Scaling Laws and Local Minima in Hebbian ICA

Part of Advances in Neural Information Processing Systems 14 (NIPS 2001)

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Magnus Rattray, Gleb Basalyga


We study the dynamics of a Hebbian ICA algorithm extracting a sin- gle non-Gaussian component from a high-dimensional Gaussian back- ground. 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  examples are required for  -dimensional data and  

 exam- ples are required to extract a symmetrical signal with non-zero kurtosis.