Exploring behavior of t-SNE on linear data

tsne.R

n <- 200
m <- 40
set.seed(1)
x <- runif(n, -1, 1)
library(rafalib)
bigpar(2,2,mar=c(3,3,3,1))
library(RColorBrewer)
cols <- brewer.pal(11, "Spectral")[as.integer(cut(x, 11))]
plot(x, rep(0,n), ylim=c(-1,1), yaxt="n", xlab="", ylab="", 
     col=cols, pch=20, main="underlying data")
library(pracma)
ortho <- rortho(m)
X <- cbind(x, matrix(0,ncol=m-1,nrow=n)) %*% ortho
plot(X[,1:2], asp=1, col=cols, pch=20, xlab="", ylab="", main="embed in higher dim")
pc <- prcomp(X)
plot(pc$x[,1:2], asp=1, col=cols, pch=20, xlab="", ylab="", main="PC1 & PC2")
library(tsne)
res <- tsne(X)
plot(res, col=cols, pch=20, xlab="", ylab="", main="t-SNE")

bigpar(2,2,mar=c(3,3,1,1))
for (i in 2:5) {
  set.seed(i)
  x <- runif(n, -1, 1)
  cols <- brewer.pal(11, "Spectral")[as.integer(cut(x, 11))]
  ortho <- rortho(m)
  X <- cbind(x, matrix(0,ncol=m-1,nrow=n)) %*% ortho
  res <- tsne(X)
  plot(res, col=cols, pch=20, xlab="", ylab="")
}

How about this mixture of Gaussians example.

library(Rtsne)
library(tsne)
library(RColorBrewer)
cols <- brewer.pal(4, "Dark2")

#build 200 samples with 1000 'genes' in 4 distinct clusters
set.seed(1)
dat<-matrix(rnorm(200000,0,1),1000,200)
cen1<-rnorm(1000,0,1)
cen2<-rnorm(1000,0,1)
cen3<-rnorm(1000,0,1)
cen4<-rnorm(1000,0,1)
sim2<-dat
sim2[,1:50]<-dat[,1:50]+cen1
sim2[,51:100]<-dat[,51:100]+cen2
sim2[,101:150]<-dat[,101:150]+cen3
sim2[,151:200]<-dat[,151:200]+cen4
colors <- c(rep(cols[1], 50), rep(cols[2],50), rep(cols[3], 50), rep(cols[4], 50))

par(mfrow=c(1, 2))
#t-SNE
tmp<-tsne(t(sim2))
plot(tmp, col=colors, pch=20, xlab="", ylab="", main="tsne")

#Alternative implementation
tmp<-Rtsne(t(sim2), check_duplicates=FALSE)
plot(tmp$Y,col=colors,  pch=20, xlab="", ylab="", main="Rtsne")

Well, there is a bug in the tsne package:
gains = (gains + .2) * abs(sign(grads) != sign(incs))
+ gains * .8 * abs(sign(grads) == sign(incs))
change it to
gains = (gains + .2) * abs(sign(grads) != sign(incs)) + gains * .8 * abs(sign(grads) == sign(incs))

Also, for the MOG case, you need to set the parameter whiten=FALSE. Then you can get the correct results:

Have these changes been committed?

Could any help me interpreting the pattern behind the tsne plots?I have done on a small dataset I have clusters .Which I have hard time interpreting...

The fix proposed by @JerryDing has been incorporated into tsne package v0.1.3 by @jdonaldson here:

https://github.com/jdonaldson/rtsne

and has been sent to CRAN.

@JerryDing Im sorry but I fail to see any different in your change. What's different?

The change you proposed where change in github but, at least for me, the change is just a copy of what was already there.