Dear FSL users,
Thanks Gael for kindly explaining the purpose behind ICASSO. Clearly if we are talking about global optimum then every optimization problem has a unique solution! (excluding the case where all global optima are the same)
With regards to the paper:
[1] Hyvarinen 1999, Fast and robust fixed-point algorithms for independence component analysis
It seems to me that the paragraph you mention talks about local versus global "convergence". If I understand correctly global convergence is convergence to "some solution" (NOT necessarily the global optimum) from all initial points.
In other words, the FastICA algorithm (which is called internally by MELODIC) will converge to "some" solution for all initial points if the contrast function is kurtosis. This does NOT however rule out the possibility of multiple local solutions.
In my opinion, just decreasing the convergence criterion (such as eps) will not result in the same solution every time but I would be interested in what the FSL experts think about this.
Hans
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