  Independent component analysis (ICA) is a method for recovering statistically
independent signals from observations of unknown linear combinations of the
sources. Some of the most accurate ICA decomposition methods require searching
for the inverse transformation which minimizes different approximations of the
Mutual Information, a measure of statistical independence of random vectors.
Two such approximations are the Kernel Generalized Variance or the Kernel
Canonical Correlation which has been shown to reach the highest performance of
ICA methods. However, the computational effort necessary just for computing
these measures is cubic in the sample size. Hence, optimizing them becomes even
more computationally demanding, in terms of both space and time. Here, we
propose a couple of alternative novel measures based on randomized features of
the samples - the Randomized Generalized Variance and the Randomized Canonical
Correlation. The computational complexity of calculating the proposed
alternatives is linear in the sample size and provide a controllable
approximation of their Kernel-based non-random versions. We also show that
optimization of the proposed statistical properties yields a comparable
separation error at an order of magnitude faster compared to Kernel-based
measures.
