Functional Inverse Regression in an Enlarged Dimension Reduction Space
Statistics Theory
2015-03-13 v1 Machine Learning
Statistics Theory
Abstract
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions belong. Our formulation provides a unified framework so that the classical notions, such as covariance standardization, Mahalanobis distance, SIR and linear discriminant analysis, can be naturally and smoothly carried out in our enlarged space. This enlarged dimension reduction space also links to the linear discriminant space of Gaussian measures on a separable Hilbert space.
Cite
@article{arxiv.1503.03673,
title = {Functional Inverse Regression in an Enlarged Dimension Reduction Space},
author = {Ting-Li Chen and Su-Yun Huang and Yanyuan Ma and I-Ping Tu},
journal= {arXiv preprint arXiv:1503.03673},
year = {2015}
}