... nongaussianity by thecentral limit theorem. As a first practical measure of nongaussianity, we introducethe fourth-order cumulant, or kurtosis. Using kurtosis, we derive practical algorithms by gradient and ... functionsG1 and G2so thatG1isodd and G2is even, and we obtain the following approximation:J (y ) k1(E fG1(y )g)2+ k2(E fG2(y )gE fG2( )g)2(8.24)166 ICA BY MAXIMIZATION ... kurtosis, is given for comparison by the dash-dotted curve.wherek1 and k2are positive constants, and is a gaussian variable of zero mean and unit variance (i.e., standardized). The variableyis...