ICA 2007 

London, UK 9  12 September 2007 

Paper No: 150Maximization of Component Disjointness: a Criterion for Blind Source SeparationAuthor(s): Jörn AnemüllerAbstractBlind source separation is commonly based on maximizing measures related to independence of estimated sources such as mutual statistical independence assuming nonGaussian distributions, decorrelation at different timelags assuming spectral differences or decorrelation assuming source nonstationarity. Here, the use of an alternative model for source separation is explored which is based on the assumption that sources emit signal energy at mutually different times. In the limiting case, this corresponds to only a single source being ``active'' at each point in time, resulting in mutual disjointness of source signal supports and negative mutual correlations of source signal envelopes. This assumption will not be fulfilled perfectly for real signals, however, by maximizing disjointness of estimated sources (under a linear mixing/demixing model) we demonstrate that source separation is nevertheless achieved when this assumptions is only partially fulfilled. The conceptual benefits of the disjointness assumption are that (1) in certain applications it may be desirable to explain observed data in terms of mutually disjoint ``parts'' and (2) the method presented here preserves the special physical information assigned to amplitude zero of a signal which corresponds to the absence of energy (rather than subtracting the signal mean prior to analysis which for non zeromean sources destroys this information). The method of \emph{disjoint component analysis} (DCA) is derived and it is shown that its update equations bear remarkable similarities with maximum likelihood independent component analysis (ICA). Sources with systematically varied degrees of disjointness are constructed and processed by DCA and (infomax and jade) ICA, the results illustrate the behaviour of DCA and ICA under these regimes with two main results: (1) DCA leads to a higher degree of separation than ICA, (2) DCA performs particularly well on positivevalued sources, and (3) The performance peak of ICA for zeromean sources is achieved when sources are disjoint (but not independent). 


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