Alternating conditional expectations: Difference between revisions

Revision as of 02:27, 18 June 2018

Revision as of 02:27, 18 June 2018

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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.