Multivariate Gaussianization for Data Processing

Intro Iterative Gaussianization Experiments ConclusionsOn the suitable rotationWhich is the suitable rotation?Closed-form Theoretical Convergence Comput.Rotation convergence√rate costICA√×√Max ∆J O(2md(d + 1)n)PCA√√∆J = 2nd order O(d 2 (d + 1)n)RND∆J ≥ 0 O(d 3 )n samples of dimension d, FastICA running m iterationsICA guarantees the theoretical convergence of the Gaussianization processsince it seeks for the maximally non-Gaussian marginal PDFsPCA leads to non-optimal convergence rate because it does reduceredundancy to a certain extent (it removes correlation), but it does notmaximize the marginal non-Gaussianity J m(x)PCA is closed-form and is faster than ICAPCA require more iterations but Gaussianizes fasterUsing RND transforms guarantees the theoretical convergence, butconverges slowly