Estimating Non-Gaussian Subspaces by Characteristic Functions

Abstract

In this article, we consider high-dimensional data which contains a low-dimensional non-Gaussian structure contaminated with Gaussian noise and propose a new method to identify the non-Gaussian subspace. A linear dimension reduction algorithm based on the fourth-order cumulant tensor was proposed in our previous work [4]. Although it works well for sub-Gaussian structures, the performance is not satisfactory for super-Gaussian data due to outliers. To overcome this problem, we construct an alternative by using Hessian of characteristic functions which was applied to (multidimensional) independent component analysis [10,11]. A numerical study demonstrates the validity of our method.