Structure preserving dimension reduction with 2D images as predictors

Nearly all existing dimension reduction methods on 2D matrix-valued image predictors are unsupervised or supervised without preserving matrix structure, which can result in loss of the structure-specific relation between the response and predictors. In this paper, we propose a kernel-based solution for supervised dimension reduction which preserves the matrix structure of the reduced predictors. This approach is computationally efficient and offers a unified framework to handle image predictors. We illustrate the method using both simulations and applications.