Nonlinear Source Separation

Abstract

The purpose of this lecture book is to present the state of the art in nonlinear blind source separation, in a form appropriate for students, researchers and developers. Source separation deals with the problem of recovering sources that are observed in a mixed condition. When we have little knowledge about the sources and about the mixture process, we speak of blind source separation. Linear blind source separation is a relatively well studied subject. Nonlinear blind source separation is still in a less advanced stage, but has seen several significant developments in the last few years.This publication reviews the main nonlinear separation methods, including the separation of post-nonlinear mixtures, and the MISEP, ensemble learning and kTDSEP methods for generic mixtures. These methods are studied with a significant depth. A historical overview is also presented, mentioning most of the relevant results, on nonlinear blind source separation, that have been presented over the years.

Non-linear independent component analysis with diffusion maps

“…Here we assume that the data is generated by stochastic Itô processes. Non-linear ICA, other assumptions on data generation and mixing functions, and factorizing probability density functions are reviewed in [8,9].…”

Blind separation of nonlinear mixtures by variational Bayesian learning

“…Existing nonlinear BSS methods have been reviewed in [16,17], and earlier in Chapter 17 of the book [1]. The paper [16] reviews especially uniqueness results on nonlinear ICA and BSS, separation methods for post-nonlinear mixtures, and our variational Bayesian estimation methods, referring to papers in which the detailed results have been presented.…”

“…Blind separation of sources from their nonlinear mixtures-known as nonlinear blind source separation (BSS)-is generally a difficult problem, both from a theoretical and a practical point of view [1,16,17]. The task is to extract the sources s(t) that have generated the observations x(t) through a nonlinear mapping f (·):…”

Segmented Online Neural Filtering System Based On Independent Components Of Pre-Processed Information

“…Considering a practical ICA application, both the mixing environment and the sensors may present some nonlinear behavior. Providing a more general formulation, the nonlinear independent component analysis (NLICA) model considers that the measured signals x are formed by a nonlinear instantaneous mixing model (Almeida, 2006):…”

“…For NLICA, one way to address the illposedness of the problem is to restrict the range of allowed nonlinearities, generating structural constrained models for the mixing system and thus unique solutions for the problem (Jutten and Karhunen, 2003). Among these models, we can mention the postnonlinear (PNL) mixture, which has met a significant practical applicability (Almeida, 2006). There is also a method closely related to the NLICA problem, known as Local ICA, which introduces nonlinear transformations by clustering the dataset into groups of similar www.intechopen.com…”