Abstract: In this paper we present a technique to speed up
ICA based on the idea of reducing the dimensionality of the data
set preserving the quality of the results. In particular we refer to
FastICA algorithm which uses the Kurtosis as statistical property
to be maximized. By performing a particular Johnson-Lindenstrauss
like projection of the data set, we find the minimum dimensionality
reduction rate ¤ü, defined as the ratio between the size k of the reduced
space and the original one d, which guarantees a narrow confidence
interval of such estimator with high confidence level. The derived
dimensionality reduction rate depends on a system control parameter
β easily computed a priori on the basis of the observations only.
Extensive simulations have been done on different sets of real world
signals. They show that actually the dimensionality reduction is very
high, it preserves the quality of the decomposition and impressively
speeds up FastICA. On the other hand, a set of signals, on which the
estimated reduction rate is greater than 1, exhibits bad decomposition
results if reduced, thus validating the reliability of the parameter β.
We are confident that our method will lead to a better approach to
real time applications.