We study the dynamics of a Hebbian ICA algorithm extracting a single non-Gaussian component from a high-dimensional Gaussian background. For both on-line and batch learning we find that a surprisingly large number of examples are required to avoid trapping in a sub-optimal state close to the initial conditions. To extract a skewed signal at least O(N2) examples are required for N-dimensional data and O(N3) examples are required to extract a symmetrical signal with non-zero kurtosis.
['Magnus Rattray', 'Gleb Basalyga']
Scaling Laws and Local Minima in Hebbian ICA