How to obtain the best pairwise mapping from one set to another

I have a set of one dimensional points in a vector A, and another set of points in a vector B. I need to pair up points in A with their nearest equivalent points in B - without allowing any points to be in more than one pair.

Sounded simple, but it's proved more difficult that I thought.

I've tried knnsearch(), but this just maps A to nearest B and allows duplicates. I've looked at clustering but this does not seem to distinguish the set A from set B.

Seems like their should be an established way to do this...?

Answer 1

[Star Strider]

My solution:

A = randi(50,1,10)                      % Origin Vector
B = randi(50,1,10)                      % ‘Target’ Vector
Bc = B;                                 % ‘Target’ Vector for Comparisons 
for k1 = 1:size(Bc,2)
    [~,I] = min(abs(A(k1) - Bc));       % Find Nearest B to A(k1)
    D(k1,:) = [A(k1) k1 B(I) I];        % Store Result
    Bc(I) = NaN;                        % Use ‘NaN’ to Prevent Repeats
end
Q = D(:,[1 3])                          % Output — [A, Closest *Remaining* Value in B]

There may be better and more efficient ways to do this, but I can’t think of them this morning.