Maximization of Component Disjointness: A Criterion for Blind Source Separation

Abstract

Blind source separation is commonly based on maximizing measures related to independence of estimated sources such as mutual statistical independence assuming non-Gaussian distributions, decorrelation at different time-lags assuming spectral differences or decorrelation assuming source non-stationarity.

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 zero-mean sources destroys this information).

The method of 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. 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 positive-valued sources as long as they are at least moderately disjoint, and (3) The performance peak of ICA for zero-mean sources is achieved when sources are disjoint (but not independent).