June 2008
We develop an extension of sliced inverse regression (SIR) that we call localized sliced inverse regression (LSIR). This method allows for supervised dimension reduction on nonlinear subspaces and alleviates the issue of degenerate solutions in the classical SIR method. We introduce a simple algorithm that implements this method. The method is also extended to the semisupervised setting where one is given labeled and unlabeled data. We illustrate the utility of the method on real and simulated data. We also note that our approach can interpolated between SIR and principle components analysis (PCA) depending on parameter settings.
Keywords: Dimension reduction, sliced inverse regression,localization, semi-supervised learning
The manuscript is available PDF format.