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First we considered the EM-algorithm for finding independent components
with low noise. The problem of slow convergence was noted and
an improvement was proposed. When finding the sources one at a time, the
contributions of the unwanted sources was treated as noise, which leads
to faster convergence. Although the approach was found to be implicitly
the same as in the FastICA algorithm, it is valid for other situations too.
In Bayesian ICA for i.i.d. sources, the modification can be applied
as proposed. Other possibilities include finding groups of components that
are not mutually independent but are independent related to other components not in the
group. The independent components are then projections to multidimensional
subspaces instead of one-dimensional projections.
This has been proposed e.g. in [3,4].
The modification proposed in this paper applies to this case too,
since the contributions of sources not in the group can
be regarded as approximately Gaussian noise.
Further work includes finding more general principles, where the modification
could be derived for other cases, such as time-dependent sources or nonlinear
ICA.

*Harri Lappalainen*

*2000-03-09*