B0332
Title: A comparative study of linear and nonlinear sufficient dimension reduction
Authors: Jiyeong Kang - Ewha Womans University (Korea, South) [presenting]
Kyongwon Kim - Ewha Womans University (Korea, South)
Abstract: dr package is a widely used tool to implement linear sufficient dimension reduction, which is useful to extract core information from a high-dimensional dataset. However, because big data can include a complicated nonlinear structure, some features of the dataset cannot be fully explained by a linear sufficient dimension reduction. The nonlinear sufficient dimension reduction can be an alternative to address this issue. However, the theoretical formulation of nonlinear sufficient dimension reduction relies on the linear operators in Hilbert space, and this hampers many users from applying nonlinear sufficient dimension reduction methods in real data analysis. We compare the theoretical background and numerical results between linear and nonlinear sufficient dimension reduction using a widely used dr package and a recently developed nsdr package. We further present nonlinear sufficient dimension reduction methods can be applied to a classification problem by using the wine cultivar dataset.
