On Fri, Oct 14, 2011 at 12:44:43PM +0100, Debby Klooster wrote:
> The thing I don't quite get, is why ICA is not completely reproducible.
Could you explicit your question: are you witnessing some non
reproducibility in a dataset or simulations, or are is the question more
general. In general, they are two reasons that might explain the lack of
reproducibility of ICA.
The first reason is that ICA is a non-convex optimization problem: it has
local minima. As a consequence, the result of the algorithm depends on
the starting conditions: it can fall it different local minima. These can
often be implemented as a random choice. Thus running the algorithm twice
on the same data may give different results.
The second reason is that people might be interested in running the
algorithm on two different dataset that are similar, for instance because
they can from the same population [1] or in a test-retest situation [2].
In this situation, it is normal that the results of the algorithm vary.
The question is: is it possible to give bounds on the variability of the
results given the variability of the input data. The theoretical answer
is: in general no. This is due to the non-convexity of the problem: the
estimated outputs may jump from one local minima to another. In practice,
it really depends, and in some cases it can be reasonably reproducible,
as shown be [1] and [2].
> I also found in literature and in textbooks that it might be a good
> idea to run ICA multiple times and check for the ICs that keep on
> occurring. Is something like this already implemented in FSL? What is
> your opinion about it?
I cannot answer for the FSL team, but I can give my opinion. What you are
referring to may be what is implemented in the ICASSO software [3]. It
studies both sources of variability, and tries to find clusters of
components that are robust to these variability. I personally think that
it is a very good idea to resort to such randomized methods, as they give
you bounds on the reproducibility and thus help interpretation. I am
biased, I have advocated similar methods in [2] :).
Hope this helps,
Gaël
[1] http://www.sciencedirect.com/science/article/pii/S1053811910001618
[2] http://www.sciencedirect.com/science/article/pii/S1053811909011525
[3] http://research.ics.tkk.fi/ica/icasso/
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