File:Em old faithful.gif
Em_old_faithful.gif (360 × 360 pixels, file size: 272 KB, MIME type: image/gif, looped, 30 frames, 6.0 s)
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DescriptionEm old faithful.gif | An animation of the EM algorithm to a 2 component Gaussian mixture model on the Old Faithful dataset |
Date | |
Source | Own work |
Author | 3mta3 (talk) 16:55, 23 March 2009 (UTC) |
Created in R with code below (released under same license as image), combined into animated gif using ImageMagick.
There should be a way to make this file smaller (e.g. using less colours or an animated PNG). If you can, feel free to upload a new copy.
#load library for multivariate normal library(mvtnorm) #load Old Faithful data frame data(faithful) #setup grid for plotting xpts <- seq(from=1,to=6,length.out=100) ypts <- seq(from=40,to=100,length.out=100) #initial parameter estimates (chosen to be deliberately bad) theta <- list( tau=c(0.5,0.5), mu1=c(2.8,75), mu2=c(3.6,58), sigma1=matrix(c(0.8,7,7,70),ncol=2), sigma2=matrix(c(0.8,7,7,70),ncol=2) ) #E step: calculates conditional probabilities for latent variables E.step <- function(theta) t(apply(cbind( theta$tau[1] * dmvnorm(faithful,mean=theta$mu1,sigma=theta$sigma1), theta$tau[2] * dmvnorm(faithful,mean=theta$mu2,sigma=theta$sigma2) ),1,function(x) x/sum(x))) #M step: calculates the parameter estimates which maximise Q M.step <- function(T) list( tau= apply(T,2,mean), mu1= apply(faithful,2,weighted.mean,T[,1]), mu2= apply(faithful,2,weighted.mean,T[,2]), sigma1= cov.wt(faithful,T[,1])$cov, sigma2= cov.wt(faithful,T[,2])$cov) #function to plot current data plot.em <- function(theta){ mixture.contour <- outer(xpts,ypts,function(x,y) { theta$tau[1]*dmvnorm(cbind(x,y),mean=theta$mu1,sigma=theta$sigma1) + theta$tau[2]*dmvnorm(cbind(x,y),mean=theta$mu2,sigma=theta$sigma2) }) contour(xpts,ypts,mixture.contour,nlevels=5,drawlabel=FALSE,col="red",xlab="Eruption time (mins)",ylab="Waiting time (mins)",main="Waiting time vs Eruption time of the Old Faithful geyser") points(faithful) } #plot initial contours iter <- 1 png(filename=paste("em",formatC(iter,width=4,flag="0"),".png",sep="")) plot.em(theta) dev.off() #run EM and plot for (iter in 2:30){ T <- E.step(theta) theta <- M.step(T) png(filename=paste("em",formatC(iter,width=4,flag="0"),".png",sep="")) plot.em(theta) dev.off() }
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:10, 23 March 2009 | 360 × 360 (272 KB) | 3mta3 (talk | contribs) | A bit smaller | |
16:55, 23 March 2009 | 480 × 480 (365 KB) | 3mta3 (talk | contribs) | {{Information |Description=An animation of the EM algorithm to a 2 component Gaussian mixture model on the [http://stat.ethz.ch/R-manual/R-patched/library/datasets/html/faithful.html Old Faithful dataset] |Source=self-made |Date=2009-03-23 |Author= ~~~~ | |
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