A1278
Title: On non-redundant and linear operator-based nonlinear dimension reduction
Authors: Zhoufu Ye - Zhejiang University (China)
Wei Luo - Zhejiang University (China) [presenting]
Abstract: Kernel principal component analysis (KPCA), a popular nonlinear dimension reduction technique, has the redundancy issue that each kernel principal component can be a measurable function of the preceding components. This harms the effectiveness of dimension reduction and leaves the dimension of the reduced data a heuristic choice. The purpose is to rebuild the theory of nonlinear dimension reduction centered on recovering the sigma-field of the original data, and, using appropriate linear operators between RKHSs, two sequential dimension reduction methods are proposed that address the redundancy issue, maintain the same level of computational complexity as KPCA, and rely on more plausible assumptions regarding the singularity of the original data. Compared with the existing nonlinear dimension reduction methods that also address the redundancy issue, the methods enjoy the parametric asymptotic rate and do not specify distributions on the reduced data, thereby preserving other patterns, if any, of the original data. By constructing a measure of the exhaustiveness of the reduced data, consistent order determination is also provided for these methods. Some numerical studies are presented at the end. A novel characterization of conditional mean independence is involved, which may attract independent research interest.
