The ICA method depends on certain measurement of the non-Gaussianity:
Kurtosis is defined as the normalized form of the fourth central moment of a distribution:
(209) |
The entropy of a random variable with density function
is
defined as
(210) |
(211) |
This result can be generalized from random variables to random vectors,
such as
, and we want to find a matrix
so that
has the maximum negentropy
, i.e.,
is
most non-Gaussian. However, exact
is difficult to get as
its calculation requires the specific density distribution function
.
The negentropy can be approximated by
(212) |
(213) |
(214) |
(215) |