel methods, manifold learning
The manuscript is available PDF format.