File:Distance Correlation Examples.svg
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Summary
DescriptionDistance Correlation Examples.svg |
English: Recreation of File:Correlation_examples2.svg using the distance correlation method (dcor from the R energy library) |
Date | |
Source | Created in R using a modification of DenisBoigelot's script at File:Correlation_examples2.svg |
Author | Naught101 |
- Other information
#Title: An example of the correlation of x and y for various distributions of (x,y) pairs #Tags: Mathematics; Statistics; Correlation #Author: Denis Boigelot #Packets needed : mvtnorm (rmvnorm), RSVGTipsDevice (devSVGTips) #How to use: output() # #This is an translated version in R of an Matematica 6 code by Imagecreator. library(mvtnorm) library(energy) library(RSVGTipsDevice) MyPlot <- function(xy, xlim = c(-4, 4), ylim = c(-4, 4), eps = 1e-15) { title = round(dcor(xy[,1], xy[,2]), 1) if (sd(xy[,2]) < eps) title = "" # corr. coeff. is undefined plot(xy, main = title, xlab = "", ylab = "", col = "darkblue", pch = 16, cex = 0.2, xaxt = "n", yaxt = "n", bty = "n", xlim = xlim, ylim = ylim) } MvNormal <- function(n = 1000, cor = 0.8) { for (i in cor) { sd = matrix(c(1, i, i, 1), ncol = 2) x = rmvnorm(n, c(0, 0), sd) MyPlot(x) } } rotation <- function(t, X) return(X %*% matrix(c(cos(t), sin(t), -sin(t), cos(t)), ncol = 2)) RotNormal <- function(n = 1000, t = pi/2) { sd = matrix(c(1, 1, 1, 1), ncol = 2) x = rmvnorm(n, c(0, 0), sd) for (i in t) MyPlot(rotation(i, x)) } Others <- function(n = 1000, spread = 1) { # x = seq(-1, 1, length.out = n) #generates a time series (serial dependence) x = runif(n, -1, 1) #same image, not a time series (no serial dependence) y = 4 * (x^2 - 1/2)^2 + runif(n, -1, 1) /3 * spread MyPlot(cbind(x,y), xlim = c(-1, 1), ylim = c(-1/3, 1+1/3)) y = runif(n, -1, 1) xy = rotation(-pi/8, cbind(x,y)) lim = sqrt(2+sqrt(2)) / sqrt(2) MyPlot(cbind(xy[,1], xy[,2]*spread), xlim = c(-lim, lim), ylim = c(-lim, lim)) xy = rotation(-pi/8, xy) MyPlot(cbind(xy[,1], xy[,2]*spread), xlim = c(-sqrt(2), sqrt(2)), ylim = c(-sqrt(2), sqrt(2))) y = 2*x^2 + runif(n, -1, 1) * spread MyPlot(cbind(x,y), xlim = c(-1, 1), ylim = c(-1, 3)) y = (x^2 + runif(n, 0, 1/2) * spread) * sample(seq(-1, 1, 2), n, replace = TRUE) MyPlot(cbind(x,y), xlim = c(-1.5, 1.5), ylim = c(-1.5, 1.5)) y = cos(x*pi) + rnorm(n, 0, 1/8) * spread x = sin(x*pi) + rnorm(n, 0, 1/8) * spread MyPlot(cbind(x,y), xlim = c(-1.5, 1.5), ylim = c(-1.5, 1.5)) xy1 = rmvnorm(n/4, c( 3, 3), diag(2)*spread) xy2 = rmvnorm(n/4, c(-3, 3), diag(2)*spread) xy3 = rmvnorm(n/4, c(-3, -3), diag(2)*spread) xy4 = rmvnorm(n/4, c( 3, -3), diag(2)*spread) MyPlot(rbind(xy1, xy2, xy3, xy4), xlim = c(-3-4, 3+4), ylim = c(-3-4, 3+4)) } output <- function() { devSVGTips(width = 7, height = 4.4) # remove first and last line for no svg exporting par(mfrow = c(4, 7), oma = c(0,0,0,0), mar=c(2,2,2,0)) MvNormal(800, c(1.0, 0.8, 0.4, 0.0, -0.4, -0.8, -1.0)); RotNormal(200, c(0, pi/12, pi/6, pi/4, pi/2-pi/6, pi/2-pi/12, pi/2)); Others(800) Others(800, 0.3) dev.off() # remove first and last line for no svg exporting
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 05:38, 2 March 2012 | 506 × 318 (1.02 MB) | wikimediacommons>Naught101 | {{subst:Upload marker added by en.wp UW}} {{Information |Description = {{en|Recreation of File:Correlation_examples2.svg using the distance correlation method (dcor from the R energy l... |
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