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Finding elements of one vector that are closest to elements of another

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I have two vectors, x and y. Both vectors contain numbers from 0 to 1. Vector x is 964 elements. Vector y is 51 elements.
I need to find the values from vector x that are closest to the values of vector y, without replacement. So if x(1) is closest to y(1), it returns x(1) - but when it moves to find the closest element to x(2), it cannot return x(1) again and must return a different value, even if x(1) was closer to y(2) than the value it returns. Basically, I need to find the 51 unique values in x that most closely align with the values in y.
Any ideas?
Thank you!

Akzeptierte Antwort

Matt J
Matt J am 5 Nov. 2020
Bearbeitet: Matt J am 5 Nov. 2020
D=abs(y(:)-x(:).');
result=sortrows( matchpairs(D,10*max(D(:))) ,1)
  3 Kommentare
Erik J
Erik J am 5 Nov. 2020
Wow that's slick. Works perfectly. Thank you!

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Adam Danz
Adam Danz am 5 Nov. 2020
Bearbeitet: Adam Danz am 5 Nov. 2020
Here's a lower-level approach (~10x faster than matchpairs but that function is also quite fast).
  1. Use implicit expansion to create a matix of y-x values.
  2. Replace the paired x-minimum with NaN so it cannot be chosen again
  3. Create table to show results.
Demo
% Create x,y values
rng('default') % for reproducibility
x = rand(1,964);
y = rand(1,51);
% Loop through each y-value to find x-min pair
minIdx = nan(numel(y),1);
xCopy = x;
for i = 1:numel(y)
diffs = abs(y(:)-xCopy(:).');
[~,minIdx(i)] = min(diffs(i,:));
xCopy(minIdx(i)) = NaN;
end
% Confirm at all values are unique
assert(numel(unique(minIdx))==numel(minIdx), 'Index values are not unique.')
% Show pairs
T = table(y(:), x(minIdx)', y(:)-x(minIdx)', minIdx(:), ...
'VariableNames', {'y','xMin','y-x','xMinIndex'})
T = 51x4 table
y xMin y-x xMinIndex ________ ________ ___________ _________ 0.32583 0.32515 0.00068795 418 0.54645 0.54659 -0.00014367 478 0.39888 0.39859 0.00029126 690 0.41509 0.41452 0.00057085 716 0.18074 0.18185 -0.0011093 133 0.25539 0.2551 0.00029163 62 0.020536 0.019578 0.00095815 556 0.92368 0.92338 0.00029597 222 0.6537 0.65369 9.755e-06 935 0.93261 0.93285 -0.00024 527 0.16351 0.16357 -5.7541e-05 951 0.9211 0.92033 0.00076522 342 0.79466 0.79483 -0.00017353 200 0.57739 0.57672 0.00067268 290 0.44004 0.44009 -4.9543e-05 427 0.25761 0.25751 0.00010548 70
The table shows the original y-values, the paired x-minimum values, the difference between y-x (absolute), and the index of x that paired with y.
Plot the results comparing y to the paird x values and use color to indicate the difference between y and x.
figure()
scatter(T.xMin, T.y, 60, T.('y-x'), 'LineWidth', 1.5)
xlabel('x-pair')
ylabel('y')
colormap('jet')
cb = colorbar();
ylabel(cb, '|y-x|')
axis equal
grid on

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