ICA based on Split Generalized Gaussian

TL;DR

This paper introduces an ICA method based on the Split Generalized Gaussian distribution, effectively handling heavy-tailed and asymmetric data, improving over traditional kurtosis-based approaches.

Contribution

The paper presents a novel ICA approach using SGGD, addressing limitations of kurtosis-based methods by better modeling heavy tails and asymmetry in data.

Findings

Outperforms classical ICA methods on heavy-tailed data

Handles asymmetric data more effectively

Demonstrates improved independence separation

Abstract

Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE. However, their assumption of fourth-order moment (kurtosis) may not always be satisfied in practice. One of the possible solution is to use third-order moment (skewness) instead of kurtosis, which was applied in $ICA_{SG}$ and EcoICA. In this paper we present a competitive approach to ICA based on the Split Generalized Gaussian distribution (SGGD), which is well adapted to heavy-tailed as well as asymmetric data. Consequently, we obtain a method which works better than the classical approaches, in both cases: heavy tails and non-symmetric data. \end{abstract}