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-->:: <math>\tilde{\varphi}_k = E[\theta(Y)-\sum_{i\neq k} \varphi_i(X_i) | X_k]</math>
# Iterate the above three steps until <math>e^2</math> is within error tolerance.
==Bivariate Case==
The optical transformation <math>\theta^*(Y), \varphi^*(X)</math>for <math>p=1</math> satisfies
: <math> \rho^*(X, Y) = \rho^*(\theta^*, \varphi^*) = \max_{\theta, \varphi} \rho[\theta(Y), \varphi(X)]</math>
where <math>\rho<\math> is [[Pearson correlation coefficient]]. <math> \rho^*(X, Y)</math> is known as the maximal correlation between <math>X</math> and <math>Y</math>. It can be used as a general measure of dependence.
In the bivariate case, ACE algorithm can also be regarded as a method for estimating the maximal correlation between two variables.
== References ==
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