A weaker form of independence is uncorrelatedness.
Two random variables
and y2 are said to be uncorrelated, if
their covariance is zero:
On the other hand, uncorrelatedness does not imply independence.
For example, assume that (y1,y2) are discrete valued and follow
such a distribution that the pair are
with probability 1/4 equal to any of the following values:
(0,1),(0,-1),(1,0),(-1,0). Then y1 and y2 are uncorrelated, as
can be simply calculated. On the other hand,
Since independence implies uncorrelatedness, many ICA methods constrain the estimation procedure so that it always gives uncorrelated estimates of the independent components. This reduces the number of free parameters, and simplifies the problem.