The first thought I had would be to put this into HSV, and then index that with an R-tree [1]. This way, you can do nearest neighbor kind of stuff, similar to geospatial indexing.
What is interesting about this color system is that it isn't symmetric (your eye is better at differentiating certain hues like blue at more maximal values than others) so more care is needed on the nearest neighbour lookups.
If you are using this coloring scheme for labelling colors in a photograph then you also need to adjust for colors that are especially vibrant and overtake the photo. For example this photo:
[1]: http://en.wikipedia.org/wiki/R-tree