In my understanding, "the absolute correlation" is not such a common expression. Can anyone kindly explain the significance of the built-in symbol AbsoluteCorrelation, especially compared with Pearson's and Spearman's correlation coefficients?
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1$\begingroup$ The "absolute correlation" search in Google google.com.ua/… brings nothing but reference.wolfram.com/language/ref/AbsoluteCorrelation.html . $\endgroup$– user64494Commented Mar 20, 2020 at 18:31
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I'd say it's not only "not such a common expression" but at best a very misleading expression. What one obtains is not a correlation measure in the sense that the values are only between 0 and 1.
From the online help for multivariate probability distributions one obtains
As an example:
d = MultinormalDistribution[{3, 2, 1}, {{2, -2/3, -1/3}, {-2/3, 3, -1/3}, {-1/3, -1/3, 7}}];
AbsoluteCorrelation[d] // MatrixForm
So one is not getting correlations. I would steer clear of it for any statistical applications at least until the documentation gets better (or even never).
Addition:
Because of the definition used (as described in the online help), there is no apparent use of "absolute value" (at least when real numbers and statistical distributions are concerned). Consider the following example:
d = MultinormalDistribution[{0, 0, 0}, {{1, -2/3, -1/3}, {-2/3, 1, -1/3}, {-1/3, -1/3, 1}}];
AbsoluteCorrelation[d] // MatrixForm
All but the diagonal elements are negative.
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$\begingroup$ Thank you. I'm a bit surprised that the (curated) built-in symbol lacks a sufficient description. I've used the AbsoluteCorrelation function for my analysis and got an interesting result. I hope somebody will provide a document for that. $\endgroup$ Commented Mar 22, 2020 at 4:26