A1261
Title: Structure-preserving nonlinear sufficient dimension reduction for scalar-on-tensor regression
Authors: Dianjun Lin - Pennsylvania State University (United States) [presenting]
Lingzhou Xue - The Pennsylvania State University (United States)
Bing Li - The Pennsylvania State University (United States)
Abstract: A novel approach is presented to nonlinear sufficient dimension reduction for scalar-on-tensor regression and classification problems. The method introduces the tensor envelope, a framework designed to preserve the intrinsic multidimensional structure of tensor-valued predictors while achieving effective dimension reduction. Additionally, the central dimension folding subspace is defined within which the tensor envelope acts as an operator. Using coordinate mapping, two optimization algorithms are developed to enhance the operators' objective function. The performance of the proposed estimators is assessed through comprehensive simulations and real-world applications.
