Editing Pearson correlation coefficient (section)

===Reflective correlation coefficient===
The reflective correlation is a variant of Pearson's correlation in which the data are not centered around their mean values.{{citation needed|date=January 2011}} The population reflective correlation is

:<math>\operatorname{corr}_r(X,Y) = \frac{\operatorname\mathbb{E}[\,X\,Y\,]}{\sqrt{\operatorname\mathbb{E}[\,X^2\,]\cdot \operatorname\mathbb{E}[\,Y^2\,]}}.</math>

The reflective correlation is symmetric, but it is not invariant under translation:

:<math>\operatorname{corr}_r(X, Y) = \operatorname{corr}_r(Y, X) = \operatorname{corr}_r(X, bY) \neq \operatorname{corr}_r(X, a + b Y), \quad a \neq 0, b > 0.</math>

The sample reflective correlation is equivalent to [[cosine similarity]]:

:<math>rr_{xy} = \frac{\sum x_i y_i}{\sqrt{(\sum x_i^2)(\sum y_i^2)}}.</math>

The weighted version of the sample reflective correlation is

:<math>rr_{xy, w} = \frac{\sum w_i x_i y_i}{\sqrt{(\sum w_i x_i^2)(\sum w_i y_i^2)}}.</math>