Kernel sliced inverse regression: Regularization and consistency

Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data.