Independent component analysis

In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that the subcomponents are non-Gaussian signals and that they are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the 'cocktail party problem' of listening in on one person's speech in a noisy room. In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that the subcomponents are non-Gaussian signals and that they are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the 'cocktail party problem' of listening in on one person's speech in a noisy room. Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by mixing for analysis purposes. A simple application of ICA is the 'cocktail party problem', where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. Note that a filtered and delayed signal is a copy of a dependent component, and thus the statistical independence assumption is not violated. An important note to consider is that if N { extstyle N} sources are present, at least N { extstyle N} observations (e.g. microphones if the observed signal is audio) are needed to recover the original signals. This constitutes the case where the matrix is square ( D = J { extstyle D=J} , where D { extstyle D} is the number of observed signals and J { extstyle J} is the number of source signals hypothesized by the model). Other cases of underdetermined ( D < J { extstyle D<J} ) and overdetermined ( D > J { extstyle D>J} ) have been investigated.