Sliced inverse regression (SIR) was introduced by Li to find the effective dimension reduction directions for exploring the intrinsic structure of high-dimensional data. In this study, we propose a hybrid SIR method using a kernel machine which we call kernel SIR. The kernel mixtures result in the transformed data distribution being more Gaussian like and symmetric; providing more suitable conditions for performing SIR analysis. The proposed method can be regarded as a nonlinear extension of the SIR algorithm. We provide a theoretical description of the kernel SIR algorithm within the framework of reproducing kernel Hilbert space (RKHS). We also illustrate that kernel SIR performs better than several standard methods for discriminative, visualization, and regression purposes. We show how the features found with kernel SIR can be used for classification of microarray data and several other classification problems and compare the results with those obtained with several existing dimension reduction techniques. The results show that kernel SIR is a powerful nonlinear feature extractor for classification problems.
Journal of Computational and Graphical Statistics 17(3), pp.590-610