Parametric independent component analysis for stable distributions

Independent component analysis is a solution for blind source separation problem. The goal of Independent Component Analysis (ICA) is to find a linear transformation of multivariate data such as random vectors such that its components becomes statistically independent. Independent components also are called sources and input vectors are known as observations.

Considering stable random vectors as an input for ICA requires a new assumption rather than Central Limit Theorem that says the standardized sum of Independent and Identically Distributed (IID) random variables converge to a random variable with Gaussian distribution, but Generalized Central Limit Theorem informally states that a normalized sum of a sequence of IID random variables with infinitive variance converges to a non-Gaussian stable random variable [5].

In this work, we consider non-Gaussian stable sources and propose a parametric ICA as an especial case of Kidmose’s suggestion described in [6, 7]. Sahmodi et al. [8] introduced a BSS method for the symmetric class of stable distributions. Extension of [8] to the case of random matrix A is given in [9] by a semi-parametric approach.

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(Author: Mohammad Reza Ameri, Mona Shokripour, Adel Mohammadpour, Vahid Nassiri

 Published by Sciedu Press)