Reliability of Independent Component Analysis (ICA)

Independent component analysis (

ICA) is a widely used powerful data-driven signal processing technique. It has proved to be helpful in many fields, such as, biomedical systems, telecommunication, finance and natural image processing. Yet, some problems persist in its wide adoption. One concern is reliability of solutions found with ICA algorithms, resulting from the fact they may slightly change each time the analysis is performed. The behavior stems from the stochastic nature of the analyzed data and of many estimation algorithms commonly used to solve the general problem of blind source separation (BSS).

The reliability of the analysis can be improved by clustering solutions from multiple runs of bootstrapped ICA, to analyze the consistency of the solutions by exploiting the inherent variability. Several methods have been recently published to either analyze algorithmic stability or reduce the variability. The goal of our study has been to extract additional information from the data, by focusing on the nature of the variability itself. The usefulness of our approach has been tested with real functional magnetic resonance imaging (fMRI) experiments.

Usually, several independent components are found to be consistent. Moreover, the additional information helps to interpret the underlying phenomena of the less consistent ones.

**Figure 1:** The idea of bootstrapping. In (a)--(c) the data is resampled (shown as thick curves) to slightly change the shape of the true 2-dimensional error-surface (shown as thin curves). This allows the algorithm to converge to different solutions (marked as ``&circle;''), which may fall on local minima. The best solution is given by (d) the mean of all solutions.
(a)	(b)	(c)	(d)