One-ICA Version of the Mixca Algorithm - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 180

T ; we can write Considering the vector f ð y Þ¼ f ð y 1 Þ f ð y 2 Þ ...f ð y M Þ ½

d log p ð y Þ
dW

¼ f ð y Þ x T

ð A : 13 Þ

Using the results of equations ( A.7 ) and ( A.13 ), we may finally write equation
( A.6 ) as:

dL ð W Þ

dW ¼ð W T Þ 1 þ f ð y Þ x T

ð A : 14 Þ

Then we can apply equation ( A.14 ) in the gradient updating algorithm to
iteratively find the optimum matrix

W ð i þ 1 Þ¼ W ð i Þþ a dL ð W Þ
dW

ð i Þ ð A : 15 Þ