A New RKHS-based Approach To Nonlinear Dimension Reduction For Survival Data

Sparse-high-dimensional data emerges more and more frequently in various academic fields, such as genomics and economics. It brings us much more sig-nificant information, however, curse of dimensionality is inevitable at the same time. How to effectively deal with the sparse-high-dimensional data is a current research hotspot and dimension reduction is a detailed critical orientation. Large quantities of literature have done adequate work associated with linear and non-linear research for the complete data which we all know. The linear research for the censored data is also studied very well, however, rare literature has done sufficient research on the nonlinear situation. Proposed a new approach to re-ducing nonlinear dimension for survival data based on the reproducing kernel Hilbert space theory, that is reproducing kernel-based Double SIR (RDSIR). An isometrically isomorphism is constructed based on RKHS property, converting the study of infinite dimensional function to a finite one. The sufficient dimen-sion reduction (SDR) subspace can be estimated by the regularization generalized eigen-decomposition problem,and the censored information is used in the double slice part, we also focus our research on selection of parameters and the realization of the algorithm, Finally, we illustrate the performance of this new approach on simulated and real data.