Mapping distances to colors

Question

Assuming a matrix of distances between a number of samples, I would like to somehow reasonably map these distances to a color space. So for example if you have three apparent clusters, they should have different colors, and within a cluster you would have a number of shades of a color. However, I would like to avoid explicit clustering, if possible.

Clearly, the mapping cannot be perfect and universal: rather, it is a heuristic.

Is there a known algorithm for that? Or, perhaps, a ready solution for R?

Answer 1

Here is one possibility. No matter how many dimensions your original data was, you can use multi-dimensional scaling with the distance matrix to project the data to three dimensions, in a way that coarsely preserves distances. If you treat the three dimensions as R, G and B this will give a color scheme in which points that are close should have "close" colors.

Here is a simple example. I generate some 5-dimensional data with 4 clusters (although no cluster analysis is performed). From that, we get the distance matrix. Then, as above we use multi-dimensional scaling to turn this into a color map. The points are plotted to show the result.

## Generate some sample data
set.seed(1234)
v = c(rnorm(80,0,1), rnorm(80,0,1), rnorm(80,4,1), rnorm(80,4,1)) 
w = c(rnorm(80,0,1), rnorm(80,4,1), rnorm(80,0,1), rnorm(80,4,1)) 
x = c(rnorm(80,0,1), rnorm(80,0,1), rnorm(80,4,1), rnorm(80,4,1)) 
y = c(rnorm(80,0,1), rnorm(80,4,1), rnorm(80,0,1), rnorm(80,4,1)) 
z = c(rnorm(80,0,1), rnorm(80,4,1), rnorm(80,-4,1), rnorm(80,8,1)) 
df = data.frame(v,w,x,y,z)

## Distance matrix
D = dist(df)

## Project to 3-dimensions
PROJ3 = cmdscale(D, 3)

## Scale the three dimensions to [0,1] interval
ScaledP3 = apply(PROJ3, 2, function(x) { (x - min(x))/(max(x)-min(x)) })
colnames(ScaledP3) = c("red", "green", "blue")
X = as.data.frame(ScaledP3)
## Convert to color map
ColorMap = do.call(rgb, X)
plot(x,y, pch=20, col=ColorMap)