On the relevance of independent components

Signal Processing, 2007

Signal Processing, 2007

Many researchers have recently used independent component analysis (ICA) to generate codebooks or features for a single channel of data. We examine the nature of these codebooks and identify when such features can be used to extract independent components from a stationary scalar time series. This question is motivated by empirical work that suggests that single channel ICA can sometimes be used to separate out important components from a time series. Here we show that as long as the sources are reasonably spectrally disjoint then we can identify and approximately separate out individual sources. However, the linear nature of the separation equations means that when the sources have substantially overlapping spectra both identification using standard ICA and linear separation are no longer possible.

Independent Component Analysis (ICA), a computationally efficient blind source separation technique, has been an area of interest for researchers for many practical applications in various fields of science and engineering. This paper attempts to cover the fundamental concepts involved in ICA techniques and review its applications. A thorough discussion of the applications and ambiguities problems of ICA has been carried out.Different ICA methods and their applications in various disciplines of science and engineering have been reviewed. In this paper, we present ICA methods from the basics to their potential applications to serve as a comprehensive single source for an inquisitive researcher to carry out research in this field.

Independent Component Analysis (ICA), a computationally efficient blind source separation technique, has been an area of interest for researchers for many practical applications in various fields of science and engineering. This paper attempts to cover the fundamental concepts involved in ICA techniques and review its applications. A thorough discussion of the applications and ambiguities problems of ICA has been carried out.Different ICA methods and their applications in various disciplines of science and engineering have been reviewed. In this paper, we present ICA methods from the basics to their potential applications to serve as a comprehensive single source for an inquisitive researcher to carry out research in this field.

International Journal of Computer Science and Informatics

This paper deals with the study of Independent Component Analysis. Independent Component Analysis is basically a method which is used to implement the concept of Blind Source Separation. Blind Source Separation is a technique which is used to extract set of source signal from set of their mixed source signals. The various techniques which are used for implementing Blind Source Separation totally depends upon the properties and the characteristics of original sources. Also there are many fields nowadays in which Independent Component Analysis is widely used. This paper deals with the theoretical concepts of Independent Component Analysis, its principles and its widely used applications.

Blind Source Separation (BSS) refers to the process of recovering source signals from a given mixture of unknown source signals were in no prior information about source and mixing methodology is known. Independent Component Analysis (ICA) is widely used BSS technique which allows separation of source components from complex mixture of signals based on certain statistical assumptions. This paper covers up the fundamental concepts of ICA and reviews different algorithms of Independent Component Analysis. In addition, the merits and demerits of each algorithm are outlined. Finally brief description of recent application in ICA is presented.

The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept oflCA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution. Zusammenfassung Die Analyse unabhfingiger Komponenten (ICA) eines Vektors beruht auf der Suche nach einer linearen Transformation , die die statistische Abh~ingigkeit zwischen den Komponenten minimiert. Zur Definition geeigneter Such-Kriterien wird die Entwicklung gemeinsamer Information als Funktion von Kumulanten steigender Ordnung genutzt. Es wird ein effizienter Algorithmus vorgeschlagen, der die Berechnung der ICA ffir Datenmatrizen innerhalb einer polynomischen Zeit erlaubt. Das Konzept der ICA kann eigentlich als Erweiterung der 'Principal Component Analysis' (PCA) betrachtet werden, die nur die Unabh~ingigkeit bis zur zweiten Ordnung erzwingen kann und deshalb Richtungen definiert, die orthogonal sind. Potentielle Anwendungen der ICA beinhalten Daten-Analyse und Kompression, Bayes-Detektion, Quellenlokalisierung und blinde Identifikation und Entfaltung.

(ICA) approach to the separation of nonlinear mixtures in the complex domain. Source separation is performed by a complex INFOMAX approach. Nonlinear complex functions involved in the processing are realized by pairs of spline neurons called "splitting functions", working on the real and the imaginary part of the signal respectively. A simple adaptation algorithm is derived and some experimental results that demonstrate the effectiveness of the proposed method are shown. f z is said analytic in a point 0 z if its derivative exists throughout some neighbourhood of 0 z . If ( ) f z is analytic in all points z ∈ , it is called entire.

Trends in Cognitive Sciences, 2002

Independent component analysis (ICA) is a method for automatically identifying the underlying factors in a given data set. This rapidly evolving technique is currently finding applications in analysis of biomedical signals (e.g. ERP, EEG, fMRI, optical imaging), and in models of visual receptive fields and separation of speech signals. This article illustrates these applications, and provides an informal introduction to ICA.

Many algorithms based on information theoretic measures and/or temporal statistics of the signals have been proposed for ICA in the literature. There have also been analytical solutions suggested based on predictive modeling of the signals. In this paper, we show that finding an analytical solution for the ICA problem through solving a system of nonlinear equations is possible. We demonstrate that this solution is robust to decreasing sample size and measurement SNR. Nevertheless, finding the root of the nonlinear function proves to be a challenge. Besides the analytical solution approach, we try finding the solution using a least squares approach with the derived analytical equations. Monte Carlo simulations using the least squares approach are performed to investigate the effect of sample size and measurement noise on the performance.