Paper No: 55
Is the general form of Renyi's entropy a contrast for source separation?
Author(s): Frédéric Vrins, Dinh-Tuan Pham, Michel Verleysen
Renyi's entropy-based criterion has been proposed as an objective
function for independent component analysis because of its
relationship with Shannon's entropy and its computational
advantages in specific cases. These criteria were suggested based
on "convincing" experiments. However, there is no theoretical
proof that globally maximizing those functions would lead to
separate the sources; actually, this was implicitly conjectured.
In this paper, the problem is tackled in a theoretical way; it is
shown that globally maximizing the Renyi's entropy-based
criterion, in its general form, does not necessarily provide the
expected independent signals. The contrast function property of
the corresponding criteria simultaneously depend on the value of
the Renyi parameter, and on the (unknown) source densities.