How to find minimal distance between elements?

I have a vector, and I would like to find the minimal distance between element values. Any element distance from any element in the set. Is it possible to do this without a for cycle?

[Image Analyst]

Mr. M, you've now asked 311 questions and "Accepted" virtually none of them. Perhaps now you can "thank" the people who took their time to try to help you by Accepting their answers so that they get reputation points. That's the etiquette in this forum. Thanks in advance.

Answer 1

[Roger Stafford]

Let your vector be called v. Then do this:

d = min(diff(sort(v)));

This finds the minimum distance between any two elements of v, but it does not show the points in v where that occurs. To do that requires the use of the index returned as a second output of the 'sort' function as well as an index from the 'min' function. Let us know if that is what you want.

[Guillaume]

Indeed, as long as we're talking about a vector of numbers, this is the most efficient. To get the original indices of the two closest numbers:

v = randi(1000, 1, 10)  %demo data
[sorted, originalidx] = sort(v);
[mindistance, where] = min(diff(sorted));
closestindex = originalidx([where, where+1]);
fprintf('elements at index %d and %d have got the minimum distance of %d\n', closestindex, mindistance)

[Jan]

+1. Sorting at first is the cheapest approach.

Answer 2

[Jos (10584)]

Without creating a possibly large intermediate N-ny-N matrix or using a possibly slow sort

V = [1 8 6 4 2 10] ;
W = nchoose2(V)         % all pairs of distinct elements
D = abs(W(:,2)-W(:,1))  % distance between pairs
[minD, ix] = min(D)     % minD = 1 
minPair = W(ix,:)       % minPair = [1 2]

nchoose2 is a fast function to get all combinations of two elements, and can be downloaded from the Matlab File Exchange: https://uk.mathworks.com/matlabcentral/fileexchange/20144-nchoose2-x-

Answer 3

[Image Analyst]

If the "vector" is actually a matrix of (x,y) locations, you can use pdist2(). Let me know if that's the case and I'll give you an example.

[aciara]

Could you give me an example please? I have to find minimal distance between elements of 2 different matrices. Is it possible?

[Image Analyst]

numPoints = 7;
xy1 = rand(numPoints, 2);
xy2 = rand(numPoints, 2);
distances = pdist2(xy1, xy2);
% Set 0's to inf since we don't want to find the min
% distance of a point to itself, which is 0.
distances(distances==0) = inf
% Find min distance
minDistance = min(distances(:))
% Find row and column where it occurs.
[row1, row2] = find(distances == minDistance)
% Plot all points
plot(xy1(:, 1), xy1(:, 2), 'r.', 'MarkerSize', 30); % Plot set 1.
hold on;
plot(xy2(:, 1), xy2(:, 2), 'b.', 'MarkerSize', 30); % Plot set 1.
% Plot the line
x1 = xy1(row1, 1);
y1 = xy1(row1, 2);
x2 = xy2(row2, 1);
y2 = xy2(row2, 2);
plot([x1, x2], [y1, y2], 'k-', 'LineWidth', 2);
grid on;
legend('Set 1', 'Set 2', 'Closest Pair');
caption = sprintf('Min Distance = %.4f', minDistance);
title(caption, 'fontSize', 20);

Please vote for my Answer if it helped you.

[aciara]

Thank you!! Very helpful

Answer 4

[Von Duesenberg]

This will get you started:

dumVect = [1 3 5 30]';
[minVal, idxMin] = min(diff(dumVect))

If you work with more dimensions, you may want to use pdist instead of diff. And of course, I'll let you figure out how you want to handle ties.

[Jan]

This is the minimal distance between neighboring elements, not between all elements.

[Von Duesenberg]

Oops, you're right.

Answer 5

[Jan]

n      = 10;
v      = rand(1, n);
dist   = abs(v - v.');                 % Auto-expand since R2016b
dist(1:(n+1):end) = Inf;               % Mask the zeros [EDITED]
% dist = bsxfun(@minus, v, v.') .^ 2;  % For older versions
[minValue, minIndex] = min(dist(:));

[Jos (10584)]

This just will give zeros ...

[Jan]

@Jos: Of course 0 is the correct answer to the original question: "Any element distance from any element in the set". This includes the distance from an element to itself, which is zero. :-)

Of course, this was not meant, and I have edited the code now to solve: "Any element distance from any other element in the set".

Thanks for finding my mistake.

[Mr M.]

What is this? v.'

[Jan]

@Mr M.: You can simply try it.

v = rand(2,3)
v.'

It is the transpose operator. The quote without the dot before replies the conjugate complex value in addition.

Answer 6

[Jos (10584)]

By definition the minimum distance is zero because v(i)==v(i) for any element i of the vector v.

But I assume you want the minimum distance between v(i) and v(j) for all pairs (i,j) where i is unequal to j, but forgot to mention that ... :p

[Mr M.]

yes, of course