Independent Component Analysis and Blind Source Separation - Biomedical Signal Analysis: Contemporary Methods and Applications - page 119

alpha=0, kurt=1.8948 alpha=10, kurt=2.4502

alpha=20, kurt=2.914 alpha=30, kurt=3.0827

alpha=40, kurt=2.8828 alpha=50, kurt=2.404

alpha=60, kurt=1.859 alpha=70, kurt=1.4866

alpha=80, kurt=1.4423 alpha=90, kurt=1.7264

Figure 4.7
Kurtosis maximization, second example: histograms. For explanation, see figure 4.6.
The data set is shown in figure 4.6. The kurtosis as function of the angle is also
given in figure 4.6.

claimed: The points of maximal Gaussianity correspond to the ICA
solutions.
Indeed, this can also be shown in higher dimensions (see [120]).

Algorithm
Of course, s is not known, so after whitening z = Vx we have to search
for w

n with w z maximal non-Gaussian. Because of q =( VA ) w

∈ R

we get

2 = q q =( w VA )( A V w )= 2

| | | |

q w

S n−1 also. Hence, we get the following
Algorithm: ( kurtosis maximization ) Maximize w

S n−1 , w

so if q ∈ ∈

kurt( w z )

→| | on

S n−1 after whitening.