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

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!

Answer 1

[Matt J]

D=abs(y(:)-x(:).');

result=sortrows(   matchpairs(D,10*max(D(:)))  ,1)

[Adam Danz]

I didn't know about matchpairs. This is great.

You need to transpose x(:), though.

D=abs(y(:)-x(:)');

and if you apply sortrows to result the indices are in order of y-values.

[Matt J]

Yep. Thanks!

[Erik J]

Wow that's slick. Works perfectly. Thank you!

Answer 2

[Adam Danz]

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