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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. == Introduction == 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 a 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. An important note to consider is that if ''N'' sources are present, at least ''N'' observations (e.g. microphones) are needed to recover the original signals. This constitutes the square case (''J'' = ''D'', where ''D'' is the input dimension of the data and ''J'' is the dimension of the model). Other cases of underdetermined (''J'' > ''D'') and overdetermined (''J'' < ''D'') have been investigated. That the ICA separation of mixed signals gives very good results are based on two assumptions and three effects of mixing source signals. Two assumptions: #The source signals are independent of each other. #The values in each source signal have non-gaussian distributions. Three effects of mixing source signals: #Independence: As per assumption 1, the source signals are independent; however, their signal mixtures are not. This is because the signal mixtures share the same source signals. #Normality: According to the Central Limit Theorem, the distribution of a sum of independent random variables with finite variance tends towards a gaussian distribution. Loosely speaking, a sum of two independent random variables usually has a distribution that is closer to gaussian than any of the two original variables. Here we consider the value of each signal as the random variable. #Complexity: The temporal complexity of any signal mixture is greater than that of its simplest constituent source signal. Those principles contribute to the basic establishment of ICA. If the signals we happen to extract from a set of mixtures are independent like sources signals, or have non-gaussian histograms like source signals, or have low complexity like source signals, then they must be source signals. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「independent component analysis」の詳細全文を読む スポンサード リンク
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