[seminarios-tcrp] summary of next seminar
- From: "Luis B. Almeida" <luis.almeida@xxxxxxxx>
- To: seminarios-tcrp@xxxxxxxxxxxxx
- Date: Mon, 13 Apr 2009 13:31:42 +0100
Hi all,
Please find below the summary of the seminar that I'll present next
Wednesday.
See you there,
Luis
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Title:
Removing the ill-posedness of nonlinear source separation (with a bonus)
Summary:
While linear blind source separation based on independent component
analysis is, essentially, a well-posed problem (the indeterminations
that remain, of scale and permutation, always keep the sources separated
from one another), it is well known that, when one moves to nonlinear
separation, the independence criterion, by itself, leaves the problem
with essential indeterminations: there is an infinite number of
solutions, with independent components, in which each component depends
on more than one source. Therefore, the independence criterion, as
usually stated, does not guarantee source separation.
Two kinds of solutions have been used, until recently, to solve this
difficulty: (1) strongly restricting the kinds of nonlinear mixtures
that are considered, so that the independence criterion again yields
separated sources (the main example is the restriction to post-nonlinear
mixtures), and (2) using regularization (which, in fact, is a form of
soft restriction). Although both kinds of solutions are useful in
practice, both are applicable only to a limited range of situations, and
none of them really solves the basic indetermination problem.
My presentation will focus on a different approach, recently proposed by
David Levin: Instead of placing restrictions on the mixture, one
strengthens the independence assumption, by assuming that not only the
values of the source signals, but also their time derivatives, are
jointly independent among sources. With this stronger assumption, the
nonlinear separation problem becomes essentially well-posed: the
indeterminations that remain always keep the sources separated from one
another. And, while the new independence assumption is much stronger
than the usual one, it is still rather plausible whenever the various
sources are generated by independent physical systems. An unexpected
bonus of this approach is that it provides a constructive, non-iterative
method to find the separated sources.
In the end of the seminar I'll also briefly mention another important
result obtained by David Levin: The possibility of defining an intrinsic
representation of a system, independent from the way in which the system
is observed: two observers, using different, possibly nonlinear,
observation systems, will arrive at (essentially) the same
representation of the system.
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