Localized Sliced Inverse Regression

We develop a supervised dimension reduction method that integrates the idea of localization from manifold learning with the sliced inverse regression framework. We call our method localized sliced inverse regression (LSIR) since it takes into account the local structure of the explanatory variables. The resulting projection from LSIR is a linear subspace of the explanatory variables that captures the nonlinear structure relevant to predicting the response. LSIR applies to both classification and regression problems and can be easily extended to incorporate the ancillary unlabeled data in semi-supervised learning. We illustrate the utility of LSIR on real and simulated data. Computer codes and datasets from simulations are available online.