Second-Order Multidimensional ICA: Performance Analysis

Abstract

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting a number of mutually independent elements from a set of observed linear mixtures. Motivated by various applications, this paper considers a more general and more flexible model: the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups. We argue that this is tantamount to considering multidimensional components as opposed to the standard ICA case which is restricted to one-dimensional components. The core of the paper is devoted to the statistical analysis of the blind separation of multidimensional components based on second-order statistics, in a piecewise-stationary model. We develop the likelihood and the associated estimating equations for the Gaussian case. We obtain closed-form expressions for the Fisher information matrix and the Cramér-Rao bound of the de-mixing parameters, as well as the mean-square error (MSE) of the component estimates. The derived MSE is valid also for non-Gaussian data. Our analysis is verified through numerical experiments, and its performance is compared to classical ICA in various dependence scenarios, quantifying the gain in the accuracy of component recovery in presence of multidimensional components.

Joint Block Diagonalization Algorithms for Optimal Separation of Multidimensional Components

“…for any two m × m positive-definite matrices R 1 and R 2 , the log-likelihood for the model just described is [6] log p(…”

“…A closed-form expression for the CRLB and MSE is obtained in [6], where it is shown that this MSE is achievable also for non-Gaussian data.…”

Capacity Analysis and Information Optimization of WSDM

“…Finally, we provide a linear optimal separating matrix for signal separation of mixed signals by maximizing the objective function. Compared to other signal separation methods, such as blind source separation (BSS) and independent component analysis (ICA) [9]- [11], the proposed method is more feasible and performs better according to computer simulations.…”

An Efficient Algorithm by Kurtosis Maximization in Reference-Based Framework

“…Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible [1]. In a multi-input/multioutput (MIMO) context, the problem of ICA has found interesting solutions through the optimization of so-called contrast (objective) functions [2], many of which rely on higherorder statistics (e.g., the kurtosis contrast [3], [4]) or can be linked to higher-order statistics (e.g., the constant modulus contrast function [5]).…”