# Mapping discrete variables

Let's say I have a set of discrete, arbitrary variables sampled at continuous co-ordinates, e.g.

==================================
= x       = y       = Value      =
==================================
= 4.1     = 3.4     = A          =
= 4.6     = 7.9     = A          =
= 4.7     = 8.1     = A          =
= 2.1     = 5.0     = B          =
= 3.5     = 9.0     = B          =
= 7.0     = 1.1     = C          =
= 9.8     = 4.2     = C          =
==================================


I would like to generate a map showing the distribution of the values across a range of co-ordinates (e.g. 0<x<=10, 0<y<=10), where each value has an arbitrary colour assigned, and every point within those co-ordinates has a calculated interpolated value, where it is reasonable to do so.

E.g. we give a colour to each of A, B and C.

the point (5.0,5.0) is in the middle of the cluster of As so should be coloured as per A.

the point (7.0,4.0) is between the As and Cs so the colour should be calculated via some analysis of distance to each of those surrounding points.

Broadly I would expect the top-left quadrant to be a colour assigned to B, the bottom right quadrant to be a colour assigned to C, with a band of colour assigned to A between and the point at which the boundaries between the 3 colours occur calculated via some kind of nearest-neighbour algorithm.

Are there any existing algorithms to map the kind of information I wish to display? It should take into account any inliers (if that's the right term).

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What kind of thing or observation do these values represent? –  whuber Oct 26 '11 at 21:03
survey responses from people at given geographical locations –  meepmeep Oct 27 '11 at 10:06
Ah! What sense does it make to interpolate categorical survey responses over a map, then? Your answer to this will suggest appropriate interpolation methods. –  whuber Oct 27 '11 at 16:46