High dimensional gaussian classification

TL;DR

This paper provides a theoretical framework for high-dimensional Gaussian classification, linking geometric error analysis with nonparametric regression, and proposes an algorithm with thresholding estimation that can extend beyond Gaussian data.

Contribution

It introduces a new geometric error analysis approach for high-dimensional Gaussian classification and proposes a straightforward algorithm based on this theory.

Findings

Theoretical analysis of classification error in high dimensions.

An algorithm with thresholding estimation for high-dimensional data.

Potential extension of methods beyond Gaussian frameworks.

Abstract

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem of classification with a problem of nonparametric regression. We give an algorithm designed for high dimensional data which appears straightforward in the light of our theoretical work, together with the thresholding estimation theory. We finally attempt to give a general treatment of the problem that can be extended to frameworks other than gaussian.