Independent component analysis: A statistical perspective

Abstract

1. z $ N p (0, I p ) ) multivariate normal (Gaussian) model. 2. z spherical, that is, Uz $ z for all orthogonal U ) elliptical model. 3. z has independent components ) independent component model. Both the elliptical model and IC model are extensions of the Gaussian model but in diverse directions. In the case of the Gaussian and elliptical model, A is identifiable only up to a postmultiplication by an orthogonal matrix, and the inference is only for parameters E(x) = b and Cov(x) = AA 0. Classical multivariate statistical inference methods, such as Hotelling's T 2 , multivariate analysis of variance, multivariate regression, and PCA, rely on the assumption of multivariate normality. Gaussianity and ellipticity assumptions mean that no hidden structures or latent variables are allowed in the data analysis.The IC model is a so called BSS model with latent variables in z and latent structures caused by different marginal distributions of the components of z. In the case of the IC model one tries to estimate an unmixing matrix to go back to the non-2 of 23 NORDHAUSEN AND OJA

Robust wireless statistic division multiplexing and its performance analysis

“…No prior knowledge of source signals and mixing system is available in the separation process. [6][7][8][9][10] The essential framework of the separation algorithms is illustrated in Figure 4.…”

Blind Source Separation for the Aggregation of Machine Learning Algorithms: An Arrhythmia Classification Case

“…A number of novel algorithms related to BSS have been developed recently, and these have played an important role in many disciplines [28]. These algorithms can be systemized in several ways taking into account the source separation condition or the restrictions to the source features, including independent component analysis (ICA) [29], sparse component analysis (SCA) [30], nonnegative matrix factorization (NMF) [31], and bounded component analysis (BCA) [32].…”

Extracting Conditionally Heteroskedastic Components using Independent Component Analysis

“…As shown later in this article, PVC is closely related to another widely used dimention reduction method for the analysis of multivariate financial data, that is, the independent component analysis (ICA). In ICA, the goal is to find a linear transformation of the multivariate data set which has mutually independent components (Hyvärinen and Oja, ; Nordhausen and Oja, ). The purpose of carrying out ICA can be to separate interesting components from the uninteresting ones, or to shift from a multivariate analysis to multiple univariate analyses.…”