Question

I have a centroid, e.g., A. and I have other 100 points. All of these points are of high-dimensions, e.g, 1000 dimensions. Is there a way to visualize these points in a two-dimensional space in-terms of their distance with A.

Answer 1

A common (though simple) way to visualize high-dimensional points in low dimensional space is to use some form of multi-dimensional scaling:

dat <- matrix(runif(1000*99),99,1000)
#Combine with "special" point
dat <- rbind(rep(0.1,1000),dat)

out <- cmdscale(dist(dat),k = 2)

#Plot everything, highlighting our "special" point
plot(out)
points(out[1,1],out[1,2],col = "red")

You can also check out isoMDS or sammon in the MASS package for other implementations in R.