Icasso: software for investigating the reliability of ICA estimates by clustering and visualization

A major problem in application of independent component analysis (ICA) is that the reliability of the estimated independent components is not known. Firstly, the finite sample size induces statistical errors in the estimation. Secondly, as real data never exactly follows the ICA model, the contrast function used in the estimation may have many local minima which are all equally good, or the practical algorithm may not always perform properly, for example getting stuck in local minima with strongly suboptimal values of the contrast function. We present an explorative visualization method for investigating the relations between estimates from FastICA. The algorithmic and statistical reliability is investigated by running the algorithm many times with different initial values or with differently bootstrapped data sets, respectively. Resulting estimates are compared by visualizing their clustering according to a suitable similarity measure. Reliable estimates correspond to tight clusters, and unreliable ones to points which do not belong to any such cluster. We have developed a software package called Icasso to implement these operations. We also present results of this method when applying Icasso on biomedical data.