knitr::opts_chunk$set(echo = TRUE) require(NNS) require(knitr) require(rgl)
The limitations of linear correlation are well known. Often one uses correlation, when dependence is the intended measure for defining the relationship between variables. NNS dependence
NNS.dep is a signal:noise measure robust to nonlinear signals.
Below are some examples comparing NNS correlation
NNS.dep with the standard Pearson's correlation coefficient
x=seq(0,3,.01); y=2*x cor(x,y) NNS.dep(x,y,print.map = T)
x=seq(0,3,.01); y=x^10 cor(x,y) NNS.dep(x,y,print.map = T)
set.seed(123) df<- data.frame(x=runif(10000,-1,1),y=runif(10000,-1,1)) df<- subset(df, (x^2 + y^2 <= 1 & x^2 + y^2 >= 0.95)) NNS.dep(df$x,df$y,print.map = T)
If the user is so motivated, detailed arguments and proofs are provided within the following:
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